cohomCalg-0.32/000077500000000000000000000000001322050713700133325ustar00rootroot00000000000000cohomCalg-0.32/.gitignore000066400000000000000000000001441322050713700153210ustar00rootroot00000000000000# Compiled Object files *.slo *.lo *.o *.obj # Precompiled Headers *.gch *.pch *.ipch .vs/ /build/cohomCalg-0.32/LICENSE000066400000000000000000001045051322050713700143440ustar00rootroot00000000000000 GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007 Copyright (C) 2007 Free Software Foundation, Inc. Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. Preamble The GNU General Public License is a free, copyleft license for software and other kinds of works. The licenses for most software and other practical works are designed to take away your freedom to share and change the works. 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If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Lesser General Public License instead of this License. But first, please read . cohomCalg-0.32/Makefile000066400000000000000000000036361322050713700150020ustar00rootroot00000000000000######################################################################### # # # Makefile for the cohomCalg application (including modified PolyLib) # # # ######################################################################### # compilers & flags CC := g++ CFLAGS := -O3 LD := g++ # Note: (1) If you want to enforce 32-bit or 64-bit compilation, # add "-m32" or "-m64" to both CFLAGS and LDFLAGS. # (2) If you want to enforce a static linking of all libraries # (i.e. include everything into one binary), add "-static" to LDFLAGS # global defs DEFS := -DPOLYLIB_BITS=64 # directories COHOMCALG_SRC_DIR := source POLYLIB_SRC_DIR := source/polylib_mod BUILD_DIR := build/polylib_mod build # source and object files COHOMCALG_SRC := $(foreach sdir,$(COHOMCALG_SRC_DIR),$(wildcard $(sdir)/*.cpp)) COHOMCALG_OBJ := $(patsubst source/%.cpp,build/%.o,$(COHOMCALG_SRC)) POLYLIB_SRC := $(foreach sdir,$(POLYLIB_SRC_DIR),$(wildcard $(sdir)/*.c)) POLYLIB_OBJ := $(patsubst source/%.c,build/%.o,$(POLYLIB_SRC)) INCLUDES := $(addprefix -I,$(COHOMCALG_SRC_DIR) $(POLYLIB_SRC_DIR)) vpath %.c $(POLYLIB_SRC_DIR) vpath %.cpp $(COHOMCALG_SRC_DIR) # macros for .c/.cpp dirs define make-goal-cpp $1/%.o: %.cpp $(CC) $(INCLUDES) $(DEFS) $(CPPFLAGS) $(CXXFLAGS) -c $$< -o $$@ endef define make-goal-c $1/%.o: %.c $(CC) $(INCLUDES) $(DEFS) $(CPPFLAGS) $(CFLAGS) -c $$< -o $$@ endef .PHONY: all checkdirs clean all: checkdirs bin/cohomcalg bin/cohomcalg: $(COHOMCALG_OBJ) $(POLYLIB_OBJ) $(LD) $^ $(LDFLAGS) -lpthread -o $@ #-static -lsource/polylib-5.22.5/.libs/libpolylib64.a checkdirs: $(BUILD_DIR) $(BUILD_DIR): @mkdir -p $@ clean: @rm -rf $(BUILD_DIR) $(eval $(call make-goal-c, build/polylib_mod)) $(eval $(call make-goal-cpp, build)) cohomCalg-0.32/Proper Citation.txt000066400000000000000000000075171322050713700171070ustar00rootroot00000000000000Dear reader, if you used cohomCalg in your work and would like to properly cite the program in your paper, please use one of the following two BibTeX source codes: Use \cite{cohomCalg:Implementation} at the appropiate place of your TeX file ------------------------------- +----------------------+ "Fancy" BibTeX entry: <-| Use this if possible | ===================== +----------------------+ @Misc{cohomCalg:Implementation, title = "{\fontfamily{put}\bfseries\footnotesize\selectfont cohomCalg} package", howpublished = "Download link", url = "https://github.com/BenjaminJurke/cohomCalg", note = "High-performance line bundle cohomology computation based on \cite{CohomOfLineBundles:Algorithm}", year = "2010" } @Article{CohomOfLineBundles:Algorithm, author = "Blumenhagen, Ralph and Jurke, Benjamin and Rahn, Thorsten and Roschy, Helmut", title = "{Cohomology of Line Bundles: A Computational Algorithm}", publisher = "AIP", year = "2010", journal = "J.~Math.~Phys.", volume = "51", number = "10", eid = "103525", numpages = "15", pages = "103525", doi = "10.1063/1.3501132", eprint = "1003.5217", archivePrefix = "arXiv", primaryClass = "hep-th", SLACcitation = "%%CITATION = 1003.5217;%%" } This one uses a different font for the cohomCalg application name. Note that the usage of the font 'put' might cause problems on some older (La)TeX distributions. On a halfway reasonable modern machine it should give you no trouble. Standard BibTeX entry: ====================== @Misc{cohomCalg:Implementation, title = "cohomCalg package", howpublished = "Download link", url = "https://github.com/BenjaminJurke/cohomCalg", note = "High-performance line bundle cohomology computation based on \cite{CohomOfLineBundles:Algorithm}", year = "2010" } @Article{CohomOfLineBundles:Algorithm, author = "Blumenhagen, Ralph and Jurke, Benjamin and Rahn, Thorsten and Roschy, Helmut", title = "{Cohomology of Line Bundles: A Computational Algorithm}", publisher = "AIP", year = "2010", journal = "J.~Math.~Phys.", volume = "51", number = "10", eid = "103525", numpages = "15", pages = "103525", doi = "10.1063/1.3501132", eprint = "1003.5217", archivePrefix = "arXiv", primaryClass = "hep-th", SLACcitation = "%%CITATION = 1003.5217;%%" } Choose what best suits your needs. Furthermore, if you want to cite the Proof paper of the algorithm or the Applications paper, you can use the following BibTeX entries: Additional BibTeX entries: ========================== @Article{CohomOfLineBundles:Proof, author = "Rahn, Thorsten and Roschy, Helmut", title = "{Cohomology of Line Bundles: Proof of the Algorithm}", publisher = "AIP", year = "2010", journal = "J.~Math.~Phys.", volume = "51", number = "10", eid = "103520", numpages = "11", pages = "103520", doi = "10.1063/1.3501135", eprint = "1006.2392", archivePrefix = "arXiv", primaryClass = "hep-th", SLACcitation = "%%CITATION = 1006.2392;%%" } @article{CohomOfLineBundles:Applications, author = "Blumenhagen, Ralph and Jurke, Benjamin and Rahn, Thorsten and Roschy, Helmut", title = "{Cohomology of Line Bundles: Applications}", year = "2010", note = "* Temporary entry *", journal = "submitted to JHEP", eprint = "1010.3717", archivePrefix = "arXiv", primaryClass = "hep-th", SLACcitation = "%%CITATION = 1010.3717;%%" } Best regards, the authorscohomCalg-0.32/README.md000066400000000000000000000144241322050713700146160ustar00rootroot00000000000000# cohomCalg [![GitHub release](https://img.shields.io/github/release/BenjaminJurke/cohomCalg.svg)](https://github.com/BenjaminJurke/cohomCalg/releases) [![GitHub issues](https://img.shields.io/github/issues/BenjaminJurke/cohomCalg.svg)](https://github.com/BenjaminJurke/cohomCalg/issues) [![GitHub license](https://img.shields.io/badge/license-GPL%203-lightgrey.svg)](https://raw.githubusercontent.com/BenjaminJurke/cohomCalg/master/LICENSE) > ![cohomCalg logo with Koszul extension](https://raw.githubusercontent.com/BenjaminJurke/cohomCalg/master/cohomCalg_koszul_logo.png) > A software package for computation of sheaf cohomologies > for line bundles on toric varieties. **Authors:** [Ralph Blumenhagen](http://wwwth.mpp.mpg.de/members/blumenha/), [Benjamin Jurke](https://benjaminjurke.com), Thorsten Rahn, Helmut Roschy # Project history The algorithm for the computation of sheaf cohomologies for line bundles on toric varieties presented in [arXiv:1003.5217 [hep-th]](http://arxiv.org/abs/1003.5217) *"Cohomology of Line Bundles: A Computational Algorithm"* has been implemented in a convenient and high-performance C/C++ application called **cohomCalg**. The optional **cohomCalg Koszul** extension serves as a Mathematica 7 frontend and allows for the easy computation of hypersurface and complete intersection cohomologies, following the material presented in [arXiv:1010.3717 [hep-th]](http://arxiv.org/abs/1010.3717). About three months after the initial conjecture's preprint release, a proof of the algorithm was presented in [arXiv:1006.2392 [hep-th]](http://arxiv.org/abs/1006.2392), which also clarifies much of the underlying mathematical structures. At the same time an independant proof was developed in [arXiv:1006.0780 [math.AG]](http://arxiv.org/abs/1006.0780) - published in fact a few days earlier - which utilized alternative methods. The [full background story](https://benjaminjurke.com/academia-and-research/cohomcalg/) can be found here along with some simple examples. The source code is freely available under the GNU GPL v3 license terms. Furthermore, the implementation makes use of The Polyhedral Library (or [PolyLib](http://icps.u-strasbg.fr/polylib/) for short), which is available here under the same license. # Documentation A full documentation and several example input files are included in the cohomCalg download package, see "[manual.pdf](https://github.com/BenjaminJurke/cohomCalg/blob/master/manual.pdf)". Furthermore, you can [eMail us](mailto:mail@benjaminjurke.com?subject=cohomCalg) for technical support or other related questions. For ease of use the package includes pre-compiled binaries for Microsoft Windows both in 32- and 64-bit versions, with the latter being considerably faster. # Changelog * **v0.32** (December 26, 2017): Replaced TinyThread++ by C++11 std::thread, Intel C++ 18.0 Windows binaries. * **v0.31d** (January 16, 2017): Several minor updates and corrections. * **v0.31c** (January 14, 2017): Minor update due to GCC 6.2 compatibility issues, recompiled Windows binaries. * **v0.31b** (April 18, 2012): Minor bugfix due to GCC 4.6 compatibility issues. * **v0.31** (May 25, 2011): Multi-core support, new vector bundle routines, overall improvements. * **v0.21** (October 18, 2010): cohomCalg Koszul extension added! * **v0.13** (July 23, 2010): Integration mode added, see command line option `--integrated` in manual. * **v0.12** (June 25, 2010): Several minor bugfixes and improvements. * **v0.11** (May 4, 2010): Original public release of the cohomCalg implementation. * **v0.04** (March 29, 2010): Original public release of the Mathematica 7 script, which is still available [here](https://github.com/BenjaminJurke/cohomCalg/tree/master/old/cohomcalg-script-v004). # Known bugs & Shortcomings Certain invalid input data is at the moment not safely handled by the PolyLib. For the moment, the crash situation is circumvented in a Quick&Dirty manner. In such cases you will see a message like `Counting of the rationoms errorneous - is your input geometry valid?` in those cases, which caused the original release version to crash. So far, all such cases could be traced back to bad input data. Further implementation-related shortcomings are explained in the manual. # License & Proper Citation As mentioned, the entire package is published under the GNU GPL v3 License, as required by the included PolyLib. This means that any derivative work also has to be published under the GPL v3 License or an equivalent license. The package contains a small text file "Proper Citation.txt" providing a BibTeX entry for cohomCalg, which you can use if you use the program in your work. Or you can simply **Copy&Paste the following BibTeX snippet** provided for convenience: ```tex @Article{Blumenhagen:2010pv, author = "Blumenhagen, Ralph and Jurke, Benjamin and Rahn, Thorsten and Roschy, Helmut", title = "{Cohomology of Line Bundles: A Computational Algorithm}", journal = "J. Math. Phys.", volume = "51", pages = "103525", issue = "10", year = "2010", doi = "10.1063/1.3501132", eprint = "1003.5217", archivePrefix = "arXiv", primaryClass = "hep-th"} @Misc{cohomCalg:Implementation, title = "{cohomCalg package}", howpublished = "Download link", url = "https://github.com/BenjaminJurke/cohomCalg", note = "High-performance line bundle cohomology computation based on \cite{Blumenhagen:2010pv}", year = "2010"} ```` # Related Links In order to derive the Stanley-Reisner ideal, which is a required input for the program, you may want to take a look at [TOPCOM](http://www.rambau.wm.uni-bayreuth.de/TOPCOM/), which can also enumerate all possible fans for a given set of vertices. The Maple script package [SCHUBERT](http://stromme.uib.no/schubert/) can be used to compute intersection numbers and further geometrical quantities of toric varieties. Furthermore, there is the package [PALP](http://hep.itp.tuwien.ac.at/~kreuzer/CY/CYpalp.html) which is useful for computing invariants of hypersurfaces, Mori cone vectors etc. You may also want to take a look at the [SAGE Library](http://www.sagemath.org/) of freely available mathematical software. The [Macaulay2](http://www.math.uiuc.edu/Macaulay2/) software, which allows similar computations, was heavily used during the development process.cohomCalg-0.32/bin/000077500000000000000000000000001322050713700141025ustar00rootroot00000000000000cohomCalg-0.32/bin/CP2.in000066400000000000000000000016111322050713700150150ustar00rootroot00000000000000%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Example input file for cohomCalg % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % This file contains the geometry data of the CP^2 projective space % % The vertices and GLSM charges: vertex u1 = ( -1, -1 ) | PIC: H | GLSM: ( 1 ); vertex u2 = ( 1, 0 ) | GLSM: ( 1 ); vertex u3 = ( 0, 1 ) | GLSM: ( 1 ); % The Stanley-Reisner ideal: srideal [u1*u2*u3]; % Computation time for this example is quasi-instantaneous, % so turn off intermediate files: monomialfile off; % And finally the requested line bundle cohomologies: ambientcohom O( 0 ); ambientcohom O( -1 ); ambientcohom O( -2 ); ambientcohom O( -3 ); ambientcohom O( -4 ); ambientcohom O( -6 ); ambientcohom O( -8 ); ambientcohom O(-10 ); ambientcohom O(-12 ); ambientcohom O(-14 ); ambientcohom O(-16 );cohomCalg-0.32/bin/P31SU7.in000066400000000000000000000053171322050713700153420ustar00rootroot00000000000000% Input file for the ralfsalg program... % % Part 1: Specify the vertex name and the GLSM charges % ======= % In order to simplify the transition from "the toric triangulizer" % you can also specify the actual vertex data and select coordinate % Picard generators - this information will simply be ignored but is % of course subject to a syntax check. This allows for easy copy&paste % from our other app... % NOTE THE SYNTAX CHANGE IN COMPARISON TO THE OLD INPUT FORMAT!!! %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% vertex y = ( 0, 0, 0, 0, 1) | GLSM: ( 0, 3, 0, 1, 1, 0, 1, 0, 1); vertex x = ( 0, 0, 0, 1, 0) | GLSM: ( 0, 2, 0, 1, 0, 1, 0, 1, 0); vertex z = ( 0, 0, 0, -2, -3) | PIC: F | GLSM: (-4, 1, 2, 0, 0, 0, 0, 0, 0); vertex v1 = ( 0, 0, 1, 0, 0) | GLSM: (1, 0, -1, 0, 0, 0, 0, 0, 0); vertex v2 = ( 0, 1, 0, 0, 0) | GLSM: (1, 0, 0, 0, 0, 0, 0, 0, 0); vertex v3 = ( 1, 0, 0, 0, 0) | GLSM: (1, 0, 0, 0, 0, 0, 0, 0, 0); vertex v4 = ( -1, -1, -1, -8,-12) | PIC: H | GLSM: (1, 0, 0, 0, 0, 0, 0, 0, 0); vertex s1 = ( 0, 0, -1, -4, -6) | GLSM: (0, 0, -1, 1, 0, 0, 0, 0, 0); % SU(5) vertex s2 = ( 0, 0, -1, -3, -5) | GLSM: (0, 0, 0, -1, 1, 0, 0, 0, 0); vertex s3 = ( 0, 0, -1, -3, -4) | GLSM: (0, 0, 0, 0, -1, 1, 0, 0, 0); vertex s4 = ( 0, 0, -1, -2, -4) | GLSM: (0, 0, 0, 0, 0, -1, 1, 0, 0); vertex s5 = ( 0, 0, -1, -2, -3) | GLSM: (0, 0, 0, 0, 0, 0, -1, 1, 0); vertex s6 = ( 0, 0, -1, -1, -3) | GLSM: (0, 0, 0, 0, 0, 0, 0, -1, 1); vertex s7 = ( 0, 0, -1, -1, -2) | GLSM: (0, 0, 0, 0, 0, 0, 0, 0, -1); % Part 2: Specify the Stanley-Reisner ideal, which is to be investigated % ======= % Simply specify the Stanley-Reisner ideal of the triangulation of % interest. Input format is simply the output format of the great % toric triangulizer. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% srideal [y*s2, y*s4, y*s6, x*z, x*s1, x*s2, x*s3, x*s4, x*s5, z*s3, z*s5, z*s7, v1*s1, v1*s2, v1*s3, v1*s4, v1*s5, v1*s7, s1*s4, s1*s5, s1*s6, s1*s7, s2*s5, s2*s6, s2*s7, s3*s6, s3*s7, s5*s6, v2*v3*v4]; % Part 3: Specify the ambient space line bundle % ======= % Provide the line bundle with respect to the charges implied % by the choice of GLSM charges assigned to the vertices. % NOTE THE CHARACTER 'O' IN FRONT OF THE CHARGE VECTOR %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% monomialfile off; ambientcohom O(0,0,0,0,0,0,0,0,0);cohomCalg-0.32/bin/P31SU8.in000066400000000000000000000015761322050713700153460ustar00rootroot00000000000000% Input file for the ralfsalg program... % vertex y|GLSM:(0,3,0,1,1,0,1,0,1,0); vertex x|GLSM:(0,2,0,1,0,1,0,1,0,1); vertex z|GLSM:(-4,1,2,0,0,0,0,0,0,0); vertex v1|GLSM:(1,0,-1,0,0,0,0,0,0,0); vertex v2|GLSM:(1,0,0,0,0,0,0,0,0,0); vertex v3|GLSM:(1,0,0,0,0,0,0,0,0,0); vertex v4|GLSM:(1,0,0,0,0,0,0,0,0,0); vertex s1|GLSM:(0,0,-1,1,0,0,0,0,0,0); vertex s2|GLSM:(0,0,0,-1,1,0,0,0,0,0); vertex s3|GLSM:(0,0,0,0,-1,1,0,0,0,0); vertex s4|GLSM:(0,0,0,0,0,-1,1,0,0,0); vertex s5|GLSM:(0,0,0,0,0,0,-1,1,0,0); vertex s6|GLSM:(0,0,0,0,0,0,0,-1,1,0); vertex s7|GLSM:(0,0,0,0,0,0,0,0,-1,1); vertex s8|GLSM:(0,0,0,0,0,0,0,0,0,-1); srideal [s1*y,s2*y,s4*y,s6*y,x*z,s1*x,s2*x,s3*x,s4*x,s5*x,s6*x,s7*x,s4*z,s5*z,s6*z,s7*z,s8*z,s1*v1,s3*v1,s5*v1,s7*v1,s1*s4,s1*s5,s1*s6,s1*s7,s1*s8,s2*s5,s2*s6,s2*s7,s2*s8,s3*s6,s3*s7,s3*s8,s4*s8,s5*s6,s5*s8,s8*v1*y,s2*s3*z,v2*v3*v4]; ambientcohom O(0,0,0,0,0,0,0,0,0,0);cohomCalg-0.32/bin/Quintic.in000066400000000000000000000015701322050713700160510ustar00rootroot00000000000000%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Example input file for cohomCalg % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % This file contains the geometry data of the del-Pezzo-3 surface, which % corresponds to the triple blowup of the CP^2 projective space % % The vertices and GLSM charges: vertex u1 = ( -1, -1, -1, -1 ) | PIC: H | GLSM: ( 1 ); vertex u2 = ( 1, 0, 0, 0 ) | GLSM: ( 1 ); vertex u3 = ( 0, 1, 0, 0 ) | GLSM: ( 1 ); vertex u4 = ( 0, 0, 1, 0 ) | GLSM: ( 1 ); vertex u5 = ( 0, 0, 0, 1 ) | GLSM: ( 1 ); % The Stanley-Reisner ideal: srideal [u1*u2*u3*u4*u5]; % Computation time for this example is quasi-instantaneous, % so turn off intermediate files: monomialfile off; % And finally the requested line bundle cohomologies: ambientcohom O( -3 ); ambientcohom O( 2 );cohomCalg-0.32/bin/WCP11114.in000066400000000000000000000013031322050713700154500ustar00rootroot00000000000000%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Example input file for cohomCalg % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % This file contains the geometry data of the weightes projective % space WCP^4 with coordinate weights 1,1,1,1,4. % % The vertices and GLSM charges: vertex u1 | GLSM: ( 1 ); vertex u2 | GLSM: ( 1 ); vertex u3 | GLSM: ( 1 ); vertex u4 | GLSM: ( 1 ); vertex u5 | GLSM: ( 4 ); % The Stanley-Reisner ideal: srideal [u1*u2*u3*u4*u5]; % Computation time for this example is quasi-instantaneous, % so turn off intermediate files: monomialfile off; % And finally the requested line bundle cohomologies: ambientcohom O(-8); ambientcohom O(0);cohomCalg-0.32/bin/cohomCalg Koszul extension v0.3.nb000066400000000000000000035663111322050713700222520ustar00rootroot00000000000000(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 7.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 977935, 21028] NotebookOptionsPosition[ 976022, 20967] NotebookOutlinePosition[ 976399, 20983] CellTagsIndexPosition[ 976356, 20980] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[ 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"Commented References" section %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @Misc{cohomCalg:Implementation, title = "{\fontfamily{put}\bfseries\footnotesize\selectfont cohomCalg} package", howpublished = "Download link", url = "https://github.com/BenjaminJurke/cohomCalg", note = "High-performance line bundle cohomology computation based on \cite{CohomOfLineBundles:Algorithm}", year = "2010" } @Article{CohomOfLineBundles:Algorithm, author = "Blumenhagen, Ralph and Jurke, Benjamin and Rahn, Thorsten and Roschy, Helmut", title = "{Cohomology of Line Bundles: A Computational Algorithm}", publisher = "AIP", year = "2010", journal = "J.~Math.~Phys.", volume = "51", number = "10", eid = "103525", numpages = "15", pages = "103525", doi = "10.1063/1.3501132", eprint = "1003.5217", archivePrefix = "arXiv", primaryClass = "hep-th", SLACcitation = "%%CITATION = 1003.5217;%%" } @Article{CohomOfLineBundles:Proof, author = "Rahn, Thorsten and Roschy, Helmut", title = "{Cohomology of Line Bundles: Proof of the Algorithm}", publisher = "AIP", year = "2010", journal = "J.~Math.~Phys.", volume = "51", number = "10", eid = "103520", numpages = "11", pages = "103520", doi = "10.1063/1.3501135", eprint = "1006.2392", archivePrefix = "arXiv", primaryClass = "hep-th", SLACcitation = "%%CITATION = 1006.2392;%%" } @article{CohomOfLineBundles:Applications, author = "Blumenhagen, Ralph and Jurke, Benjamin and Rahn, Thorsten and Roschy, Helmut", title = "{Cohomology of Line Bundles: Applications}", year = "2010", eprint = "1010.3717", archivePrefix = "arXiv", primaryClass = "hep-th", SLACcitation = "%%CITATION = 1010.3717;%%" } @Article{Jow:2010arXiv1006.0780J, author = "Shin-Yao Jow", title = "{Cohomology of toric line bundles via simplicial Alexander duality}", archivePrefix = "arXiv", eprint = "1006.0780", primaryClass = "math.AG", year = "2010", } @article{Blumenhagen:2011xn, author = "Blumenhagen, Ralph and Jurke, Benjamin and Rahn, Thorsten", title = "{Computational Tools for Cohomology of Toric Varieties}", year = "2011", eprint = "1104.1187", archivePrefix = "arXiv", primaryClass = "hep-th", } @article{BRTargetSpaceDuality, author = "Blumenhagen, Ralph and Rahn, Thorsten", title = "{Landscape Study of Target Space Duality of $(0,2)$ Heterotic String Models}", journal = "JHEP", volume = "09", year = "2011", pages = "098", doi = "10.1007/JHEP09(2011)098", eprint = "1106.4998", archivePrefix = "arXiv", primaryClass = "hep-th", reportNumber = "MPP-2011-71", SLACcitation = "%%CITATION = ARXIV:1106.4998;%%" }cohomCalg-0.32/manual/latex_source/manual.tcp000066400000000000000000000002731322050713700212730ustar00rootroot00000000000000[FormatInfo] Type=TeXnicCenterProjectInformation Version=4 [ProjectInfo] MainFile=manual.tex UseBibTeX=1 UseMakeIndex=0 ActiveProfile=LaTeX ⇨ PDF ProjectLanguage=en ProjectDialect=US cohomCalg-0.32/manual/latex_source/manual.tex000066400000000000000000001776371322050713700213300ustar00rootroot00000000000000\documentclass[12pt, a4paper]{article} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \pdfminorversion=5 % PDF 1.5 (Acrobat 6.0 / 2003) \pdfcompresslevel=9 % max. content stream compression \pdfobjcompresslevel=9 % max. object compression %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % before submission, change a4paper % to letterpaper and remove the a4-package. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usepackage{a4} \usepackage{graphicx} \usepackage{amsmath} \usepackage{amssymb} \usepackage{mathrsfs} % calligraphic letters for sheaves \usepackage[shortcuts, cyremdash]{extdash} \def\manualversion{v0.32} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Hyperref \usepackage{hyperref} \usepackage{hyperxmp} \hypersetup{ pdfdisplaydoctitle=true, pdftitle={cohomCalg Manual \manualversion}, pdfauthor={{Benjamin Jurke}; {Thorsten Rahn}}, pdfsubject={Mathematical Software, Algebraic Geometry, Mathematical Methods in Physics}, pdfkeywords={{cohomCalg}; {Koszul}; {manual}; {documentation}; {cohomology}; {arXiv:1003.5217}; {line}; {vector}; {bundles}; {implementation}}, pdfstartview={FitH}, pdfpagelayout={TwoColumnRight}, pdfcreator={LaTeX2e with hyperref/xmp package}, pdfcopyright={(c) 2010-2017 Benjamin Jurke, Thorsten Rahn; in collaboration with Ralph Blumenhagen, Helmut Roschy}, pdflicenseurl={https://github.com/BenjaminJurke/cohomCalg}, bookmarksopen, bookmarksnumbered, bookmarksopenlevel=2, breaklinks=true, colorlinks=true, linkcolor=darkred, citecolor=darkgreen, filecolor=dullmagenta, urlcolor=darkblue} \usepackage{xcolor} % existing: black, white, blue, red, green, yellow \definecolor{darkgrey}{rgb}{0.3,0.3,0.3} \definecolor{grey}{rgb}{0.4,0.4,0.4} \definecolor{lightgrey}{rgb}{0.5,0.5,0.5} \definecolor{xlightgrey}{rgb}{0.7,0.7,0.7} \definecolor{darkred}{rgb}{0.5,0.0,0.0} \definecolor{darkblue}{rgb}{0,0,0.4} \definecolor{darkgreen}{rgb}{0,0.4,0} \definecolor{dullmagenta}{rgb}{0.4,0,0.4} \definecolor{orange}{rgb}{1,0.5,0} \definecolor{lightbrown}{rgb}{0.75,0.5,0.25} \definecolor{tan}{cmyk}{0.14,0.42,0.56,0} \definecolor{djunglegreen}{cmyk}{0.99,0,0.52,0} \definecolor{lightgreen}{rgb}{0,1,0} \definecolor{olivegreen}{cmyk}{0.64,0,0.95,0.40} \definecolor{midgreen}{rgb}{0.0,0.675,0.0} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % NOTE: If we are NOT using hyperref, UNCOMMENT the following line to avoid compile errors!!! %\newcommand{\texorpdfstring}[2]{#1} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usepackage[latin1]{inputenc} \usepackage[T1]{fontenc} \renewcommand*\ttdefault{txtt} \newcommand{\cohomCalgSmall}{{\text{\fontfamily{put}\bfseries\scriptsize\selectfont cohomCalg}}} \newcommand{\cohomCalg}{{\text{\fontfamily{put}\bfseries\footnotesize\selectfont cohomCalg}}} \newcommand{\cohomCalgMed}{{\text{\fontfamily{put}\bfseries\selectfont cohomCalg}}} \newcommand{\cohomCalgHuge}{{\text{\fontfamily{put}\bfseries\huge\selectfont cohomCalg}}} \newcommand{\cohomCalgKoszulSmall}{{\text{\fontfamily{put}\bfseries\scriptsize\selectfont cohomCalg Koszul}}} \newcommand{\cohomCalgKoszul}{{\text{\fontfamily{put}\bfseries\footnotesize\selectfont cohomCalg Koszul}}} \newcommand{\cohomCalgKoszulMed}{{\text{\fontfamily{put}\bfseries\selectfont cohomCalg Koszul}}} \newcommand{\cohomCalgKoszulHuge}{{\text{\fontfamily{put}\bfseries\huge\selectfont cohomCalg Koszul}}} \newcommand{\addPP}[1]{#1\nolinebreak\hspace{-.05em}\raisebox{.4ex}{\tiny\bf +}\nolinebreak\hspace{-.10em}\raisebox{.4ex}{\tiny\bf +}} \newcommand{\CPP}{\addPP{C}} \newcommand{\beq}{\begin{equation}} \newcommand{\eeq}{\end{equation}} \newcommand{\bal}{\begin{aligned}} \newcommand{\eal}{\end{aligned}} \newcommand{\BeginExampleBlock}{\begin{description} \item[Example:]} \newcommand{\EndExampleBlock}{\end{description}} \def\ov{\overline} \def\IR{\mathbb{R}} \def\IC{\mathbb{C}} \def\IP{\mathbb{P}} \def\IZ{\mathbb{Z}} \def\cO{\mathcal{O}} \def\cS{\mathcal{S}} \def\cP{\mathcal{P}} \def\cQ{\mathcal{Q}} \def\cH{\mathcal{H}} \def\cM{\mathcal{M}} \def\cV{\mathcal{V}} \def\fh{\mathfrak{h}} \def\fC{\mathfrak{C}} \def\fU{\mathfrak{U}} \def\fV{\mathfrak{V}} \def\shF{\mathscr{F}} \def\shG{\mathscr{G}} \def\shH{\mathscr{H}} \def\shI{\mathscr{I}} \def\labs{\left\|} \def\rabs{\right\|} \DeclareMathOperator{\indlim}{\underrightarrow{\lim}} \def\clap#1{\hbox to 0pt{\hss#1\hss}} \def\mllap{\mathpalette\mathllapinternal} \def\mrlap{\mathpalette\mathrlapinternal} \def\mclap{\mathpalette\mathclapinternal} \def\mathllapinternal#1#2{% \llap{$\mathsurround=0pt#1{#2}$}} \def\mathrlapinternal#1#2{% \rlap{$\mathsurround=0pt#1{#2}$}} \def\mathclapinternal#1#2{% \clap{$\mathsurround=0pt#1{#2}$}} \def\ce{\mathrel{\mathop:}=} % a proper definition symbol := \def\fto{\longrightarrow} \def\injto{\lhook\joinrel\relbar\!\!\:\joinrel\rightarrow} \def\surjto{\relbar\joinrel\twoheadrightarrow} \setlength{\fboxsep}{3mm} \def\uspc{${}^\big.$} % ugly "spaceholders" for table formatting \def\lspc{${}_\big.$} \begin{document} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%% TITLE %%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{picture}(0,0)(0,0) \put(380,50){\includegraphics[height=1.3cm]{img_GPLv3_logo_black}} \put(400,0) {\includegraphics[height=1.5cm]{img_open_source_logo_gray}} \end{picture} \begin{center} % Main title \includegraphics[height=7cm]{cohomCalg_logo.png}\\[1cm] {\LARGE {\bf\---Manual {\manualversion} ---} }\\[15mm] {\sc Benjamin Jurke}~~~and~~~{\sc Thorsten Rahn} \\[5mm] in collaboration with\\[2mm] {\sc Ralph Blumenhagen}, {\sc Helmut Roschy}\\[5mm] \today\\[5mm] \end{center} %\vspace{1cm} \vfill \subsection*{Contact info} Please send all C/{\CPP}~implementation ({\cohomCalg} core program) related or other technical questions to \href{https://benjaminjurke.com}{Benjamin~Jurke}, reachable via eMail: \href{mailto:mail@benjaminjurke.com?subject=cohomCalg}{mail@benjaminjurke.com}.\label{contactaddress}\\[2mm] For all questions regarding the {\cohomCalgKoszul} extension please refer to Thorsten~Rahn (\href{mailto:thorsten.rahn@gmail.com?subject=cohomCalg}{thorsten.rahn@gmail.com}). \clearpage %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%% %%%%%%%%%%%%%%%%%%% %%%%%%%%%%% DOCUMENT BODY %%%%%%%%%%%%%%%%%%% %%%%%%%%%%% %%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section*{Introduction} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% {\cohomCalg} (an acronym pronounced ``cohom-calc'') is an implementation of the sheaf cohomology computation algorithm for line bundles on toric spaces presented in detail in \cite{CohomOfLineBundles:Algorithm} and subsequently proven in \cite{CohomOfLineBundles:Proof, Jow:2010arXiv1006.0780J}. Several applications are discussed in \cite{CohomOfLineBundles:Applications, Blumenhagen:2011xn}. The program is freely available under the GNU General Public Licence version 3.0 (\href{http://www.gnu.org/licenses/gpl.html}{GPLv3}) on the repository site \[ \text{\href{https://github.com/BenjaminJurke/cohomCalg}{https://github.com/BenjaminJurke/cohomCalg}.} \] The main program is written in {\CPP} and consists of a single main program executable file. Due to the implementation structure of the program and the ever-increasing spreading of 64-bit capable processors and operating systems, we consider the 64-bit version of the application to be the natural choice with the 32-bit version provided only as a fallback option for legacy computers. Furthermore, the 64-bit version is considerably faster compared to the 32-bit version on the same platform. The Koszul extension of the {\cohomCalg} package is a {\it Mathematica 7} and {\it 8} script and consists of a single file as well, but depends of the main program's executable.\\ {\bf Note:} Throughout this manual we assume some basic knowledge of toric geometry. A concise introduction to the subject can be found in \cite{CohomOfLineBundles:Algorithm}.\\ {\bf Acknowledgement:} Thanks to \href{http://www2.piedmont.edu/math/dtorrance/}{Doug Torrance} for several improvements and reorganizing {\cohomCalg} into a Debian package.\\[5cm] {\bf External dependencies}: The {\cohomCalg} package makes use of the following external libraries: \begin{itemize} \item The Polyhedral Library ({\tt PolyLib}); \href{http://www.gnu.org/licenses/gpl.html}{GPLv3 license}; mathematical library for computations involving polyhedra, used in the counting of monomials; available for download at \href{http://icps.u-strasbg.fr/polylib/}{http://icps.u-strasbg.fr/polylib/} \end{itemize} \clearpage \tableofcontents \clearpage %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Installation Guidelines} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Main program} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsubsection*{Windows platform} The package comes with precompiled 64-bit and 32-bit binaries called {\it cohomcalg.exe} or {\it cohomcalg32.exe} in the `{\tt /bin/}' subdirectory for Microsoft Windows, which are statically linked to all required run-time libraries in order to avoid any troubles you might have running them. No further steps are required. \subsubsection*{Linux/Unix and Mac} On a Linux/Unix or MacOS X-platform you have to compile the binaries from the source code yourself, which is a fully automated process. Providing precompiled binaries would enlarge the package unnecessarily and not make use of platform-specific speedups. In order to compile {\cohomCalg} from source under a Unix-based platform (e.g.~Linux or MacOS X), just open a terminal, change into the {\cohomCalg} directory and use the \[ \text{\tt make} \] command. Now the script will compile the source files, link them together and produce the new executable {\it cohomcalg} (without any extension) in the `{\tt /bin/}' subdirectory, where the shipped Windows binaries are found as well. Using \[ \text{\tt make clean} \] deletes the temporarily generated subdirectory `{\tt /build/}' which contains the intermediate object files from the compilation process. \subsubsection*{General remarks} Unfortunately, there is no such automated build process available for the Microsoft Windows environment. The program code is fully cross-platform compatible, provided a few minor modifications (a limited number of preprocessor definitions in the source header {\it platform.h}) are applied for other platforms. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Koszul extension} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% The Koszul extension of the {\cohomCalg} package requires a running copy of {\it Mathematica 7} or {\it 8}.\footnote{The script does not use any commands special to Version 7 or 8 of {\it Mathematica}, i.e.~in principle there are no obstacles to using an older version. However, lacking such older software, we were unable to test such usage. Please understand that we cannot offer any help regarding older versions of {\it Mathematica}.} Simply open the {\it Mathematica} notebook file from the program and make sure that the {\cohomCalg} main program is in the same directory. Right in the beginning of the notebook file you find a variable containing the name of the executable file that is used by the script. Change this variable to the correct name of the main executable, e.g.~{\tt cohomcalg.exe} or {\tt cohomcalg32.exe}. Then save the file for future usage. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Package contents} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Naturally, you can find the pre-compiled binaries in the directory `{\tt /bin/}' of the package. The Windows binaries {\it cohomcalg.exe} and {\it cohomcalg32.exe} can be distinguished for the Unix/Linux/MacOS X binary {\it cohomcalg} by the file extension `{\it .exe}', which is not required to be typed explicitly in the Windows command prompt\---Windows only considers files with certain extensions to be executable. The binaries directory also contains the {\it Mathematica 7} or {\it 8} notebook file of the Koszul extension. Under `{\tt /source/}' the source code of {\cohomCalg} is found. It also includes the modified version of the {\tt PolyLib} under `{\tt /source/polylib\_mod/}', which was stripped down to all necessary source files required for compilation. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Version history} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Like most other open source projects, we started {\cohomCalg} with a version number below v1.0 in order to reflect ongoing development before reaching a suitable level of stability. Each increase of the first digit after the dot reflects a major upgrade, the second digit is used for medium changes that warrant a manual upgrade. Furthermore, a lower-case letter may be added (like in v0.21d) to reflect minor internal bug-fixing or upgrades that do not require any change on the user's side. \begin{description} \item[v0.31] (May 25, 2011): Routines for discrete group actions, multi-core support, significant performance improvements. \item[v0.21] (October 18, 2010): {\cohomCalgKoszul} extension added. \item[v0.13] (July 23, 2010): Integration mode added. \item[v0.12] (June 25, 2010): Several minor bugfixes and improvements. \item[v0.11] (May 4, 2010): Original release of the {\cohomCalg} {\CPP} implementation. \item[v0.04] (March 29, 2010): Original public release of the {\it Mathematica 7} script, which is still available from the website. \end{description} \clearpage %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \part[Main {\cohomCalgMed} program]{Main {\cohomCalgHuge} program} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Usage} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Command line parameters} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% The program can be entirely controlled directly from the terminal. However, due to the usually somewhat lengthy input and output data, it is strongly suggested to use text input files. We make it a habit to append the extension {\it.in} to such input files, e.g.~{\it dP3.in}, however you are free to choose whatever name you like. Furthermore, it is recommended to redirect the program's standard output to a file via `{\tt > dP3.out}'. The most basic command line therefore takes the form \[ \boxed{\text{{\tt\bfseries cohomcalg dP3.in > dP3.out}}} \] and effective uses the data in {\it dP3.in} for input and prints the output into {\it dP3.out}. Instead of using an input file, you can also use the option `{\tt --in="..."}', where everything between the quotation marks is treated exactly like the data from an input file. All command line options are always specified before the input file name, i.e.~the general command line syntax is \[ \text{{\tt cohomcalg [--option1] [...] [--optionN] [inputfile] [> outputfile]}} \] and calling the program without any additional parameters shows a concise overview of all options. You can specify any combination of options from the following list: \begin{description} \item[\textnormal{{\tt -?}, {\tt /?}, {\tt --?}, {\tt -help}, {\tt /help}, {\tt --help}}\hspace{5mm}] Shows a concise list of command line options and the general syntax structure. The program will terminate after showing the list, so this option should not be paired with anything else. \item[{\tt --in="..."}\hspace{5mm}] Treats everything between the quotation marks like input data from a file. You may use both an input file and the `{\tt --in}' option, in which case the input data from the command line is effectively analyzed after the file contents. This is useful if you want to specify the geometry of a variety in a file and want to compute a number of different line bundle cohomologies subsequently without having to change the file each time. \item[{\tt --nomonomfile}\hspace{5mm}] As the size of the Stanley-Reisner ideal powerset grows exponentially with the number of generators, traversing all elements to compute the secondary/remnant sequences is a rather time consuming process for complicated geometries. Therefore, the program automatically looks for a file {\it inputfilename.monoms}, e.g.~{\it dP3.in.monoms} in order to skip this computation. The filename can be changed using the `{\tt monomialfile}' input command, see sec.~\ref{inputformat}. Furthermore, in case this file is missing or could not be read the program automatically saves the computed secondary sequences to this file. Using the `{\tt --nomonomfile}' command line option deactivates the usage of this file and also deactivates the generation of a new file. If due to the sole usage of the `{\tt --in}' option without an input file no filename has been specified via the `{\tt monomialfile}' input command, the program automatically deactivates the usage of those intermediate files. \item[{\tt --checkserre}\hspace{5mm}] When using this option, the program automatically computes the cohomology for the Serre-dual line bundle and compares the results according to $H^k(\cO(D))\cong H^{n-k}(K\otimes\cO(-D))^*$. Note that this effectively doubles the computation time in the second part of the program. \item[{\tt --noreduction}\hspace{5mm}] Deactivates the Serre-duality reduction, which tries to reduce the number of ambiguously contributing monomials by comparing to Serre-dual complement monomials. If this reduction is deactivated and ambiguous contributions are found, both the entire range of all possible ``normal'' and Serre-dual cohomologies has to be computed and compared in order to identify a consistent pair. Note that this requires huge amounts of memory and might easily lead to the program quitting prematurely, see sec.~\ref{knownproblems}. Use with caution! \item[{\tt --hideinput}\hspace{5mm}] Deactivates the formatted output of the entire input data. Remember that it might be rather useful to have the results along with the input data in the same file, in particular if you make usage of the `{\tt --in}' option to supply additional input data. \item[{\tt --showtime}\hspace{5mm}] Activates output of computation time statistics even for very short runtimes. This option is automatically activated if the computation takes longer than one second. \end{description} The following command line options are only useful for debugging or if you want to know a little bit more, what is happening on the inside: \begin{description} \item[{\tt --showbits}\hspace{5mm}] Activates an explicit output of the bit-masks used internally. \item[{\tt --mathematica}\hspace{5mm}] Outputs the input data and the output data in a form directly suitable for Copy\&Paste into the legacy {\it Mathematica 7} script. \item[{\tt --integrated}\hspace{5mm}] If the integrated mode is activated the output passed to the standard output channel {\tt stdout} is always a single line of the form \[ \begin{aligned} & \texttt{\{True,{\it Cohomology1},{\it Cohomology2},\dots,{\it CohomologyN}\}} \quad \text{or} \\ & \texttt{\{False,"Invalid command line parameters"\}} \end{aligned} \] The first boolean value tells if the application run was either entirely successful (``{\tt True}'') or if an error occured during the run (``{\tt False}''). If an error happens, a brief error message is supplied. In case of a successful run, a listing of all computed cohomology group dimensions and some intermediate information follows in the order requested in the input file. The cohomology data is of the form \[ \texttt{{\it CohomologyM} = \{}\overbrace{\texttt{\{0,2,0\}}}^{\mclap{\substack{\text{cohomology group} \\ \text{dimensions $h^\bullet$}}}}\texttt{,}\overbrace{\texttt{\{}\underbrace{\texttt{\{1,1*u1*u2*u5\}}}_{\mclap{\substack{\text{$u_1u_2u_5$ contributes with} \\ \text{factor 1 to cohomology $h^1$}}\quad}}\texttt{,}\underbrace{\texttt{\{0,2*u2*u3*u5\}}}_{\mclap{\quad\substack{\text{$u_2u_3u_5$ contributes with} \\ \text{factor 2 to cohomology $h^0$}}}}\texttt{\}}}^{\mclap{\text{list of contributing denominator monomials}}}\texttt{\}}, \] i.e.~the final cohomology group dimensions $h^{\bullet}(\cO(D))$ are a list at the first position inside the cohomology output vector. Note that this option overrides any verbose level. Together with the `{\tt --in}' option this allows for simple integration of {\cohomCalg} into external applications. It should, however, be emphazised that the output format of this option is subject to potential changes in future version. \item[{\textnormal{{\tt --verbose1}, ..., {\tt --verbose5}}}\hspace{5mm}] Activates debug output, where a higher number produces more detailed information. The different levels are: \begin{enumerate} \item[1)] Shows the ultimately computed list of all contributing denominator monomials with factors determined via the secondary/remnant cohomology and the number of rational functions. As it might become internally necessary to use information from the Serre-dual cohomology, this prints a two-column list of this data for both the ``normal'' and Serre-dual contributions. \item[2)] In order to reduce computation time and memory consumption, the ambiguously contributing denominator monomials are mapped to their complement monomials. This verbose level prints the list of all contributing monomials before and after the reduction. \item[3)] Prints the reduced list of secondary/remnant sequences, where all obvious cases (exact sequences, or sequences containing just a single non-zero entry) are removed. Note that this output only appears if the secondary/remnant cohomology is actually computed, compare option {\tt --nomonomfile}. \item[4)] Prints the full list of secondary/remnant sequences. Note that this output only appears if the secondary/remnant cohomology is actually computed, compare option {\tt --nomonomfile}. \item[5)] Shows all polyhedron condition matrices which are passed to {\tt PolyLib} in order to compute the number of rational functions for the corresponding denominator monomial. \end{enumerate} \end{description} In most cases, passing no options at all will serve you just fine, i.e.~it prints the input data and the computed cohomology group dimensions. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Input format and structure}\label{inputformat} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% The input format is both the same for the input file and the input data passed via terminal using the `{\tt --in}' command. Keep in mind, that the command line data is always considered after the data read from the input file. The general structure of the input is in the form of some rather basic data commands. Each such command has to be terminated by a semicolon, just like C/{\CPP} code. Other than keeping the right syntax structure, you are free to format your input data using spaces, tabulators or line breaks just as you like. You may also use comments in the input file using the `{\tt \%}' character. Everything following a `{\tt \%}' character till the end of the line is completely ignored. Note that this effectively prohibits usage of comments when passing data via the command line, as the entire remainder of the data after the percent sign will be ignored. The following commands for providing input data are available: \begin{description} \item[{\textnormal{{\tt vertex }[name] {\tt | GLSM: (}[GLSM charge 1]{\tt, }...{\tt ,} [GLSM charge $r$]{\tt );}}}\hspace{5mm}] This command specifies a new coordinate (or vertex of the fan in the corresponding toric description, thus the name) and its GLSM charges, i.e.~for each coordinate you use one corresponding `{\tt vertex}' command. The name of the coordinate must be an alphanumeric sequence of characters not starting with a number. The number of GLSM charges must be equal for all coordinates and the GLSM charge value has to stay within a certain range. As an example, the following commands specify the coordinates and GLSM charges of the del-Pezzo 1 surface: \[ \parbox{6cm}{\tt vertex u1 | GLSM: ( 1, 0 );\\ vertex u2 | GLSM: ( 1, 0 );\\ vertex u3 | GLSM: ( 1, 1 );\\ vertex u4 | GLSM: ( 0, 1 );} \] Note that due to internal limitations the maximum number of vertices is limited to 63. \item[{\textnormal{{\tt srideal [}[SR generator 1]{\tt ,}...{\tt ,}[SR generator $N$]{\tt ];}}}\hspace{5mm}] This command specifies the Stanley-Reisner ideal, i.e.~you have to specify the generators as products of the coordinates like in the following $dP_1$ example: \[ \text{{\tt srideal [u1*u2, u3*u4];}} \] Note that the coordinates used in the products have to be previously declared, i.e.~it only makes sense to use the `{\tt srideal}' command after the `{\tt vertex}' commands. The number of Stanley-Reisner ideal generators $N$ is limited to 63, however, on modern desktops computational time will explode at around 40 generators, which is due to the exponential $2^N$ growth of the powerset of the Stanley-Reisner ideal generators. \item[{\textnormal{{\tt ambientcohom O(}[charge 1]{\tt, }...{\tt,}[charge $r$]{\tt );}}}\hspace{5mm}] Using this command you can specify the GLSM charges of the target divisor $D$ that determines the line bundle $\cO(D)$ for which the sheaf cohomology on the ambient space is computed. Please note the upper-case letter `O' behind the command. For example, \[ \text{{\tt ambientcohom O(0, 0);}} \] computes the ambient space sheaf cohomology for the holomorphic line bundle $\cO(0,0)=\cO$. Obviously, the number of charges $r$ has to be equal to the number of GLSM charges specified in the `{\tt vertex}' commands. You may specify several target line bundles for batch computation by simply using the `{\tt ambientcohom}' command multiple times. \item[{\textnormal{{\tt monomialfile {"}}[filename]{\tt ";}}}\hspace{5mm}] This command allows you to specify a different filename for the intermediate monomial file between the quotation marks: \[ \text{{\tt monomialfile "my-dP1-monomial-file.dat";}} \] This filename is both used for reading and saving of the monomial file. Please keep in mind, that the intermediate data saved to file is crucially dependant on the geometry data specified via the other commands, see sec.~\ref{knownproblems}. You can therefore turn off the usage and generation of those files using the input command line \[ \text{{\tt monomialfile off;}} \] which might come in handy, when you frequently change the geometry of the variety specified in the input file and want to avoid the usage of the `{\tt --nomonomfile}' parameter. \end{description} All commands are subject to a precise syntax, range and consistency check, so it is basically impossible to run the program with invalid data. In such cases, you will see a syntax error message indicating where the problem occured in the input data. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Output format} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Following the prior $dP_1$ example, after saving the six input commands to file and running the program via `{\tt cohomcalg dP1.in > dP1.out}', the output file contains after the obligatory header the following data:\\[1cm] \begin{minipage}[center]{12cm} \begin{verbatim} Input data: =========== The described ambient space is of dimension 2. There are 4 coordinates, each having 2 GLSM charges: coord 1: u1 | 1 0 coord 2: u2 | 1 0 coord 3: u3 | 1 1 coord 4: u4 | 0 1 There are 2 generators of the Stanley-Reisner ideal: SRgen 1: u1*u2 SRgen 2: u3*u4 There is 1 ambient space sheaf cohomology requested: cohom 1: H^i(A; O( 0, 0 )) Cohomology dimensions: ====================== dim H^i(A; O( 0, 0 )) = ( 1, 0, 0 ) \end{verbatim} \end{minipage}\\[1cm] This output is fairly self-explanatory and should not require further comment. However, for more involved and complicated examples a couple of non-ideal things may happen. You may see the line\\[1mm] \[ \parbox{12cm}{\tt The Serre dualization reduction was unable to uniquely resolve 88 of the original 1049 ambiguous monoms.} \]\\ which indicates that the Serre-dual complement monomial reduction technique (compare the command line option `{\tt --noreduction}') was unable to resolve all ambiguously contributing denominator monomials. This is in principle not a problem, provided that the much more computationally expensive fallback technique, which compares all possible cohomologies to the corresponding Serre dual cohomologies, is able to uniquely resolve the issue. However, if this fails as well you will see an output like\\[0.8cm] \begin{minipage}[center]{13cm} \begin{verbatim} dim H^i(A; O( 2, 4, 1, ..., 3, -2, 1 )) is ambiguous candidate results are: = ( 580, 353, 171, 1, 919, 0 ) = ( 580, 353, 0, 1,1090, 0 ) \end{verbatim} \end{minipage}\\[0.8cm] which gives you all possible cohomology configurations the algorithm was able to sort out. Unfortunately, you may also be graced by the message\\[0.8cm] \begin{minipage}[center]{11cm} \begin{verbatim} dim H^i(A; O( 2, ..., 1 )) could not be determined. \end{verbatim} \end{minipage}\\[0.8cm] but in all our extensive testing, we never encountered this problem. Finally, for any computations longer than one second or if you use the `{\tt --showtime}' option you will encounter runtime statistics like\\[0.8cm] \begin{minipage}[center]{13cm} \begin{verbatim} Application run took 14.27 seconds, more precisely 11.02 seconds sec for the computation of the sec. cohom. 3.23 seconds sec for the counting of rational functions \end{verbatim} \end{minipage}\\[0.8cm] which gives you an idea of the time consumption. Also, during longer runtimes, you will see an output like \[ \text{{\tt SR powerset traverse 14.54\% done (12 secs remaining)...}} \] which reports the progress of computing the secondary/remnant cohomologies and gives a rough time estimate for this part of the program to finish. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Obtaining geometric data} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Naturally, you need to get the input data from somewhere, and a couple of very useful packages for those tasks are available freely on the net. In order to derive the Stanley-Reisner ideal, which is a required input for the program, you may want to take a look at \[ \text{{\tt TOPCOM}: \href{http://www.rambau.wm.uni-bayreuth.de/TOPCOM/}{http://www.rambau.wm.uni-bayreuth.de/TOPCOM/},} \] which can also enumerate all possible fans for a given set of vertices. The Maple script package \[ \text{{\tt SCHUBERT}: \href{http://folk.uib.no/nmasr/schubert/0.996/}{http://folk.uib.no/nmasr/schubert/0.996/},} \] can be used to compute intersection numbers and further geometrical quantities of toric varieties, however, the software is somewhat dated at this point. Furthermore, there is the package \[ \text{{\tt PALP}: \href{http://hep.itp.tuwien.ac.at/~kreuzer/CY/CYpalp.html}{http://hep.itp.tuwien.ac.at/~kreuzer/CY/CYpalp.html},} \] which is useful for computing invariants of hypersurfaces, Mori cone vectors etc. You may also want to take a look at the \[ \text{{\tt SAGE} Library: \href{http://www.sagemath.org/}{http://www.sagemath.org/},} \] of freely available mathematical software. Finally, the environment \[ \text{{\tt Macaulay2}: \href{http://www.math.uiuc.edu/Macaulay2/}{http://www.math.uiuc.edu/Macaulay2/},} \] which allows similar computations, was heavily used during the development process. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Implementation} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Internal design} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% This implementation heavily relies on the usage of bit-wise operations on 64-bit integer variables. The $i$th coordinate of the input data is represented by the $i$th bit of such a variable, such that a Stanley-Reisner ideal generator simply becomes a bit-mask. Via this coding scheme, computing the union of Stanley-Reisner ideal generators is equivalent to using the bit-wise non-exclusive OR operator, which is a superfast operation on any 64-bit architecture machine. Furthermore, when traversing the powerset of the Stanley-Reisner ideal, we also encode the presence of the $j$th generator by the $j$th bit, such that running through all subsets of the set of generators reduces to a simple loop running from 0 to $2^N$, where $N$ is the number of generators. Using a couple of bit-mask buffers, those two elementary encoding techniques allowed us to gain a speedup of several orders of magnitude on any other implementation approach. On the other hand, this puts the strict upper limit of 63 on the number of coordinates and Stanley-Reisner ideal generators, but as the number of Stanley-Reisner ideal generators is usually much larger and somewhat maxes out current computers at around 40 generators, those constraints are currently rather theoretical and do not present any practical restrictions. Since version 0.31 of the {\cohomCalg} core program the computation of the secondary sequences is carried out in a multi-threaded fashion, i.e.~all available (logical) processor cores of the machine are used simultaneously. Depending on the hardware, this leads to a significant speed improvement factor scaling almost linearly with the number of cores. By computing the secondary sequences, a number of uniquely and ambiguously contributing denominator monomials is found. Ambiguously in this sense means that the secondary/remnant cohomology has more than one non-zero contribution, i.e.~the number of rational functions for this denominator monomial might contribute to different groups of the cohomology, e.g.~to $H^1$ and $H^2$. This ambiguity arises due to the fact that the mappings in the secondary/remnant sequences are currently not considered in the computation. It is therefore necessary to employ the Serre duality in order to resolve this issue, which basically means to take the complement monomial\---the monomial consisting of all the remaining coordinates\---into account. This step is carried out during the Serre-duality reduction, which can be turned off using the `{\tt --noreduction}' command line option. In most cases, this eliminates all ambiguities by turning the ambiguous contributions in unique contributions. In the next step, the number of rational functions is computed for each monomial using The Polyhedron Library.\footnote{Note that we use a very slightly modified version of the {\tt PolyLib}, where a number of standard output responses are removed. It is therefore not recommended to simply replace the {\tt PolyLib} version included in the source package by another version.} Basically, with {\tt PolyLib} we are constructing a polyhedron from a number of equalities and inqualities and then count the number of integer lattice points inside of it using Ehrhart polynomial approximations. For the uniquely determined contributions, the resulting cohomology group dimension is simply the factor derived from the secondary/remnant sequences times the number of rational functions. However, if there are still ambigous contributions leftover, this requires a branching of the current number of possible cohomology dimensions by the ambiguity, i.e.~if you have 10 ambiguous contributions with 3 possibilities each, this already yields $3^{10}= 59049$ possible configurations. In case of ambiguities it is necessary to entirely compute all those possibilities both for the ``normal'' and Serre-dual configuration and then match those possibilities in order to determine compatible ones. Unfortunately, due to the rapid growth of the number of configurations, one quickly runs out of memory, which is a still unresolved issue of the implementation. Again, this problem ultimately originates in the fact, that the mappings in the secondary/remnant sequences are not implemented at the moment. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Potential improvements} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% The counting of monomials (rational functions) in the current algorithm is currently still implemented as a single-threaded application, i.e.~it only makes use of one processor core\---whereas modern desktops already may have up to 6 cores per processor with an increasing trend. While a parallelization has been attempted, it appears that the PolyLib is not implemented in a thread-safe fashion, which leads to a memory (heap) corruption as soon as more than one PolyLib thread is executed at the same time. This problem is currently investigated in more detail but may remain unsolved for the foreseeable future. As a second improvement in the long run one might offer the option of arbitrary-length bitmasks, which would effectively remove the 63 coordinates and Stanley-Reisner generators upper limits. On the other hand, such a change would most likely impair performance quite a bit, and for the moment those limits are far out of reach for reasonable computation times. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Known problems}\label{knownproblems} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% The implementation is rather robust aside from the potential memory-con\-sump\-tion issue, when the number of ambiguous contributions becomes too large. For the moment, we can only recommend the usage of the 64-bit version for such cases (which is recommended anyways), as it somewhat alleviates the problem and gives the program access to more memory. It should be mentioned however, that without enforcing this issue via the `{\tt --noreduction}' option, the problem is mostly kept in check even in extremely complicated cases. A somewhat minor problem is the instability of the monomial files. As the computed monomials are effectively stored via bit-masks, changing the geometry of the variety in the input data (i.e.~the order or number of the vertices as well as the number of Stanley-Reisner generators) effectively corrupts this data. Currently, there is no sophisticated check if the intermediate monomial data stored in the file corresponds to the geometry specified via the input data. In worst case scenarios such a corruption might crash the program. In case you are worried about the results while using an intermediate monomial file try rebuilding this one by deleting or renaming the old one or turning off the monomial file usage alltogether. \vspace{3mm} Aside from that we are reasonably certain that quite a number of bugs and problems are still included. Please let us know any problems you may find, see page \pageref{contactaddress} for contact information. \clearpage %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \part[{\cohomCalgKoszulMed} extension]{{\cohomCalgKoszulHuge} extension} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Usage} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Preparations} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% The {\it Mathematica} Koszul extension serves as a wrapper for the {\cohomCalg} program. Simply open {\it Mathematica 7} or {\it 8} on your computer and load the notebook file. Make sure that the {\cohomCalg} executable variable at the top of the script points to the correct executable file, e.g.~{\it cohomcalg32.exe} on a Windows 32-bit platform. Also make sure that the correct path of the executable is inserted. There are no further parameters or options. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Input format and structure} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% The script in its current form consists of three parts: \begin{enumerate} \item The main portion of the file contains the actual routines used for the program. Each time you open the script file, you briefly have to re-run this part, such that the {\it Mathematica} kernel working in the background has all the necessary definitions etc.~available. This is done, for example, by pressing {\tt Shift+Enter} while the cursor is still in the upper part of the script. \item The second portion is clearly marked by the words ``{\tt Ambient geometry data}''. Here you have to specify the relevant toric data for the ambient space variety $X$. The following data is required in list form: \begin{itemize} \item \emph{Coordinates:} A list of the coordinate names like the seven variables in {\tt \{x1,x2,x3,x4,x5,x6,x7\}}. \item \emph{Stanley-Reisner ideal:} A list of lists corresponding to the generators of the Stanley-Reisner ideal, e.g.~{\tt \{\{x1,x6\},\{x2,x3,x4,x5,x7\}\}}. \item \emph{GLSM relations:} A list of lists corresponding to the GLSM charges or projective relations associated to each coordinate, for example\\ {\tt \{\{1,3\},\{0,1\},\{0,1\},\{0,1\},\{0,1\},\{1,0\},\{0,1\}\}}. The number of those lists obviously has to be equal to the number of coordinates. \end{itemize} This data is assigned to a list variable, which for book-keeping purposes should carry a name suggesting the described toric variety, e.g.~{\tt P111113}. \item Finally the command part follows, where the user can access the functions provided by the \cohomCalgKoszul extension. Here depending on what kind of bundle one wants to calculate the program needs some additional input parameters: \begin{itemize} \item \emph{Complete intersection charges:} A list of divisor charges for the complete intersection like {\tt\{\{1,4\},\{1,4\}\}}. An empty list {\tt\{\}} always returns the result for the ambient space. \item \emph{Line bundle charges:} A list that specifies the required line bundle charges, e.g.~{\tt\{22,30\}}. \item \emph{Monad bundle charges :} A list of lists corresponding to the monad bundle charges $N_k$ in \eqref{eq_monadsequence}, for example {\tt\{\{1,0\},\{0,1\},\{0,1\},\{0,1\},\{0,2\}\}}. \item \emph{Monad bundle constraints:} A list of lists of the required monad bundle constraints $M_i$ in \eqref{eq_monadsequence}, for instance {\tt\{\{1,5\}\}}. \item \emph{$V_r$:} Power of the $\mathcal{O}_S$ bundle in the monad sequence \eqref{eq_monadsequence}, e.g. {\tt 2}. \beq\label{eq_monadsequence} 0 \fto \cO_S^{\oplus V_r} {\fto} \bigoplus_{k=1}^{V_n} \cO_S(N_k){\fto} \bigoplus_{i=1}^{V_l} \cO_S(M_i)\,, \eeq \item \emph{$\mathbb Z^n$-action: A list that specifies how the involution acts on the coordinates, e.g. {\tt \{x1,x2,x3,x4,x5,x6,-x7\}} } for a $\mathbb Z^2$ action \end{itemize} \end{enumerate} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Bundle types} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Various different bundle types are provided by the {\cohomCalgKoszul} extension. The structure of the input is similar for all bundles and looks like: % \begin{equation*} \begin{matrix} \textnormal{{\tt CohomologyOf[}{[}Bundle Type{]}{\tt , }{[}Ambient Space{]}{\tt , }{[}Additional Input{]}{\tt , }}\\ \textnormal{{{[}Optional: Type of Subvariety{]}{\tt , }{[}Optional: Verbose Level{]}{\tt , }}}\\ \textnormal{{[}Optional: Output Type{]}{\tt , }{[}Optional: Line Bundle Collector{]}{\tt ]}\hspace{5mm}} \end{matrix} \end{equation*} % The optional input can be inserted in an arbitrary order. In the following we describe how the different bundle types can be evaluated. Here we will not use the last two of the optional input parameters and explain their use afterwards. From the mandatory part of the input data only the {[}Bundle Type{]} and the {[}Additional Input{]} change: \subsubsection{Line bundles} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \item[{\textnormal{{\tt Koszul[}{[}Ambient space{]}{\tt , }[Divisors]{\tt , }[Line bundle]{\tt ]}\hspace{5mm}}}] %\item{\textnormal{{\tt CohomologyOf[}{[}''LineBundle``{]}{\tt , }[Ambient space]{\tt , }[Additional input]{\tt ]}\hspace{5mm}}} \begin{itemize} \item {[}Bundle Type{]}: {\tt''LineBundle``} \item {[}Additional Input{]}: {\tt\{}\emph{Complete intersection charges}, \emph{Line bundle charges}{\tt\}} \end{itemize} % This command is the main routine of the \cohomCalgKoszul~extension. Given an ambient space $X$ and a set of divisors $S_1,\dots,S_l\subset X$ as well as a line bundle divisor $E$ it computes the sheaf cohomology group dimensions $\dim H^i(S; \cO_{S}(E))$ on the hypersurface or complete intersection $S=S_1\cap \dots \cap S_l$. Note that there is no checking if the intersection geometry is actually well-defined, i.e.~the \cohomCalgKoszul~extension does not test for transversality or other conditions. Furthermore, it does not actually evaluate the mappings in the Koszul complex, but rather attempts to derive the dimensions from indirect exactness arguments and constraints. However, as those methods may not always lead to a solution, the output may contain parameters which are unresolved. %The ambient space variable is a list of lists of the format specified in the second part of the script. Similarly, the list of divisors is a list of lists of GLSM charges, which specifies the divisors $D_i\subset X$. The line bundle is specified by a list of GLSM charges that define the divisor $E$ associated to the line bundle. Ultimately all those charges depend on the coordinate and GLSM charges specified in the ambient space data. The input data for the ambient space, the complete intersection and the line bundle charges has to be specified as explained above. Here the additional input is a list of two lists, namely the data specifying the complete intersection as well as the charges of the line bundle you want to compute. For the complete intersection data, an empty list {\tt \{\}} of divisors return the cohomology of the ambient space itself, i.e.~it computes $\dim H^i(X;\cO_X(E))$. \BeginExampleBlock Consider the ambient space $\tilde{\mathbb P}^5_{111113}$ described before. If you type % \begin{table*} % P111113 = \{\\ % (*Coordinates*)\{x1,x2,x3,x4,x5,x6,x7\},\\ % (*Stanley Reisner*)\{\{x1,x6\},\{x2,x3,x4,x5,x7\}\},\\ % (*Equivalence Relations*)\{\{1,3\},\{0,1\},\{0,1\},\{0,1\},\{0,1\},\{1,0\},\{0,1\}\}\};\\[1.4mm] % CohomologyOf["LineBundle",P111113,\{\{\{1,4\},\{1,4\}\},\{2,8\}\}] % \end{table*} % \begin{verbatim*} P111113={ (*Coordinates*){x1,x2,x3,x4,x5,x6,x7}, (*Stanley Reisner*){{x1,x6},{x2,x3,x4,x5,x7}}, (*Equivalence Relations*){{1,3},{0,1},{0,1},{0,1},{0,1},{1,0},{0,1}}}; CohomologyOf["LineBundle",P111113,{{{1,4},{1,4}},{2,8}}] \end{verbatim*} you will get the result {\tt \{487,0,0,0\}}, which means that $\dim H^0(S; \cO_{S}(E))=487$ and $\dim H^j(S; \cO_{S}(E))=0$ for $j=1,2,3$. \EndExampleBlock \subsubsection{Equivariant Cohomology of Line Bundles} If you consider an ambient space that allows for a discrete action your cohomology obtains a grading into invariant and non-invariant parts under this action. You can compute this equivariant cohomology of line bundles. To do that the following input parameters are needed: \begin{itemize} \item {[}Bundle Type{]}: {\tt''EquivariantLineBundle``} \item {[}Additional Input{]}: {\tt\{\{\},} \emph{Line bundle charges}, \emph{$\mathbb Z^n$-action}{\tt\}} \end{itemize} % The program then returns two cohomology vectors where the first contains the invariant part of the cohomology, $\dim H^\bullet_{\text{inv}}(X; \cO_{X}(E))$ and the non-invariant part of the cohomology $\dim H^\bullet_{\text{non-inv}}(X; \cO_{X}(E))$. Note that the program does not check whether such an action is allowed on this space, so you have to figure that out yourself beforehand. You can also ask the program to print the representatives of the cohomology by using the verbose options described below. \BeginExampleBlock Consider the ambient space $\tilde{\mathbb P}^5_{111113}$ as specified above. If you evaluate the order \begin{verbatim*} CohomologyOf[ (*Bundle specification*)"EquivariantLineBundle", (*Ambient Space*)P111113, (*Remaining Data:Complete Intersection,LineBundle Charges,Discrete Action*) {{},{5,3},{x1 x2,x3,x4,x5,x6,-x7}} ]; \end{verbatim*} you will get the result two resulting line bundle cohomology vectors where the first one denotes the invariant part of the equivariant cohomology and the second one the non-invariant part. For this explicit example you will get {\tt\{\{25,0,0,0,155,0\},\{11,0,0,0,250,0\}\}}. So we have the only non-vanishing contibutions \begin{eqnarray*} h^0_{\text{inv}}(X;\mathcal O(5,3))=25 &,& h^4_{\text{inv}}(X;\mathcal O(5,3))=155,\\ h^0_{\text{non-inv}}(X;\mathcal O(5,3))=11 &,& h^4_{\text{non-inv}}(X;\mathcal O(5,3))=250\,. \end{eqnarray*} \EndExampleBlock \subsubsection{Tangent bundle of a subvariety} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \item[{\textnormal{{\tt Koszul[}{[}Ambient space{]}{\tt , }[Divisors]{\tt , }[Line bundle]{\tt ]}\hspace{5mm}}}] %\item{\textnormal{{\tt CohomologyOf[}{[}''LineBundle``{]}{\tt , }[Ambient space]{\tt , }[Additional input]{\tt ]}\hspace{5mm}}} \begin{itemize} \item {[}Bundle Type{]}: {\tt''TangentBundle``} \item {[}Additional Input{]}: {\tt\{}\emph{Complete intersection charges}{\tt\}} \item {[}Optional: Type of Subvariety{]}: {\tt''Calabi-Yau``}/ {\tt''Unknown''} \end{itemize} % Computes the cohomology dimensions of the tangent bundle of $S$, i.e.~$\dim H^i(S;T_S)$. If you choose the type of the subvariety to be ``Calabi-Yau'', this will be taken into account in the calculation. As always an empty list of intersecting surfaces returns the cohomology of the tangent bundle of the ambient toric variety. % \BeginExampleBlock Consider the ambient space $\tilde{\mathbb P}^5_{111113}$ as specified above. If you evaluate the order \[ \texttt{CohomologyOf["TangentBundle",P111113,\{\{1,4\},\{1,4\}\},``Calabi-Yau''];} \] you will get the result {\tt \{0,86,2,0\}} which means that $\dim H^0(S;T_S)=\dim H^3(S;T_S)=0$, $\dim H^1(S;T_S)=86$ and $\dim H^2(S;T_S)=2$. \EndExampleBlock \subsubsection[\texorpdfstring{$\Lambda^k$(Cotangent Bundle) of a subvariety for $k=0,1,2$}{Exterior powers of the Cotangent Bundle of a subvariety}]{\boldmath{$\Lambda^k$}(Cotangent Bundle) of a subvariety for \boldmath{$k=0,1,2$}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \item[{\textnormal{{\tt Koszul[}{[}Ambient space{]}{\tt , }[Divisors]{\tt , }[Line bundle]{\tt ]}\hspace{5mm}}}] %\item{\textnormal{{\tt CohomologyOf[}{[}''LineBundle``{]}{\tt , }[Ambient space]{\tt , }[Additional input]{\tt ]}\hspace{5mm}}} \begin{itemize} \item {[}Bundle Type{]}: {\tt''Lambda\underline{$k$}CotangentBundle``} \item {[}Additional Input{]}: {\tt\{}\emph{Complete intersection charges}{\tt\}} \item {[}Optional: Type of Subvariety{]}: {\tt''Calabi-Yau``} / {\tt''Unknown''} \end{itemize} % Those three commands compute the exterior powers $k=0,1,2$ of the cotangent bundle of the hypersurface or complete intersection $S=D_1\cap\dots\cap D_n$: \[ \dim H^i(S;\Lambda^kT^*_S), \] The input data is exactly the same as for the tangent bundle cohomology. \BeginExampleBlock Consider the ambient space $\tilde{\mathbb P}^5_{111113}$ as specified above. If you type \begin{eqnarray*} \texttt{CohomologyOf["Lambda0CotangentBundle",P111113,}\\ \texttt{\{\{1,4\},\{1,4\}\},``Calabi-Yau''];} \end{eqnarray*} you will get {\tt \{1,0,0,1\}}. \EndExampleBlock \subsubsection[\texorpdfstring{$\Lambda^k$(Monad bundle) of a subvariety for $k=1,2$}{Exterior powers of the Monad Bundle of a subvariety}]{\boldmath{$\Lambda^k$}(Monad bundle) of a subvariety for \boldmath$k=1,2$} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \item[{\textnormal{{\tt Koszul[}{[}Ambient space{]}{\tt , }[Divisors]{\tt , }[Line bundle]{\tt ]}\hspace{5mm}}}] %\item{\textnormal{{\tt CohomologyOf[}{[}''LineBundle``{]}{\tt , }[Ambient space]{\tt , }[Additional input]{\tt ]}\hspace{5mm}}} \begin{itemize} \item {[}Bundle Type{]}: {\tt''Lambda\underline{$k$}MonadBundle``} \item {[}Additional Input{]}: {\tt\{}\emph{Complete intersection charges, Bundle charges, Bundle Constraints, $V_r$}{\tt\}} \end{itemize} % Those two commands compute the exterior powers $k=1,2$ of the specified monad bundle \eqref{eq_monadsequence} of the hypersurface or complete intersection $S=S_1\cap\dots\cap S_l$. Here in addition to the charges of the complete intersection we also need the bundle charges $N_k$ as well as the bundle constraints $M_k$ and the power $V_r$, all defined in \eqref{eq_monadsequence} . \BeginExampleBlock Consider the ambient space $\tilde{\mathbb P}^5_{111113}$ as specified above. % %\begin{minipage}[center]{12cm} \begin{verbatim} CohomologyOf["Lambda1MonadBundle",P111113,{{{1,4},{1,4}}, (*BundleCharges*){{1,0},{0,1},{0,1},{0,1},{0,2}}, (*BundleConstraints*){{1,5}}},"Calabi-Yau"]; \end{verbatim} %\end{minipage} %CohomologyOf["Lambda1MonadBundle",P111113,\{(*ComplInt*)\{\{1,4\},\{1,4\}\},(*BundleCharges*)\{\{1,0\},\{0,1\},\{0,1\},\{0,1\},\{0,2\}\},(*BundleConstraints*)=\{\{1,5\}\}\},``Calabi-Yau'']; The result will be ${\tt\left\{0,2,102+A_{70},A_{70}\right\}}$. Here the ${\tt A_{70}}$ is a constant which could not be determined using only the dimensions of the line bundle cohomologies in the long exact sequences. A method that actually evaluates the maps in order to evaluate this constant is currently not included in the program. But one can use the verbose function described below to have an explicit look at the long exact sequences. In certain cases, properties of the maps of the monad may be chosen in order to determine such a parameter in an easy way. \EndExampleBlock So far we have only considered monads that are non-exact sequences. If you want to calculate the cohomology of an exact monad, you can simply do that by putting the parameter $V_r$ to zero. Then the non-exact sequence becomes exact and the vector bundle is given as the kernel of the corresponding map: % \beq\label{eq_exactmonadsequence} 0 \fto V {\fto} \bigoplus_{k=1}^{V_n} \cO_S(N_k){\fto} \bigoplus_{i=1}^{V_l} \cO_S(M_i)\,, \eeq \subsubsection{Hodge diamond of a subvariety} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{itemize} \item {[}Bundle Type{]}: {\tt''HodgeDiamond``} \item {[}Additional Input{]}: {\tt\{}\emph{Complete intersection charges}{\tt\}} \item {[}Optional: Type of Subvariety{]}: {\tt''Calabi-Yau``}/ {\tt''Unknown''} \end{itemize} % Computes the entire Hodge diamond of the hyper surface or complete intersection $S$. Up to 4 dimensions one usually gets a unique result which may not be the case for higher dimensions. The output contains the Hodge diamond, the Betti numbers as well as the Euler character of the requested subvariety. \BeginExampleBlock The following example for a Calabi-Yau 4-fold is taken from the paper arXiv:0912.3524 and describes a compact complete intersection Calabi-Yau 4-fold used in the construction of F-theory GUT vacua. The toric data of the ambient space (found in table B.1 of the aforementioned paper) is specified by the following variable:\\ \begin{minipage}[center]{12cm} \begin{verbatim} Example4Fold = { (*Coordinates*){v1, v2, v3, v4, v5, v6, v1s, v7, v8, v9, v10}, (*Stanley Reisner*) {{v3,v9},{v5,v9},{v7,v10},{v1,v2,v3}, {v4,v1s,v8},{v4,v7,v8},{v4,v8,v9}, {v5,v6,v1s},{v5,v6,v10},{v1,v2,v6,v1s}}, (*Equivalence Relations*){{3, 3, 3, 3, 0}, {2, 2, 2, 2, 0}, {1, 0, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}, {0, 1, 0, 0, 0}, {0, 1, 1, 0, 0}, {0, 0, 1, 0, 1}, {0, 0, 1, 0, 0}, {0,-1,-1, 1,-1}, {0, 0, 0, 0, 1}} }; \end{verbatim} \end{minipage} {$\big.$} \noindent The 4-fold is given by the intersection of two divisors in the ambient space, which are specified in the variable \[ \texttt{ComplInt = \{\{6, 6, 6, 6, 0\}, \{0, 0, 2, 1, 1\}\};} \] and the actual command for the computation of the Hodge diamond is then \[ \texttt{CohomologyOf[``HodgeDiamond'',Example4Fold,ComplInt,``Calabi-Yau''];} \] which takes around 20 seconds on a current desktop computer and computes 264 intermediate ambient space line bundle cohomologies via {\cohomCalg}. The full Hodge diamond as well as the Betti numbers and the Euler character are then printed in a very readable form: \[ \begin{array}{ccccccccccc} & & & & {\tt 1} & & & & & {\tt 1} & \\ & & & {\tt 0} & & {\tt 0} & & & & {\tt 0} & \\ & & {\tt 0} & & {\tt 5} & & {\tt 0} & & & {\tt 5} & \\ & {\tt 0} & & {\tt 0} & & {\tt 0} & & {\tt 0} & & {\tt 0} & \\ {\tt 1} & & {\tt 1115} & & {\tt 4524} & & {\tt 1115} & & {\tt 1} & {\tt 6756} & {\tt \chi= 6768}\\ & {\tt 0} & & {\tt 0} & & {\tt 0} & & {\tt 0} & & {\tt 0} & \\ & & {\tt 0} & & {\tt 5} & & {\tt 0} & & & {\tt 5} & \\ & & & {\tt 0} & & {\tt 0} & & & & {\tt 0} & \\ & & & & {\tt 1} & & & & & {\tt 1} & \end{array} \] \EndExampleBlock \subsubsection{Endomorphism bundle of the tangent bundle of a subvariety} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{itemize} \item {[}Bundle Type{]}: {\tt''EndTangentBundle``} \item {[}Additional Input{]}: {\tt\{}\emph{Complete intersection charges}{\tt\}} \end{itemize} % Computes the cohomology dimensions $\dim H^i(S;{\rm End}(T_S))$ of the endomorphism bundle ${\rm End}(T_S)$, which represents the bundle deformations of the hypersurface / complete intersection $S$. For such calculations it is usually not necessary only to consider the dimensions of the line bundles, but more is needed. The routine is still useful since you can choose a verbose level in order to obtain the long exact sequences. So if you know about certain map properties you may be able to put parameters to zero manually and see how the result changes. \subsubsection{Endomorphism Bundle of the monad bundle of a Subvariety} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{itemize} \item {[}Bundle Type{]}: {\tt''EndMonadBundle``} \item {[}Additional Input{]}: {\tt\{}\emph{Complete intersection charges, Bundle charge, Bundle Constraints, $V_r$}{\tt\}} \end{itemize} % Computes the cohomology dimensions $\dim H^i(S;{\rm End}(V))$ of the endomorphism bundle ${\rm End}(V)$, which represents the bundle deformations of the monad bundle \eqref{eq_monadsequence}. As for the endomorphism bundle of the tangent bundle, here one usually needs additional information about the maps in the monad. %This routine was used extensively in \cite{BRTargetSpaceDuality} in a landscape study in order to calculate the bundle moduli of more than fifty thousands different $(0,2)$-heterotic models. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Verbose Level and Output Format} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Since it may be useful to see how the long exact sequences involved in the internal computations actually look like\---especially if one does not get a unique result in the end\---there is an option in the {\cohomCalgKoszul} extension to do so. In total there are 6 different verbose levels. \begin{itemize} \item ``{\tt Verbose-1}'': Only the final result is returned. \item ``{\tt Verbose0}'': The result is printed along with a small statistic about calculation time. \item ``{\tt Verbose1}'': All long exact sequences coming from the Euler sequence will be shown. \item ``{\tt Verbose2}'': Like ``Verbose1'' with more details. \item ``{\tt Verbose3}'': All long exact sequences coming from the Koszul sequence will be shown. \item ``{\tt Verbose4}'': All long exact sequences coming from the Euler and the Koszul sequence will be shown. \item ``{\tt Verbose5}'': Like ``Verbose4'' with more details. \item ``{\tt Verbose6}'': This Verbose function only works for the equivariant cohomology calculation and shows you the representatives of the cohomology of the corresponding line bundle. It also prints how the $\mathbb Z^n$-action acts on them and which of the Laurent monomials are invariant. \end{itemize} There is one more optional input parameter in which you can let the program know if you are using {\it Mathematica~7} in a terminal or with the graphical interface. Chose {\tt ''Terminal``} for {[Optional: Input Type]} if you are using the terminal interface. \clearpage %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section*{Proper citation} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% If you find the {\cohomCalg} package useful to your project please have a look into the file \emph{Proper Citation.txt} located in the package archive's main directory. There you find a ready-to-use BibTeX entry for {\cohomCalg} \cite{cohomCalg:Implementation}. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section*{Acknowledgements} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% We would like to thank Jim Halverson for bug reporting and general feedback as well as Fabian Rühle for pointing out compatibility issues with Mathematica~8. Furthermore, we are grateful to Prof.~Alois Kabelschacht for his help in the distribution of this project. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%% %%%%%%%%%%%%%%%%%%% %%%%%%%%%%%% BIBLIOGRAPHY %%%%%%%%%%%%%%%%%%% %%%%%%%%%%%% %%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\clearpage \bibliography{manual} \bibliographystyle{utphys} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \vfill \noindent \footnotesize {\it Mathematica} is a registered trademark of Wolfram Research, Inc. All rights reserved. {\it Windows} is a registered trademark of Microsoft Corporation in the United States and other countries. The lightbulb image used in the application logo was made by \href{http://dragonartz.wordpress.com/}{DragonArt} and is used under the \href{http://creativecommons.org/licenses/by-nc-sa/3.0/}{Creative Commons Attribution-Noncommercial-Share Alike 3.0} license. \end{document}cohomCalg-0.32/manual/latex_source/utphys.bst000066400000000000000000000621421322050713700213570ustar00rootroot00000000000000% UT Physics bibliographic style, ver. 2.7. Based on: % %X IEEE Transactions bibliography style (29-Jan-88 version) %X numeric labels, order-of-reference, IEEE abbreviations, %X quotes around article titles, commas separate all fields %X except after book titles and before "notes". Otherwise, %X much like the "plain" family, from which this is adapted. %X %X History %X 9/30/85 (HWT) Original version, by Howard Trickey. %X 1/29/88 (OP&HWT) Updated for BibTeX version 0.99a, Oren Patashnik; %X THIS `ieeetr' VERSION DOES NOT WORK WITH BIBTEX 0.98i. % % Modifications: 1) added hypertex support and "archive", "eprint" % and "url" fields. % 2) parentheses around dates, and no "pp." for article entries % 3) "publisher, address" instead of "address: publisher" % 4) added "report" field for article entries. % 5) particle physics-oriented abbreviations, rather than ieee. % 6) added "collaboration" field, as per % Jonathan Flynn' suggestion. SPIRES now supports this field. % 7) Improved output of Proceedings entries % % Modified by Jacques Distler, 2/11 % History: ver 1.0 9/96 % ver 1.1 10/96 - added "collaboration" field % ver 1.2 7/97 - added a "\providecommand{\href}[2]{#2}" % to handle case where \href is not defined % ver 1.3 12/97 - fixed lousy-looking proceedings output. % ver 1.4 1/98 - fixed format.number, address in % proceedings entries % ver 1.5 3/99 - added (nonprinting) CITATION field for % SLAC internal use % ver 1.6 4/99 - Fix to ensure %%CITATION output not broken % across lines. Added new.sentence to ensure % previous output properly terminated. % (Moral: test before you release.) % ver 1.7 10/99 - "et.~al." should be "et al." Morons! % ver 1.8 11/99 - Changed the Web URL to the more portable % arxiv.org. The "archive" field functions as % a true base-URL. This is NOT A % BACKWARDS-COMPATIBLE change! % ver 1.8a 12/99 - MACROs for arXiv and cogprints % BaseURL's defined. % ver 1.9 6/05 - eprint support for other entry types % ver 2.0 4/08 - support "new-style" eprint identifiers % ver 2.1 4/08 - support for "url" field % ver 2.2 4/08 - support for "doi" field % ver 2.3 8/09 - fix month formatting % ver 2.4 7/10 - remove some deprecated font-constructws. % fix journal number formatting. % ver 2.5 9/10 - Internationalization and some more journal % MACROs (thanks to Mateus Araujo) % ver 2.6 2/11 - Yipes! Fix capitalization of titles, spooged % in previous version. (Reported by Ling Weak) % ver 2.7 8/11 - Fix "et~al." in format.crossref.editor, too. % (Reported by Blake Stacey) % % HyperTeX Wizardry: % % The following are equivalent: % archive = arXiv % eprint = "hep-th/9605023" % and % eprint = "hep-th/9605023" % both produce % % \href{http://arxiv.org/abs/hep-th/9605023}{{\ttfamily hep-th/9605023}} % % in the bibliographic output at the appropriate point. More generally, % if the archive field is present, we produce a URL of the form % "archive/eprint" as the first argument of the \href. If absent, the base % URL defaults to "http://arxiv.org/abs" % If you are using a hypertex macropackage, like hyperref.sty, this command % will create a link to the eprint at Los Alamos (or wherever). % % "New-style" arXiv identifiers are also supported. % % archivePrefix = "arXiv", % eprint = "0707.3168", % primaryClass = "hep-th", % % produces % % \href{http://arxiv.org/abs/0707.3168}{{\ttfamily arXiv:0707.3168 [hep-th]}} % % Another (non-arXiv) example: % % archive = "http://cogprints.org", % eprint = "5542", % archivePrefix = "Cogprints", % % produces % % \href{http://cogprints.org/5542}{{\ttfamily Cogprints:5542}} % % If a % % doi = "10.xxxx" % % field is present, then the journal reference becomes a % clickable hyperlink to the online journal version of the paper. % % The bibtex output produced by SPIRES, while far from perfect, is pretty % suitable for use with this style. Indeed, this style was designed with % SPIRES in mind. FUNCTION {string.and} {" and "} FUNCTION {string.editors} {", eds."} FUNCTION {string.editor} {", ed."} FUNCTION {string.edition} {"~ed."} FUNCTION {string.volume} {"vol.~"} FUNCTION {string.capsvolume} {"Vol.~"} FUNCTION {string.of} {" of "} FUNCTION {string.number} {"no.~"} FUNCTION {string.capsnumber} {"No.~"} FUNCTION {string.in} {"in "} FUNCTION {string.spacein} {" in "} FUNCTION {string.capsin} {"In "} FUNCTION {string.multipages} {"pp.~"} FUNCTION {string.pages} {"p.~"} FUNCTION {string.chapter} {"ch.~"} FUNCTION {string.techrep} {"Tech. Rep."} FUNCTION {string.mastersthesis} {"Master's thesis"} FUNCTION {string.phdthesis} {"PhD thesis"} MACRO {jan} {"Jan."} MACRO {feb} {"Feb."} MACRO {mar} {"Mar."} MACRO {apr} {"Apr."} MACRO {may} {"May"} MACRO {jun} {"June"} MACRO {jul} {"July"} MACRO {aug} {"Aug."} MACRO {sep} {"Sept."} MACRO {oct} {"Oct."} MACRO {nov} {"Nov."} MACRO {dec} {"Dec."} MACRO {am} {"Acta Math."} MACRO {amj} {"Am. J. Phys."} MACRO {ap} {"Ann. Phys."} MACRO {cmp} {"Comm. Math. Phys."} MACRO {ijmp} {"Int. Jour. Mod. Phys."} MACRO {mpl} {"Mod. Phys. Lett."} MACRO {njp} {"New J. Phys"} MACRO {nup} {"Nucl. Phys."} MACRO {pl} {"Phys. Lett."} MACRO {pla} {"Phys. Lett. A"} MACRO {pr} {"Phys. Rev."} MACRO {pra} {"Phys. Rev. A"} MACRO {prl} {"Phys. Rev. Lett."} MACRO {repmp} {"Rep. Math. Phys"} MACRO {rmp} {"Rev. Mod. Phys."} MACRO {arXiv} {"http://arxiv.org/abs"} MACRO {cogprints} {"http://cogprints.org"} MACRO {pubmed} {"http://www.ncbi.nlm.nih.gov/pubmed"} ENTRY { address author booktitle chapter edition editor howpublished institution journal key month note number organization pages publisher school series title type volume year archive eprint report collaboration SLACcitation archivePrefix primaryClass url doi } {} { label } INTEGERS { output.state before.all mid.sentence after.quote after.sentence after.quoted.block after.block } FUNCTION {init.state.consts} { #0 'before.all := #1 'mid.sentence := #2 'after.quote := #3 'after.sentence := #4 'after.quoted.block := #5 'after.block := } STRINGS { s t } FUNCTION {output.nonnull} { 's := output.state mid.sentence = { ", " * write$ } { output.state after.quote = { " " * write$ } { output.state after.block = { add.period$ write$ newline$ "\newblock " write$ } { output.state before.all = 'write$ { output.state after.quoted.block = { write$ newline$ "\newblock " write$ } { add.period$ " " * write$ } if$ } if$ } if$ } if$ mid.sentence 'output.state := } if$ s } FUNCTION {output} { duplicate$ empty$ 'pop$ 'output.nonnull if$ } FUNCTION {output.check} { 't := duplicate$ empty$ { pop$ "empty " t * " in " * cite$ * warning$ } 'output.nonnull if$ } FUNCTION {output.bibitem} { newline$ "\bibitem{" write$ cite$ write$ "}" write$ newline$ "" before.all 'output.state := } FUNCTION {blank.sep} { after.quote 'output.state := } FUNCTION {fin.entry} { output.state after.quoted.block = 'skip$ 'add.period$ if$ write$ newline$ } FUNCTION {new.block} { output.state before.all = 'skip$ { output.state after.quote = { after.quoted.block 'output.state := } { after.block 'output.state := } if$ } if$ } FUNCTION {new.sentence} { output.state after.block = 'skip$ { output.state before.all = 'skip$ { after.sentence 'output.state := } if$ } if$ } FUNCTION {not} { { #0 } { #1 } if$ } FUNCTION {and} { 'skip$ { pop$ #0 } if$ } FUNCTION {or} { { pop$ #1 } 'skip$ if$ } FUNCTION {new.block.checka} { empty$ 'skip$ 'new.block if$ } FUNCTION {new.block.checkb} { empty$ swap$ empty$ and 'skip$ 'new.block if$ } FUNCTION {new.sentence.checka} { empty$ 'skip$ 'new.sentence if$ } FUNCTION {field.or.null} { duplicate$ empty$ { pop$ "" } 'skip$ if$ } FUNCTION {emphasize} { duplicate$ empty$ { pop$ "" } { "{\em " swap$ * "}" * } if$ } FUNCTION {capitalize} { "u" change.case$ "t" change.case$ } INTEGERS { nameptr namesleft numnames } FUNCTION {format.names} { 's := #1 'nameptr := s num.names$ 'numnames := numnames 'namesleft := { namesleft #0 > } { s nameptr "{f.~}{vv~}{ll}{, jj}" format.name$ 't := nameptr #1 > { namesleft #1 > { ", " * t * } { numnames #2 > { "," * } 'skip$ if$ t "others" = { " {\em et~al.}" * } { string.and * t * } if$ } if$ } 't if$ nameptr #1 + 'nameptr := namesleft #1 - 'namesleft := } while$ } FUNCTION {format.authors} { author empty$ { "" } { author format.names } if$ } FUNCTION {format.archive} { archivePrefix empty$ { "" } { archivePrefix ":" *} if$ } FUNCTION {format.primaryClass} { primaryClass empty$ { "" } { " [" primaryClass * "]" *} if$ } FUNCTION {format.eprint} { eprint empty$ { ""} { archive empty$ {"\href{http://arxiv.org/abs/" eprint * "}" * "{{\ttfamily " * format.archive * eprint * format.primaryClass * "}}" *} {"\href{" archive * "/" * eprint * "}" * "{{\ttfamily " * format.archive * eprint * format.primaryClass * "}}" *} if$ } if$ } FUNCTION {format.url} { url empty$ { "" } {"\url{" url * "}" *} if$ } FUNCTION {add.doi} { duplicate$ empty$ { skip$ } { doi empty$ {} {"\href{http://dx.doi.org/" doi * "}{" * swap$ * "}" *} if$ } if$ } FUNCTION {format.report} { report empty$ { ""} { report} if$ } FUNCTION {format.howpublished} { howpublished empty$ { "" } { howpublished capitalize } if$ } FUNCTION {format.editors} { editor empty$ { "" } { editor format.names editor num.names$ #1 > { string.editors * } { string.editor * } if$ } if$ } FUNCTION {format.title} { title empty$ { "" } { "``" title "t" change.case$ * ",''" * } if$ } FUNCTION {format.title.p} { title empty$ { "" } { "``" title "t" change.case$ * ".''" * } if$ } FUNCTION {n.dashify} { 't := "" { t empty$ not } { t #1 #1 substring$ "-" = { t #1 #2 substring$ "--" = not { "--" * t #2 global.max$ substring$ 't := } { { t #1 #1 substring$ "-" = } { "-" * t #2 global.max$ substring$ 't := } while$ } if$ } { t #1 #1 substring$ * t #2 global.max$ substring$ 't := } if$ } while$ } FUNCTION {format.date} { year empty$ { month empty$ { "" } { "there's a month but no year in " cite$ * warning$ month } if$ } { month empty$ 'year { month capitalize ", " * year * } if$ } if$ } FUNCTION {format.date.paren} { year empty$ { month empty$ { "" } { "there's a month but no year in " cite$ * warning$ month } if$ } { month empty$ {"(" year * ") " *} {"(" month capitalize * ", " * year * ") " *} if$ } if$ } FUNCTION {format.collaboration} { collaboration empty$ { "" } { "{\bfseries " collaboration * "} " * "Collaboration" * } if$ } FUNCTION {format.SLACcitation} { SLACcitation empty$ {""} { newline$ SLACcitation output "" newline$ } if$ } FUNCTION {format.btitle} { title emphasize } FUNCTION {tie.or.space.connect} { duplicate$ text.length$ #3 < { "~" } { " " } if$ swap$ * * } FUNCTION {either.or.check} { empty$ 'pop$ { "can't use both " swap$ * " fields in " * cite$ * warning$ } if$ } FUNCTION {format.bvolume} { volume empty$ { "" } { string.volume volume * series empty$ 'skip$ { string.of * series emphasize * } if$ "volume and number" number either.or.check } if$ } FUNCTION {format.number.series} { volume empty$ { number empty$ { series field.or.null } { output.state mid.sentence = { string.number } { string.capsnumber } if$ number * series empty$ { "there's a number but no series in " cite$ * warning$ } { string.spacein * series * } if$ } if$ } { "" } if$ } FUNCTION {format.edition} { edition empty$ { "" } { edition "l" change.case$ string.edition * } if$ } INTEGERS { multiresult } FUNCTION {multi.page.check} { 't := #0 'multiresult := { multiresult not t empty$ not and } { t #1 #1 substring$ duplicate$ "-" = swap$ duplicate$ "," = swap$ "+" = or or { #1 'multiresult := } { t #2 global.max$ substring$ 't := } if$ } while$ multiresult } FUNCTION {format.pages} { pages empty$ { "" } { pages multi.page.check { string.multipages pages n.dashify * } { string.pages pages * } if$ } if$ } FUNCTION {format.pages.nopp} { pages empty$ { "empty pages in " cite$ * warning$ "" } { pages multi.page.check { pages n.dashify } { pages } if$ } if$ } FUNCTION {format.volume} { volume empty$ { "" } { "{\bfseries " volume * "} " * } if$ } FUNCTION {format.number} { number empty$ { "" } { "no.~" number * ", " *} if$ } FUNCTION {format.chapter.pages} { chapter empty$ 'format.pages { type empty$ { string.chapter chapter * } { type "l" change.case$ chapter tie.or.space.connect } if$ pages empty$ 'skip$ { ", " * format.pages * } if$ } if$ } FUNCTION {format.in.ed.booktitle} { booktitle empty$ { "" } { string.in booktitle emphasize * editor empty$ 'skip$ { ", " * format.editors * } if$ } if$ } FUNCTION {format.thesis.type} { type empty$ 'skip$ { pop$ output.state after.block = { type "t" change.case$ } { type "l" change.case$ } if$ } if$ } FUNCTION {empty.misc.check} { author empty$ title empty$ howpublished empty$ month empty$ year empty$ note empty$ and and and and and { "all relevant fields are empty in " cite$ * warning$ } 'skip$ if$ } FUNCTION {format.tr.number} { type empty$ { string.techrep } 'type if$ number empty$ { "l" change.case$ } { number tie.or.space.connect } if$ } FUNCTION {format.paddress} { address empty$ { "" } { "(" address * ")" * } if$ } FUNCTION {format.article.crossref} { key empty$ { journal empty$ { "need key or journal for " cite$ * " to crossref " * crossref * warning$ "" } { string.in "{\em " * journal * "\/}" * } if$ } { string.in key * } if$ " \cite{" * crossref * "}" * } FUNCTION {format.crossref.editor} { editor #1 "{vv~}{ll}" format.name$ editor num.names$ duplicate$ #2 > { pop$ " {\em et~al.}" * } { #2 < 'skip$ { editor #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" = { " {\em et~al.}" * } { string.and * editor #2 "{vv~}{ll}" format.name$ * } if$ } if$ } if$ } FUNCTION {format.book.crossref} { volume empty$ { "empty volume in " cite$ * "'s crossref of " * crossref * warning$ string.capsin } { string.capsvolume volume * string.of * } if$ editor empty$ editor field.or.null author field.or.null = or { key empty$ { series empty$ { "need editor, key, or series for " cite$ * " to crossref " * crossref * warning$ "" * } { "{\em " * series * "\/}" * } if$ } { key * } if$ } { format.crossref.editor * } if$ " \cite{" * crossref * "}" * } FUNCTION {format.incoll.inproc.crossref} { editor empty$ editor field.or.null author field.or.null = or { key empty$ { booktitle empty$ { "need editor, key, or booktitle for " cite$ * " to crossref " * crossref * warning$ "" } { string.in "{\em " * booktitle * "\/}" * } if$ } { string.in key * } if$ } { string.in format.crossref.editor * } if$ " \cite{" * crossref * "}" * } FUNCTION {format.journal} { journal missing$ { "" } {journal emphasize " " * format.volume * format.number * format.date.paren * format.pages.nopp * } if$ } FUNCTION {article} { output.bibitem format.collaboration output format.authors "author" output.check format.title "title" output.check blank.sep crossref missing$ { journal missing$ {} { format.journal add.doi "journal" output.check} if$ report missing$ {format.eprint output} {blank.sep format.report output format.eprint output} if$ } { format.article.crossref output.nonnull format.pages output format.eprint output } if$ new.sentence format.url output new.sentence note output new.sentence format.SLACcitation output fin.entry } FUNCTION {book} { output.bibitem format.collaboration output author empty$ { format.editors "author and editor" output.check } { format.authors output.nonnull crossref missing$ { "author and editor" editor either.or.check } 'skip$ if$ } if$ format.btitle add.doi "title" output.check crossref missing$ { format.bvolume output new.block format.number.series output new.sentence publisher "publisher" output.check address output } { new.block format.book.crossref output.nonnull } if$ format.edition output format.date "year" output.check new.block format.eprint output new.block format.url output new.block note output new.sentence format.SLACcitation output fin.entry } FUNCTION {booklet} { output.bibitem format.collaboration output format.authors output title empty$ { "empty title in " cite$ * warning$ howpublished new.sentence.checka } { howpublished empty$ not address empty$ month empty$ year empty$ and and or { format.title.p output.nonnull } { format.title output.nonnull } if$ blank.sep } if$ format.howpublished output address output format.date output new.block format.eprint output new.block format.url output new.block note output new.sentence format.SLACcitation output fin.entry } FUNCTION {inbook} { output.bibitem format.collaboration output author empty$ { format.editors "author and editor" output.check } { format.authors output.nonnull crossref missing$ { "author and editor" editor either.or.check } 'skip$ if$ } if$ format.btitle "title" output.check crossref missing$ { format.bvolume output format.chapter.pages add.doi "chapter and pages" output.check new.block format.number.series output new.block publisher "publisher" output.check address output } { format.chapter.pages add.doi "chapter and pages" output.check new.block format.book.crossref output.nonnull } if$ format.edition output format.date "year" output.check new.block format.eprint output new.block format.url output new.block note output new.sentence format.SLACcitation output fin.entry } FUNCTION {incollection} { output.bibitem format.collaboration output format.authors "author" output.check format.title add.doi "title" output.check blank.sep crossref missing$ { format.in.ed.booktitle "booktitle" output.check format.bvolume output format.number.series output format.chapter.pages output new.block publisher "publisher" output.check address output format.edition output format.date "year" output.check } { format.incoll.inproc.crossref output.nonnull format.chapter.pages output } if$ new.block format.eprint output new.block format.url output new.block note output new.sentence format.SLACcitation output fin.entry } FUNCTION {inproceedings} { output.bibitem format.collaboration output format.authors "author" output.check format.title add.doi "title" output.check blank.sep crossref missing$ { format.in.ed.booktitle "booktitle" output.check format.bvolume output format.number.series output format.pages output organization output new.block publisher output address output format.date "year" output.check } { format.incoll.inproc.crossref output.nonnull format.pages output } if$ new.block format.eprint output new.block format.url output new.block note output new.sentence format.SLACcitation output fin.entry } FUNCTION {conference} { inproceedings } FUNCTION {manual} { output.bibitem format.collaboration output author empty$ { organization empty$ 'skip$ { organization output.nonnull address output } if$ } { format.authors output.nonnull } if$ format.btitle "title" output.check author empty$ { organization empty$ { address new.block.checka address output } 'skip$ if$ } { organization address new.block.checkb organization output address output } if$ format.edition output format.date output new.block format.eprint output new.block format.url output new.block note output fin.entry } FUNCTION {mastersthesis} { output.bibitem format.authors "author" output.check format.title add.doi "title" output.check blank.sep string.mastersthesis format.thesis.type output.nonnull school "school" output.check address output format.date "year" output.check new.block format.url output new.block note output fin.entry } FUNCTION {misc} { output.bibitem format.collaboration output format.authors output title empty$ { howpublished new.sentence.checka } { howpublished empty$ not month empty$ year empty$ and or { format.title.p output.nonnull } { format.title output.nonnull } if$ blank.sep } if$ format.howpublished output format.date output new.block format.url output new.sentence note output new.sentence fin.entry empty.misc.check } FUNCTION {phdthesis} { output.bibitem format.authors "author" output.check format.btitle add.doi "title" output.check new.block string.phdthesis format.thesis.type output.nonnull school "school" output.check address output format.date "year" output.check new.block format.eprint output new.block format.url output new.block note output new.sentence format.SLACcitation output fin.entry } FUNCTION {proceedings} { output.bibitem editor empty$ { organization output } { format.editors output.nonnull } if$ format.btitle add.doi "title" output.check format.bvolume output format.number.series output editor empty$ 'skip$ { organization output } if$ new.block publisher output address output format.date "year" output.check new.block format.eprint output new.block format.url output new.block note output new.sentence format.SLACcitation output fin.entry } FUNCTION {techreport} { output.bibitem format.collaboration output format.authors "author" output.check format.title add.doi "title" output.check blank.sep format.tr.number output.nonnull institution "institution" output.check address output format.date "year" output.check new.block format.eprint output new.block format.url output new.block note output fin.entry } FUNCTION {unpublished} { output.bibitem format.collaboration output format.authors "author" output.check format.title.p "title" output.check blank.sep note "note" output.check format.date output new.sentence format.SLACcitation output fin.entry } FUNCTION {default.type} { misc } READ STRINGS { longest.label } INTEGERS { number.label longest.label.width } FUNCTION {initialize.longest.label} { "" 'longest.label := #1 'number.label := #0 'longest.label.width := } FUNCTION {longest.label.pass} { number.label int.to.str$ 'label := number.label #1 + 'number.label := label width$ longest.label.width > { label 'longest.label := label width$ 'longest.label.width := } 'skip$ if$ } EXECUTE {initialize.longest.label} ITERATE {longest.label.pass} FUNCTION {begin.bib} { preamble$ empty$ 'skip$ { preamble$ write$ newline$ } if$ "\providecommand{\href}[2]{#2}" "\begingroup\raggedright\begin{thebibliography}{" * longest.label * "}" * write$ newline$ } EXECUTE {begin.bib} EXECUTE {init.state.consts} ITERATE {call.type$} FUNCTION {end.bib} { newline$ "\end{thebibliography}\endgroup" write$ newline$ } EXECUTE {end.bib} 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cohomCalg-0.32/old/cohomcalg-script-v004/cohom-script.txt000066400000000000000000000362001322050713700232060ustar00rootroot00000000000000 (*-------------------------------------------------- Routines --------------------------------------------------*) (*Routine generating the remnant sequence for a given element Q. It returns also the positions of the element in the Q-list*) sequenceneu[Qtemp_]:=Module[{i,positionsliste, tmpsequence}, tmpsequence = Array[0^#&,maxcdegree-mincdegree+1]; positionsliste=Position[fullQlist,Qtemp]; For[i=1,i<= Length[positionsliste],i++, tmpsequence[[fullcdegreelist[[positionsliste[[i]][[1]]]]-mincdegree+1]]++ ]; Return[{tmpsequence,positionsliste}]; ]; (*Routine that tests wether the given complex is exact or not and returns true or false as well as a possible candidate to fix the complex*) isexact[complex_]:=Module[{i,kern,exakt,n,fullcomplex}, fullcomplex=complex; n=Length[fullcomplex]; exakt=1; kern=fullcomplex[[n]]; For[i=1,i= altersum, tempsequence=sequence; tempsequence[[i]]=tempsequence[[i]]-altersum; If[isexact[tempsequence][[3]], AppendTo[result,{h,i-(1-startdim),altersum}]; ]; ]; ]; Return[result] ]; (*Subroutine the converts a set of coordinates into their positions in the coordinate-list, e.g. {u1,u2} -> {1,2}*) ConvertDenominatiorElement[element_]:=Module[{i,convertedelement}, convertedelement={}; For[i=1,i<= Length[element],i++, AppendTo[convertedelement,Position[coordinates,element[[i]]][[1]][[1]] ]; ]; Return[convertedelement]; ]; (*Subroutine: Generates the expression u1>=0 && u2>=0 && u3>=0 && ... from a given set of coordinates {u1,u2,u3,...}*) ListElementsLargerEqZero[list_]:=Module[{i,temp}, If[list!= {},temp=list[[1]]>= 0,Return[{}]]; For[i=2,i<=Length[list],i++, temp=temp && list[[i]]>= 0 ]; Return[temp] ]; (*Main counting routing: It generates the matrix m, the constant vector b and solves the linear equations m.x=b for non negative integers*) RationomsOf[DenominatorElement_]:=Module[{i,j,b,m,ConvertedElement}, ConvertedElement=ConvertDenominatiorElement[DenominatorElement]; m=equrel; For[i=1,i<=Length[equrel],i++, For[j=1,j<=Length[equrel[[1]]],j++, If[MemberQ[ConvertedElement,j], m[[i]][[j]]=-equrel[[i]][[j]], (*else*) m[[i]][[j]]=equrel[[i]][[j]] ]; ]; ]; b=Array[-Sum[m[[#]][[j]],{j,ConvertedElement}]&,Length[Qcharges]]+Qcharges; Return[Length[Reduce[m.coordinates==b&&ListElementsLargerEqZero[coordinates],coordinates,Integers]||{"dummy"}]-1] (*Here the equation is solved. The "dummy" has to be added and removed from the number of solutions in order to avoid that only one solution exists*) ]; (*Converts a list into a string*) ListToString[listinput_]:=Module[{a,i}, a=""; For[i=1,i<=Length[listinput],i++, a=StringJoin[a,ToString[listinput[[i]]] ] ]; Return[a]; ]; (*------------------------------------------------ Main routines ------------------------------------------------*) (*------------------------------------------------ Main routines ------------------------------------------------*)(*------------------------------------------------ Main routines ------------------------------------------------*)(*------------------------------------------------ Main routines ------------------------------------------------*) (*Main routine 1: Generates first the List of all possible Q's and the corresponding c-degrees and afterwards a list of all secondary sequences that may appear*) GenerateSecondarySequences[varietyin_]:=Module[{i,j,ii,kk}, coordinates=varietyin[[1]]; SR=varietyin[[2]]; equivalencerelations=varietyin[[3]]; dim=Length[coordinates]-Length[equivalencerelations[[1]]]; numberofvertices=Length[coordinates]; equrel=Transpose[equivalencerelations]; (*Generate the lists of Q's and c-degrees*) Print[DateList[]," ---- Part 1: Creating Q and c-degree lists"]; d=DateList[]; fullQlist=Map[{Union[Flatten[#]],Length[Union[Flatten[#]]]-Length[#]}&,Subsets[SR]]; fullcdegreelist=Delete[fullQlist,{1}][[All,2]]; fullQlist=Delete[fullQlist,{1}] [[All,1,All]]; dneu=DateList[]; Print["Listing done within ",AbsoluteTime[dneu]-AbsoluteTime[d]," seconds"]; maxsequencesize =(Length[SR]-2)+(numberofvertices-1)+1 ; mincdegree=2-Length[SR]; maxcdegree=numberofvertices-1; (*Generate the list of possible secondary sequences for all various elements in the Q-list*) Print[DateList[]," ---- Part 2: Generating remnant sequences"]; d=DateList[]; sortierttupel={}; report=19; For[i=1,i<= 2^Length[coordinates],i++, If[fullQlist!={}, report++; tempQ=fullQlist[[Length[fullQlist]]]; If[!MemberQ[sortierttupel,tempQ,3], (*Tests wether the element is not yet in the list*) tempsequence=sequenceneu[tempQ][[1]]; tmppositionslist=sequenceneu[tempQ][[2]]; If[MemberQ[sortierttupel,tempsequence,2], (*Tests wether the sequence already appeared earlier *) AppendTo[sortierttupel[[Position[sortierttupel,tempsequence][[1]][[1]]]][[1]],tempQ] (*else*),AppendTo[sortierttupel,{{tempQ},tempsequence}] ]; fullQlist=Delete[fullQlist,tmppositionslist]; fullcdegreelist=Delete[fullcdegreelist,tmppositionslist]; If[report==20, NotebookDelete[temp]; dneu=DateList[]; a=ListToString[{2^Length[SR]-Length[fullQlist]-1," elements from Q-list done within ",AbsoluteTime[dneu]-AbsoluteTime[d]," seconds"}]; report=0; temp=PrintTemporary[a]; ]; ]; ]; ]; sortierttupelsave=sortierttupel; dneu=DateList[]; Print["Generating done within: ",AbsoluteTime[dneu]-AbsoluteTime[d]," seconds"]; ];(*End of routine*) (*Subroutine of main routine 2: Tests which secondary sequences and their corresponding cohomologies are contributing to the cohomology of the line bundle in question. It also determines via subroutines, how many rationom contribute *) SubLinebundleCohomologyOf[Qchargesin_]:=Module[{i,j,ii,kk}, Qcharges=Qchargesin; sortierttupel=sortierttupelsave; For[ii=1,ii<= Length[sortierttupel],ii++, (*Sortierttupel has the following list structure {{Denominator element},{sequence}}*) AppendTo[sortierttupel[[ii]],{}]; AppendTo[sortierttupel[[ii]],0]; If[(*1==2&&*)!isexact[sortierttupel[[ii,2]]][[3]], For[kk=1,kk<=Length[sortierttupel[[ii]][[1]]],kk++, temprationomsOf=RationomsOf[sortierttupel[[ii]][[1]][[kk]]]; AppendTo[sortierttupel[[ii]][[3]],temprationomsOf]; sortierttupel[[ii]][[4]]=sortierttupel[[ii]][[4]]+temprationomsOf; ]; ]; ]; ];(*End of routine*) (*Main routine 2: Opens the subroutine above and puts the results together *) LinebundleCohomologyOf[Qchargesin_]:=Module[{i,j,ii,kk,Resultlistofcohoms,Resultlistofcohomsdual,PossibleResults,PossibleResultsDual,resultvectors,resultvectorsFromDual,output}, Qchargesstring=""; For[i=1,i<= Length[Qchargesin],i++, If[i!= 1, Qchargesstring=StringJoin[Qchargesstring, ","] ]; Qchargesstring=StringJoin[Qchargesstring,ToString[Qchargesin[[i]]]] ]; CanonicalDivisor=-Sum[equivalencerelations[[i]],{i,1,Length[equivalencerelations]}]; (*Calculate Cohomologies of the divisor*) tmp=PrintTemporary["."]; SubLinebundleCohomologyOf[Qchargesin]; (*-------------------------------------- Collecting the Results ------------------------------------------------*) Resultlistofcohoms={}; (*--------------------- The case of the empty set in the denominator is treated separately ---------------------*) leer={}; If[RationomsOf[leer]!=0, AppendTo[Resultlistofcohoms,{{h,0,RationomsOf[leer]}}]; ]; (*-------------------------------------------- Case denominator != {} -------------------------------------------*) For[i=1,i<= Length[sortierttupel],i++,e If[sortierttupel[[i]][[4]]!=0 && !isexact[sortierttupel[[i]][[2]]][[3]], cohomresult=Map[{h,#[[2]] , #[[3]]*sortierttupel[[i]][[4]]}&,CohomsOf[sortierttupel[[i]][[2]],mincdegree]]; AppendTo[Resultlistofcohoms,cohomresult] ]; ]; output=1; serredual=0; unique=1; resultvector=Array[0*#&,dim+1]; (*Check results for uniqueness and print them in case that they unique*) For[i=1,i<= Length[Resultlistofcohoms],i++, If[Length[Resultlistofcohoms[[i]]]!= 1,unique=0] ]; If[unique==1, For[i=1,i<= Length[Resultlistofcohoms],i++, resultvector[[Resultlistofcohoms[[i,1,2]]+1]]=resultvector[[Resultlistofcohoms[[i,1,2]]+1]]+Resultlistofcohoms[[i,1,3]] ]; Print[Superscript["h","*"],"(O(",Qchargesstring,")) = ",resultvector]; output=0, serredual=1 (*more fancy output for the graphical interface of mathematica*) (*Print[Superscript["h","\[FilledSmallCircle]"],"(\[ScriptCapitalO](",Qchargesstring,")) = ",resultvector]; output=0, serredual=1*) ]; unique=1; (*Calculate Cohomologies of the Serre dual divisor*) If[serredual ==1, NotebookDelete[tmp]; tmp=PrintTemporary[".."]; SubLinebundleCohomologyOf[CanonicalDivisor-Qchargesin]; (*-------------------------------------------- Printing the Results --------------------------------------------*) Resultlistofcohomsdual={}; (*------------------- The case of the empty set in the denominator is treated separately -----------------------*) leer={}; If[RationomsOf[leer]!=0, AppendTo[Resultlistofcohomsdual,{{h,0,RationomsOf[leer]}}]; ]; (*-------------------------------------------- Case denominator != {} -------------------------------------------*) For[i=1,i<= Length[sortierttupel],i++, If[sortierttupel[[i]][[4]]!=0 && !isexact[sortierttupel[[i]][[2]]][[3]], cohomresult=Map[{h,#[[2]] , #[[3]]*sortierttupel[[i]][[4]]}&,CohomsOf[sortierttupel[[i]][[2]],mincdegree]]; AppendTo[Resultlistofcohomsdual,cohomresult]; ]; ]; (*Check the Serre dual divisor for uniqueness. If it is, print the corresponding data for the divisor in question by using Serre duality*) For[i=1,i<= Length[Resultlistofcohomsdual],i++, If[Length[Resultlistofcohomsdual[[i]]]!= 1,unique=0] ]; If[unique==1, For[i=1,i<= Length[Resultlistofcohomsdual],i++, resultvector[[dim- Resultlistofcohomsdual[[i,1,2]]+1]]=resultvector[[dim-Resultlistofcohomsdual[[i,1,2]]+1]]+Resultlistofcohomsdual[[i,1,3]] ]; Print[Superscript["h","*"],"(O(",Qchargesstring,")) = ",resultvector]; output=0 (*more fancy output for the graphical interface of mathematica*) (*Print[Superscript["h","\[FilledSmallCircle]"],"(\[ScriptCapitalO](",Qchargesstring,")) = ",resultvector]; output=0*) ]; ]; (*If also the Serre dual is not trivially unique we need to consider all possible combinations and cancel them out*) (*First generate a list of all possible resulting vectors h^*(O (D)) *) resultvectors={}; resultvectorsFromDual={}; If[unique==0, NotebookDelete[tmp]; tmp=PrintTemporary["..."]; PossibleResults=Tuples[Resultlistofcohoms]; PossibleResultsDual=Tuples[Resultlistofcohomsdual]; For[j=1,j<= Length[PossibleResults],j++, tmpesultvector=Array[0*#&,dim+1]; For[i=1,i<= Length[PossibleResults[[j]]],i++, tmpesultvector[[ PossibleResults[[j]][[i,2]]+1]]=tmpesultvector[[PossibleResults[[j]][[i,2]]+1]]+PossibleResults[[j]][[i,3]] ]; AppendTo[resultvectors,tmpesultvector]; ]; For[j=1,j<= Length[PossibleResultsDual],j++, tmpesultvector=Array[0*#&,dim+1]; For[i=1,i<= Length[PossibleResultsDual[[j]]],i++, tmpesultvector[[dim- PossibleResultsDual[[j]][[i,2]]+1]]=tmpesultvector[[dim-PossibleResultsDual[[j]][[i,2]]+1]]+PossibleResultsDual[[j]][[i,3]] ]; AppendTo[resultvectorsFromDual,tmpesultvector]; ]; If[Length[Intersection[resultvectors,resultvectorsFromDual]]== 1, Print[Superscript["h","*"],"(O(",Qchargesstring,")) = ",Flatten[Intersection[resultvectors,resultvectorsFromDual]]]; output=0 (*more fancy output for the graphical interface of mathematica*) (*Print[Superscript["h","\[FilledSmallCircle]"],"(\[ScriptCapitalO](",Qchargesstring,")) = ",Flatten[Intersection[resultvectors,resultvectorsFromDual]]]; output=0*) ]; ]; If[output==1, (*------------ Uniqueness could not be achieved: Printing the remaining poossible results ----------------------*) Print[Space]; Print["The algorithm does not return a unique solution. Possible solutions are:"]; Print[ Superscript["h","*"],"(O(",Qchargesstring,")) = ", Intersection[resultvectors,resultvectorsFromDual]]; (*more fancy output for the graphical interface of mathematica*) (*Print[ Superscript["h","\[FilledSmallCircle]"],"(\[ScriptCapitalO](",Qchargesstring,")) = ", Intersection[resultvectors,resultvectorsFromDual]];*) ]; NotebookDelete[tmp]; ];(*End of routine*) (*------------------------------------------------ END OF PROGRAM --------------------------------------------------*) (*--------------------------------------------------- USER INPUT ---------------------------------------------------*) (*--------------------------------------------------- USER INPUT ---------------------------------------------------*)(*--------------------------------------------------- USER INPUT ---------------------------------------------------*)(*--------------------------------------------------- USER INPUT ---------------------------------------------------*) (*----------------------------------------------- Variety defining data ---------------------------------------------*) P1xP1={ (*Coordinates*){u1,u2,u3,u4}, (*Stanley Reisner*){{u1,u2},{u3,u4}}, (*Equivalence Relations*){{1,0},{1,0},{0,1},{0,1}} }; dP1={ (*Coordinates*){u1,u2,u3,u4}, (*Stanley Reisner*){{u1,u2},{u3,u4}}, (*Equivalence Relations*){{1,0},{1,0},{1,1},{0,1}} }; dP2={ (*Coordinates*){u1,u2,u3,u4,u5}, (*Stanley Reisner*){{u1,u2},{u1,u3},{u2,u5},{u3,u4},{u4,u5}}, (*Equivalence Relations*){{1,0,0},{1,0,1},{1,1,0},{0,1,0},{0,0,1}} }; dP3={ (*Coordinates*){u1,u2,u3,u4,u5,u6}, (*Stanley Reisner*){{u1,u2},{u1,u3},{u1,u6},{u2,u3},{u2,u5},{u3,u4},{u4,u5},{u4,u6},{u5,u6}}, (*Equivalence Relations*){{1,0,0,1},{1,0,1,0},{1,1,0,0},{0,1,0,0},{0,0,1,0},{0,0,0,1}} }; (*-------------------------------------------------- End definitions ------------------------------------------------*) (*------------------------------------------------ Start calculations -----------------------------------------------*) (*----------------------------------------- !!! Start this routine first !!! ----------------------------------------*) (*----------The routine 'GenerateSecondarySequences' needs to be started for each new variety once -----------------*) (*---------------------------------*) GenerateSecondarySequences[dP3]; (*---------------------------------*) (*------- Now one can compute the cohomology group dimensions of line bundles on the variety generated above -------*) (*---- The input of LinbundleCohomologyOf are the charges {Q_ 1,...,Q_r} of the line bundle one is interested in ----*) (* A dP3 example*) LinebundleCohomologyOf[{1,120,3,-33}]; (* (* Some more dP3 examples *) LinebundleCohomologyOf[{0,0,0,0}]; LinebundleCohomologyOf[{1,2,3,4}]; LinebundleCohomologyOf[{-9,3,6,-7}]; LinebundleCohomologyOf[{-5,-5,-5,-5}]; LinebundleCohomologyOf[{2,3,3,3}]; *) (*---------------------------------------------- Output results ---------------------------------------------------*) (*---------------------------------------------- Output results 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"winres.h" ///////////////////////////////////////////////////////////////////////////// #undef APSTUDIO_READONLY_SYMBOLS ///////////////////////////////////////////////////////////////////////////// // Neutral (Default) (unknown sub-lang: 0x8) resources #if !defined(AFX_RESOURCE_DLL) || defined(AFX_TARG_ZZZ) LANGUAGE LANG_NEUTRAL, 0x8 ///////////////////////////////////////////////////////////////////////////// // // Version // VS_VERSION_INFO VERSIONINFO FILEVERSION 0,3,2,0 PRODUCTVERSION 0,3,2,0 FILEFLAGSMASK 0x3fL #ifdef _DEBUG FILEFLAGS 0x1L #else FILEFLAGS 0x0L #endif FILEOS 0x40004L FILETYPE 0x1L FILESUBTYPE 0x0L BEGIN BLOCK "StringFileInfo" BEGIN BLOCK "000904b0" BEGIN VALUE "CompanyName", "Benjamin Jurke" VALUE "FileDescription", "Implementation of arXiv:1003.5217 algorithm" VALUE "FileVersion", "0.32" VALUE "InternalName", "cohomCalg.exe" VALUE "LegalCopyright", "Copyright (C) 2010-2017 Benjamin Jurke" VALUE "OriginalFilename", "cohomCalg.exe" VALUE "ProductName", "cohomCalg Core" VALUE "ProductVersion", "0.32" END END BLOCK "VarFileInfo" BEGIN VALUE "Translation", 0x9, 1200 END END #endif // Neutral (Default) (unknown sub-lang: 0x8) resources ///////////////////////////////////////////////////////////////////////////// ///////////////////////////////////////////////////////////////////////////// // English (United States) resources #if !defined(AFX_RESOURCE_DLL) || defined(AFX_TARG_ENU) LANGUAGE LANG_ENGLISH, SUBLANG_ENGLISH_US #ifdef APSTUDIO_INVOKED ///////////////////////////////////////////////////////////////////////////// // // TEXTINCLUDE // 1 TEXTINCLUDE BEGIN "resource.h\0" END 2 TEXTINCLUDE BEGIN "#include ""winres.h""\r\n" "\0" END 3 TEXTINCLUDE BEGIN "\r\n" "\0" END #endif // APSTUDIO_INVOKED ///////////////////////////////////////////////////////////////////////////// // // Icon // // Icon with lowest ID value placed first to ensure application icon // remains consistent on all systems. IDI_ICON ICON "..\\Lightbulb.ico" #endif // English (United States) resources ///////////////////////////////////////////////////////////////////////////// #ifndef APSTUDIO_INVOKED ///////////////////////////////////////////////////////////////////////////// // // Generated from the TEXTINCLUDE 3 resource. // ///////////////////////////////////////////////////////////////////////////// #endif // not APSTUDIO_INVOKED cohomCalg-0.32/projects/msvc17/cohomCalg.sln000066400000000000000000000023671322050713700207250ustar00rootroot00000000000000 Microsoft Visual Studio Solution File, Format Version 12.00 # Visual Studio 14 VisualStudioVersion = 14.0.25420.1 MinimumVisualStudioVersion = 10.0.40219.1 Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "cohomCalg", "cohomCalg.vcxproj", "{39FD5032-AB8D-45D1-BA61-2CCF5B4A6661}" EndProject Global GlobalSection(SolutionConfigurationPlatforms) = preSolution Debug|x64 = Debug|x64 Debug|x86 = Debug|x86 Release|x64 = Release|x64 Release|x86 = Release|x86 EndGlobalSection GlobalSection(ProjectConfigurationPlatforms) = postSolution {39FD5032-AB8D-45D1-BA61-2CCF5B4A6661}.Debug|x64.ActiveCfg = Debug|x64 {39FD5032-AB8D-45D1-BA61-2CCF5B4A6661}.Debug|x64.Build.0 = Debug|x64 {39FD5032-AB8D-45D1-BA61-2CCF5B4A6661}.Debug|x86.ActiveCfg = Debug|Win32 {39FD5032-AB8D-45D1-BA61-2CCF5B4A6661}.Debug|x86.Build.0 = Debug|Win32 {39FD5032-AB8D-45D1-BA61-2CCF5B4A6661}.Release|x64.ActiveCfg = Release|x64 {39FD5032-AB8D-45D1-BA61-2CCF5B4A6661}.Release|x64.Build.0 = Release|x64 {39FD5032-AB8D-45D1-BA61-2CCF5B4A6661}.Release|x86.ActiveCfg = Release|Win32 {39FD5032-AB8D-45D1-BA61-2CCF5B4A6661}.Release|x86.Build.0 = Release|Win32 EndGlobalSection GlobalSection(SolutionProperties) = preSolution HideSolutionNode = FALSE EndGlobalSection EndGlobal cohomCalg-0.32/projects/msvc17/cohomCalg.vcxproj000066400000000000000000000342641322050713700216250ustar00rootroot00000000000000 Debug Win32 Release Win32 Debug x64 Release x64 {39FD5032-AB8D-45D1-BA61-2CCF5B4A6661} Win32Proj cohomCalg 7.0 Application true v141_xp Unicode false v141_xp Application false v141_xp true Unicode v141_xp Application true v141_xp Unicode v141_xp Application false v141_xp true Unicode v141_xp false $(SolutionDir)\..\..\bin $(SolutionDir)\..\..\build\msvc17\$(Platform)\$(Configuration)\ cohomCalg32D $(SolutionDir)\..\..\source\polylib_mod\;$(VC_IncludePath);$(WindowsSdk_71A_IncludePath); 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//////////////////////////////////////////////////////////////////////////////////////////////////// #define MAX_INPUT_LINES 10000 // Maximal number of lines read from an input file #define MAX_GLSM_RANGE (1024*1024) // GLSM charges may range from -(val) to +(val) //////////////////////////////////////////////////////////////////////////////////////////////////// // Besides the class CInternalData defined in the header, there is the class CInputFile which // entirely handles the interpretation of the input data using the tokenizer, i.e. this class // basically serves as the "parser" and also handles the first round of checking of the input data. // Note that this class is entirely restricted to this input file and should never be handles // externally. class CInputFile { private: // Read data map< string, vector > mCoords; // Coordinates and GLSM charges vector< vector > vSRideal; // Stanley-Reisner ideal generators vector< vector > vAmbientCohoms; // Requested ambient cohomologies size_t numGLSMch; // Number of GLSM charges (for syntax check) private: // The internal parsing functions bool ParseVertexCommand(CTokenizer &tok); bool ParseSRidealCommand(CTokenizer &tok); bool ParseAmbientCohomCommand(CTokenizer &tok); bool ParseMonomialFileCommand(CTokenizer &tok); bool DiscardCommand(CTokenizer &tok); bool ParseInput(const char *pInputData); void HandleSyntaxError(size_t iCommandNumber, const char *pCmdStart, ptrdiff_t iErrOffset); bool TranslateToInternalData(CInternalData &intdata); public: CInputFile(); void Clear(); // Main data handling functions static bool ReadInputFileWithoutComments(string strFileName, string &out_contents); bool ReadAndParseInputFile(string strFileName, string strAppend, CInternalData &out); }; CInputFile::CInputFile() { Clear(); } void CInputFile::Clear() { mCoords.clear(); vSRideal.clear(); vAmbientCohoms.clear(); numGLSMch = 0; } bool CInputFile::ReadInputFileWithoutComments(string strFileName, string &out_contents) { /* This function simply reads in all lines from the text file and cuts of everything after a '%' character, which is reserved for comments. The result is a "comment-free" string containing the input file. Note that only MAX_INPUT_LINES number of lines (see definition at the top of file) are retrieved from the file. */ ifstream ifs(strFileName.c_str()); if (!ifs.is_open()) { ERR_OUT("Could not open or read the file '" << strFileName << "'."); return false; } out_contents.clear(); string line; unsigned int nLines = 0; // Work through the lines and cut of everything after a '%'-character while ((getline(ifs, line)) && (nLines++ < MAX_INPUT_LINES)) { size_t comment = line.find('%'); out_contents.append("\n"); if (comment != string::npos) out_contents.append(line.substr(0,comment)); else out_contents.append(line); } // Have we reached the legal maximum of lines - which is considered an error! if (nLines >= MAX_INPUT_LINES) { ERR_OUT("The input file '" << strFileName << "' contains more than " << MAX_INPUT_LINES << " lines."); return false; } return true; } bool CInputFile::ReadAndParseInputFile(string strFileName, string strAppend, CInternalData &out) { /* As one may provide input data by file, command line or both, this functions takes care of putting those two input sources correctly together. The resulting input is then subject to the parsing functions and finally translated into the internal data format described in the class CInternalData. */ string input_data; if (!strFileName.empty()) { if (!ReadInputFileWithoutComments(strFileName, input_data)) return false; } input_data.append(strAppend); if (!ParseInput(input_data.c_str())) return false; if (!TranslateToInternalData(out)) return false; return true; } void CInputFile::HandleSyntaxError(size_t iCommandNumber, const char *pCmdStart, ptrdiff_t iErrOffset) { /* In case the parsing functions stumble upon some unexpected input, this function handles a properly formatted output of the command line indicating where the error was raised. */ if (iErrOffset < 0) iErrOffset = 0; string error_line; ptrdiff_t error_line_offset; if (iErrOffset > 45) { // If the error comes up at a late character in the line, shorten error_line.assign(pCmdStart, 16); error_line.append(" ... "); error_line.append(pCmdStart + iErrOffset - 15, 30); error_line_offset = 16 + 7 + 15; } else { error_line.assign(pCmdStart, iErrOffset + 15); error_line_offset = iErrOffset; } // Truncate at newline or carriage return characters that may appear after the error size_t oddch = error_line.find_first_of("\n\r", error_line_offset); if (oddch != string::npos) error_line.erase(oddch); // Replace all newline, tab or carriage return characters in the final string by spaces oddch = error_line.find_first_of("\t\n\r", error_line_offset); while (oddch != string::npos) { error_line[oddch] = ' '; oddch = error_line.find_first_of("\t\n\r", error_line_offset); } // Print the error ERR_OUT("Syntax error in input file, command no. " << iCommandNumber << ":"); ERR_OUT_PLAIN(error_line); ERR_OUT_PLAIN(string(error_line_offset, ' ') << '^'); } bool CInputFile::ParseVertexCommand(CTokenizer &tok) { /* This function parses a 'vertex' command, for which the maximal prototype syntax line is vertex z = ( 0, 0, 0, -2, -3) | PIC: F | GLSM: (-4, 1, 2, 0, 0, 0, 0, 0); ******************************** vertex z = ( 0, 0, 0, -2, -3) | GLSM: (-4, 1, 2, 0, 0, 0, 0, 0) | PIC: F; *********************** ******** where the *-indicated part is optional and may be left out. However, in case it is present, it is parsed for syntax as well. */ string str, strCoordName; char c; vector dummy, GLSM; vector GLSMranged; bool bPIC = false; bool bGLSM = false; if (!tok.GetNextToken().GetWord(str)) return false; if (str.compare("vertex") != 0) return false; // Read in the vertex name and try to insert if (!tok.GetNextToken().GetWord(strCoordName)) return false; pair< map< string, vector >::iterator, bool> newcoord = mCoords.insert(pair >(strCoordName, GLSMranged)); if (newcoord.second == false) { ERR_OUT("Double vertex name '" << str << "' used."); return false; } if (!tok.GetNextToken().GetSymbol(c)) return false; if (c == '=') { // Read and discard the vertex data if (!tok.GetIntegerList(dummy)) return false; if (!tok.GetNextToken().GetSymbol(c)) return false; } while (c == '|') { if (!tok.GetNextToken().GetWord(str)) return false; if (str.compare("PIC") == 0) { if (bPIC) { ERR_OUT("Double usage of the identifier PIC."); return false; } bPIC = true; // Read and discard Picard generator if (!tok.GetNextToken().GetSymbol(c)) return false; if (c != ':') return false; if (!tok.GetNextToken().GetWord(str)) return false; if (!tok.GetNextToken().GetSymbol(c)) return false; } else if (str.compare("GLSM") == 0) { if (bGLSM) return false; // Only once! bGLSM = true; // Read in the GLSM charges if (!tok.GetNextToken().GetSymbol(c)) return false; if (c != ':') return false; GLSM.clear(); if (!tok.GetIntegerList(GLSM)) return false; size_t nCurGLSMch = GLSM.size(); if (nCurGLSMch < 1) { ERR_OUT("Invalid number of GLSM charges supplied."); return false; } // Check that we have a equal number of GLSM charges from all vertices if (numGLSMch < 1) numGLSMch = nCurGLSMch; if (numGLSMch != nCurGLSMch) { ERR_OUT("Unequal number of GLSM charges."); return false; } if (!tok.GetNextToken().GetSymbol(c)) return false; } else return false; } if (!bGLSM) { ERR_OUT("No GLSM data was supplied."); return false; } if (c != ';') return false; // We have to check if the GLSM charges are in range and convert to 32-bit vars GLSMranged.resize(numGLSMch); for (size_t i=0; i MAX_GLSM_RANGE) || (GLSM[i] < -MAX_GLSM_RANGE)) { ERR_OUT("Target divisor charge value " << GLSM[i] << " is out of allowed range."); return false; } GLSMranged[i] = (int32_t) GLSM[i]; } // If we arrive here, then the command line was sane and we can copy the retrieved GLSM data newcoord.first->second.clear(); newcoord.first->second.assign(GLSMranged.begin(), GLSMranged.end()); return true; } bool CInputFile::ParseSRidealCommand(CTokenizer &tok) { /* This function parses a 'srideal' command, for which the maximal prototype syntax line is srideal [u1*u2, u3*u4]; where all the product variables have to be present in the list of coordinates/vertices. This more or less suggest using the 'srideal' command AFTER the 'vertex' commands. */ vector vec; string str; char c; if (!tok.GetNextToken().GetWord(str)) return false; if (str.compare("srideal") != 0) return false; if (!tok.GetNextToken().GetSymbol(c)) return false; if (c != '[') return false; // Work through the array of Stanley-Reisner generators while (tok.GetNextToken().GetWord(str)) { vec.clear(); // Read in a single SR generator while (tok.GetNextToken().GetSymbol(c)) { // Check if the variable is in the list of coordinates if (mCoords.find(str) == mCoords.end()) { ERR_OUT("Coordinate/vertex '" << str << "' not specified."); return false; } else { if (vec.size() >= 63) { // In principle, this cannot really happen, as we are only allowing for 63 coordinates // in total, i.e. someone must try something like 'srideal [u*u*u*u*u*...];' ERR_OUT("Only a product of up to 63 coordinates is supported per generator"); return false; } vec.push_back(str); } if (c == ',') break; // Ends the current generator if (c == ']') break; // Ends the list of generators if (c != '*') return false; // Another coordinate following if (!tok.GetNextToken().GetWord(str)) return false; } // This check has been removed as it sometimes seems to be sensible to use single generators as well... /* if (vec.size() < 2) { // No sensible toric variety has Stanley-Reisner generators consisting of only a single coordinate ERR_OUT("Each Stanley-Reisner ideal generator must be the product of at least 2 coordinates."); return false; }*/ vSRideal.push_back(vec); if (c == ']') break; if (c != ',') return false; } if (!tok.GetNextToken().GetSymbol(c)) return false; if (c != ';') return false; return true; } bool CInputFile::ParseAmbientCohomCommand(CTokenizer &tok) { /* This function parses a 'ambientcohom' cmd, for which the maximal prototype syntax line is ambientcohom O(3,0,2,-3,-4,-5,0,2); where the number of supplied GLSM charges must comply with the number of GLSM charges specified in the vertex commands. However, in principle this command may come first, which then defines the number of GLSM charges for the vertices. */ string str; vector GLSM; char c; if (!tok.GetNextToken().GetWord(str)) return false; if (str.compare("ambientcohom") != 0) return false; if (!tok.GetNextToken().GetWord(str)) return false; if (str.compare("O") != 0) return false; // Read in the GLSM charges if (!tok.GetIntegerList(GLSM)) return false; size_t nCurGLSMch = GLSM.size(); if (nCurGLSMch < 1) { ERR_OUT("Invalid number of GLSM charges supplied."); return false; } // Check if we have the correct number of GLSM charges if (numGLSMch < 1) numGLSMch = nCurGLSMch; if (numGLSMch != nCurGLSMch) { ERR_OUT("Unequal number of GLSM charges."); return false; } if (!tok.GetNextToken().GetSymbol(c)) return false; if (c != ';') return false; // Now we have to check the 64-bit GLSM data for range and resort them into // a vector of 32-bit variables; vector GLSMranged; GLSMranged.resize(numGLSMch); for (size_t i=0; i MAX_GLSM_RANGE) || (GLSM[i] < -MAX_GLSM_RANGE)) { ERR_OUT("Target divisor charge value " << GLSM[i] << " is out of allowed range."); return false; } GLSMranged[i] = (int32_t) GLSM[i]; } // If we arrive here, everything is sane and we can add the data vAmbientCohoms.push_back(GLSMranged); return true; } bool CInputFile::ParseMonomialFileCommand(CTokenizer &tok) { /* This function parses a 'monomialfile' cmd, for which the two prototype syntax lines are monomialfile "filename"; monomialfile off; which allows to change the intermediate monomial filename or turn the monomial file usage off alltogether. */ string str; char c; if (!tok.GetNextToken().GetWord(str)) return false; if (str.compare("monomialfile") != 0) return false; const CToken &curtok = tok.GetNextToken(); if (curtok.GetString(str)) CCmdLineArguments::SetMonomialFileName(str); else if (curtok.GetWord(str)) { if (str.compare("off") == 0) CCmdLineArguments::SetUseMonomFile(false); else { ERR_OUT("Could not recognize option '" << str << "'."); return false; } } else return false; if (!tok.GetNextToken().GetSymbol(c)) return false; if (c != ';') return false; return true; } bool CInputFile::DiscardCommand(CTokenizer &tok) { /* This function parses and ignored any command like input, i.e. it looks for a starting WORD token and ignored everything up to the final symbol: anycommand (...ignored...); This is used for ignored commands for some of our internally developed programs for ease of usage concerning input files. */ string str; // We expect a word as the first token of any command if (!tok.GetNextToken().GetWord(str)) return false; // Now search for the command end symbol ';' while (!tok.GetCurToken().IsEndToken()) { char c; if (tok.GetNextToken().GetSymbol(c)) { if (c == ';') return true; } } return false; } bool CInputFile::ParseInput(const char *pInputData) { /* This functions takes responsibility of reading in the data, i.e. it starts the tokenizer and subsequently calls the relevant command parsing functions defined above. It also does some basic input checking in addition to the input checking done in the individual command parsing functions. In case of parsing errors it calls the HandleSyntaxError function to appropiately show the erroneous position. */ Clear(); // Run the input through the tokenizer CTokenizer tok; if (!tok.TokenizeInputString(pInputData)) return false; string strCommandWord; bool bResult = false; CToken token = tok.GetCurToken(); size_t numCmds = 0; size_t nVertexCmds = 0, nSRidealCmds = 0, nAmbientCohomCmds = 0, nMonomialFileCmds = 0; // Scan through the keywords while (token.GetWord(strCommandWord)) { ptrdiff_t iCmdOffset = token.GetInputOffset(); numCmds++; if (strCommandWord.compare("vertex") == 0) { // 'vertex' command detected nVertexCmds++; if (nVertexCmds > 63) { ERR_OUT("Due to internal limitations only up to 63 vertices are supported."); bResult = false; } else bResult = ParseVertexCommand(tok); } else if (strCommandWord.compare("picardgen") == 0) { bResult = DiscardCommand(tok); } else if (strCommandWord.compare("srideal") == 0) { // 'srideal' command detected nSRidealCmds++; if (nSRidealCmds > 1) { ERR_OUT("Multiple 'srideal' commands are forbidden."); bResult = false; } else bResult = ParseSRidealCommand(tok); } else if (strCommandWord.compare("ambientcohom") == 0) { // 'ambientcohom' command detected nAmbientCohomCmds++; bResult = ParseAmbientCohomCommand(tok); } else if (strCommandWord.compare("monomialfile") == 0) { // 'monomialfile' command detected nMonomialFileCmds++; if (nMonomialFileCmds > 1) { ERR_OUT("Multiple 'monomialfile' commands are forbidden."); bResult = false; } else bResult = ParseMonomialFileCommand(tok); } else { ERR_OUT("Unrecognized command '" << strCommandWord << "' in input file"); bResult = false; } // Check if there were some problems in the current run if (!bResult) { HandleSyntaxError(numCmds, pInputData + iCmdOffset, tok.GetPrevToken().GetInputOffset() - iCmdOffset); return false; } // The following routine is more of a internal safety check token = tok.GetCurToken(); if (iCmdOffset == token.GetInputOffset()) { // Internal error - we have not advanced one bit [THIS SHOULD NOT HAPPEN!] ERR_OUT("INTERNAL: Not advancing! Terminating at offset " << iCmdOffset << "."); return false; } } // A new command always has to start with a WORD, so if we are here we're either at the end of file or wrong input if (!token.IsEndToken()) { ERR_OUT("Expecting command."); HandleSyntaxError(++numCmds, pInputData + token.GetInputOffset(), 0); return false; } if (nVertexCmds < 1) { ERR_OUT("No coordinates are specified in the input file."); return false; } if (nSRidealCmds < 1) { ERR_OUT("No Stanley-Reisner ideal generators are specified in the input file."); return false; } if (nAmbientCohomCmds < 1) { ERR_OUT("No ambient line bundle charges are specified in the input file."); return false; } if (nVertexCmds > CCmdLineArguments::GetMaxVertices()) { ERR_OUT("Maximum allowed number of " << CCmdLineArguments::GetMaxVertices() << " coordinates exceeded."); return false; } if (vSRideal.size() > CCmdLineArguments::GetMaxSRgens()) { ERR_OUT("Maximum allowed number of " << CCmdLineArguments::GetMaxSRgens() << " SR generators exceeded."); return false; } if (nAmbientCohomCmds > CCmdLineArguments::GetMaxCohoms()) { ERR_OUT("Maximum allowed number of " << CCmdLineArguments::GetMaxCohoms() << " requested cohomologies exceeded."); return false; } return true; } bool CInputFile::TranslateToInternalData(CInternalData &intdata) { /* This function translates the data obtained from the file to the internal data formal described by the CInternalData class. */ // First clear out the internal data class intdata.Clear(); // Then translate the coordinates size_t numCoords = mCoords.size(); map >::const_iterator it = mCoords.begin(); for (size_t i=0; ifirst); icd.GLSMch.Clear(); for (size_t j=0; jsecond[j]; // Assign the 64-bit variable and compute the complete union icd.liVar = 0x1ull << i; intdata.liCompleteUnion |= icd.liVar; // Update the monomial width for output intdata.nMaxMonomWidth += icd.strName.length() + 1; intdata.vCoords.push_back(icd); it++; } intdata.nMaxMonomWidth--; // Now translate the Stanley-Reisner ideal size_t numSRgens = vSRideal.size(); for (size_t i=0; i= -5) { if (!strFileName.empty()) { MSG_OUT("Reading in the input file '" << strFileName << "'..."); MSG_OUT(""); } } CInputFile iof; if (!iof.ReadAndParseInputFile(strFileName, strAppend, *this)) return false; return true; } string CInternalData::Int64ToCoordProduct(uint64_t liProduct, string strSep, string strZeroVal) const { /* This output function takes a 64-bit variable and converts it into human readable form using the appropiate coordinate bit masks. */ string out; if (liProduct == 0) return strZeroVal; // If we have a non-trivial variable, loop throught the coordinates and apply the // corresponding bit masks size_t numCoords = vCoords.size(); bool bSep = false; for (size_t i=0; i0) strLine.append(","); safe_sprintf(buf, sizeof(buf), "%4d", (int) vTargetDivisors[i].x[j]); strLine.append(buf); } MSG_OUT(strLine << " ))"); } } string CInternalData::PrintInternalDataAsMathematicaScriptInput() { /* This function is used for debug output. It sort of translates the input/internal data stored in CInternalData to the form required by the legacy Mathematica 7 script. This allows for great convenience when checking the results of the C++ implementation to the results of the Mathematica script. */ // First the coordinates string out(" GeometryData = {\n (*Coordinates*){"); size_t num_coords = vCoords.size(); for (size_t i=0; i0) out.append(","); out.append(vCoords[i].strName); } // Then the Stanley-Reisner ideal generators as a list of lists out.append("},\n (*Stanley-Reisner*){"); size_t num_srs = vSRgens.size(); for (size_t i=0; i0) out.append(","); out.append("{"); out.append(Int64ToCoordProduct(vSRgens[i], ",")); out.append("}"); } // And finally the GLSM charges, which represent the projective equivalence relations out.append("},\n (*Equivalence Relations*){"); char buf[64]; for (size_t i=0; i0) out.append(","); out.append("{"); for (size_t j=0; j0) out.append(","); safe_sprintf(buf, sizeof(buf), "%d", (int) vCoords[i].GLSMch.x[j]); out += buf; } out.append("}"); } out.append("}\n };"); return out; } //////////////////////////////////////////////////////////////////////////////////////////////////// // In order to save computational time, there is the possibility to save a monomial list with the // computed secondary/remnant cohomology to a file and read it back in. This functionality is // encapsulated in the class CMonomialFile. class CMonomialFile { private: static const std::string Header; static const char DELIM; static const uint64_t Version; static const std::string Unique; static const std::string Ambiguous; static const std::string EndFile; public: static bool WriteMonomialsFile(const CInternalData &id, std::string strFileName, const CMonomialsList &ml); static bool ReadMonomialsFile(const CInternalData &id, std::string strFileName, CMonomialsList &ml); }; // File format constants const string CMonomialFile::Header = "§$ralfsalg/monomial_file/start$§"; const char CMonomialFile::DELIM = ' '; const uint64_t CMonomialFile::Version = 10001; // Increase after format change! const string CMonomialFile::Unique = "unique_monoms"; const string CMonomialFile::Ambiguous = "ambiguous_monoms"; const string CMonomialFile::EndFile = "§$ralfsalg/monomial_file/end$§"; bool CMonomialFile::WriteMonomialsFile(const CInternalData &id, string strFileName, const CMonomialsList &ml) { /* This private/internal function writes the data from a CMonomialsList class as well as some basic information of the current geometry (taken from CInternalData) to a file. */ // Open the file, if it already exists discard contents ofstream ofs(strFileName.c_str(), ios_base::out | ios_base::trunc | ios_base::binary); if (!ofs.is_open()) { ERR_OUT("Could not open the monomial file '" << strFileName << "' for writing."); return false; } // Write the header string, file format version and variety dimension ofs << Header << DELIM << Version << DELIM; ofs << id.GetDimension() << DELIM; // Write the number of uniquely contributing monomials followed by a list // of the bit-mask, the contributing cohomology group and the secondary/remnant factor ofs << Unique << DELIM << ml.unique_monoms.size() << DELIM; for (map::const_iterator itu = ml.unique_monoms.begin(); itu != ml.unique_monoms.end(); itu++) ofs << itu->first << DELIM << itu->second.Cohom.nGroup << DELIM << itu->second.Cohom.nFactor << DELIM; // Write the number of ambiguously contributing monomials followed by a list // of the bit-mask, the number of potential contributions, followed by a list // of the cohomology group and the secondary/remant factor for each possibility ofs << Ambiguous << DELIM << ml.ambiguous_monoms.size() << DELIM; for (map::const_iterator ita = ml.ambiguous_monoms.begin(); ita != ml.ambiguous_monoms.end(); ita++) { size_t num_cohoms = ita->second.vCohoms.size(); ofs << ita->first << DELIM << num_cohoms << DELIM; for (size_t i=0; isecond.vCohoms[i].nGroup << DELIM << ita->second.vCohoms[i].nFactor << DELIM; } // Write the footer string ofs << EndFile; ofs.close(); return true; } bool CMonomialFile::ReadMonomialsFile(const CInternalData &id, string strFileName, CMonomialsList &ml) { /* This private/internal function read the data from an intermediate monomial file into the CMonomialsList class. Some very basic consistency check is carried out. */ // Open the file for reading ifstream ifs(strFileName.c_str()); if (!ifs.is_open()) return false; // Read & check header string string header; ifs >> header; if (Header.compare(header) != 0) return false; // Read & check file version uint64_t version; ifs >> version; if (version != Version) return false; ml.Clear(); // Read & check variety dimension to internal data size_t var_dim; ifs >> var_dim; if (var_dim != id.GetDimension()) return false; // Read & check beginning of uniquely contributing monomials list string unique; ifs >> unique; if (Unique.compare(unique) != 0) return false; // Read the entire list of uniquely contributing monomials and store data // in the CMonomialsList class unsigned int num_uniques; ifs >> num_uniques; for (unsigned int i=0; i> monomial >> ucd.Cohom.nGroup >> ucd.Cohom.nFactor; pair::iterator, bool> ret = ml.unique_monoms.insert(pair(monomial, ucd)); if (ret.second == false) { // File already contains this unique monomial - this should never happen return false; } } // Read & check the beginning of the ambiguously contributing monomials list string ambiguous; ifs >> ambiguous; if (Ambiguous.compare(ambiguous) != 0) return false; // Read the entire list of ambiguously contributing monomials and the subsequent list // of all possible contributions - store data into the CMonomialsList class unsigned int num_ambiguous; ifs >> num_ambiguous; for (unsigned int i=0; i> monomial >> num_cohoms; acd.vCohoms.clear(); for (unsigned int j=0; j> cc.nGroup >> cc.nFactor; acd.vCohoms.push_back(cc); } pair::iterator, bool> ret = ml.ambiguous_monoms.insert(pair(monomial, acd)); if (ret.second == false) { // File already contains this ambiguous monomial - should never happen return false; } } ifs.close(); ml.ClearRationals(); return true; } //////////////////////////////////////////////////////////////////////////////////////////////////// void CMonomialsList::Clear() { unique_monoms.clear(); ambiguous_monoms.clear(); } void CMonomialsList::ClearRationals() { /* This function clears the number of rational functions for each monomial of both the lists of uniquely and ambiguously contributions. This effectively allows to reuse the same CMonomialList for different computations within the same geometry. */ for (map::iterator itu = unique_monoms.begin(); itu != unique_monoms.end(); itu++) { itu->second.nRationals = 0; itu->second.nRationalsDual = 0; } for (map::iterator ita = ambiguous_monoms.begin(); ita != ambiguous_monoms.end(); ita++) { ita->second.nRationals = 0, ita->second.nRationalsDual = 0; } } bool CMonomialsList::AddUniqueContribution(uint64_t liMonomial, unsigned int nCohomGroup, unsigned int nFactor) { /* Adds an uniquely contributing monomial and the data obtained from the secondary/remnant cohomology. */ // Prepare the new monomial entry UniqueContribData tmp; tmp.Cohom.nGroup = nCohomGroup; tmp.Cohom.nFactor = nFactor; tmp.nRationals = tmp.nRationalsDual = 0; // Add & check if the monomial is already present - this should never happen pair::iterator, bool> ret = unique_monoms.insert(pair(liMonomial, tmp)); if (ret.second == false) { ERR_OUT("Supposedly unique monomial " << CBits::IntToBinary(liMonomial) << " is already in the list of uniquely contributing monomials."); return false; } return true; } bool CMonomialsList::AddAmbiguousContribution(uint64_t liMonomial, const vector &vContributions) { /* Adds an ambiguously contributing monomial and the data obtained from the secondary/remnant cohomology, i.e. the list of all potential cohomology groups where this monomial might contribute and the corresponding contribution factor. */ // Prepare the new ambiguous monomial entry AmbiguousContribData tmp; tmp.vCohoms.assign(vContributions.begin(), vContributions.end()); tmp.nRationals = tmp.nRationalsDual = 0; // Add & check if the monomial is already presen - this should never happen pair::iterator, bool> ret = ambiguous_monoms.insert(pair(liMonomial, tmp)); if (ret.second == false) { ERR_OUT("Supposedly unique monomial " << CBits::IntToBinary(liMonomial) << " is already in list of ambiguously contributing monomials."); return false; } return true; } bool GetIntSequenceStartEnd(const vector &seq, size_t &min_out, size_t &max_out) { /* This little helper functions takes an arbitrary length vector of integer variables and finds the first and last non-zero entry. */ bool zero_seq = true; size_t sequencelen = seq.size(); // Loop FORWARDS from the beginning to the end of the vector and find first non-zero element for (size_t i=0; i=min_out; i--) { if (seq[i] != 0) { max_out = i; break; } } return true; } typedef struct { uint64_t liMonomial; const UniqueContribData *pUCD; } OutputUniqueSort; void CMonomialsList::PrintMonomialList(const CInternalData &id, bool bPrintFactors, bool bPrintRationals, bool bShortList) const { /* This output functions prints an easily readable list of all the data contained in the monomial list. The output of the secondary/remnant cohomology factors and the output of the potentially already computed number of rational functions can be turned on and of. Note that output of the rational functions automaticall turns on the output of the secondary/remnant cohomology factors. */ // We need small helper structure in order to sort the uniquely contributing monomials // by their respective cohomology group if (bPrintRationals) bPrintFactors = true; // Store the complete union uint64_t complete_union = id.GetCompleteUnion(); // Presort the unique monomials list size_t var_dim = id.GetDimension(); vector< vector > unique_sorted; unique_sorted.resize(var_dim+1); map::const_iterator itu = unique_monoms.begin(); while (itu != unique_monoms.end()) { OutputUniqueSort tmp; tmp.liMonomial = itu->first; tmp.pUCD = &itu->second; unique_sorted[itu->second.Cohom.nGroup].push_back(tmp); itu++; } // Print out the unique monomials if (unique_monoms.size() < 1) MSG_OUT(" There are no unique contribution monomials to the " << var_dim << "-dimensional variety."); else { MSG_OUT(" The " << unique_monoms.size() << " unique contribution monomials to the " << var_dim << "-dimensional variety are:"); for (unsigned int dim = 0; dim <= var_dim; dim++) { char buf[256]; size_t curmonoms = unique_sorted[dim].size(); MSG_OUT(" H^" << dim << "(X) has " << curmonoms << " contributing unique monomials:"); for (size_t i=0; inRationals; uint32_t drat = unique_sorted[dim][i].pUCD->nRationalsDual; // If a short list is requested, only print the monomials with non-zero contribution if (bShortList) { if ((rat == 0) && (drat == 0)) continue; } // Add the secondary/remnant cohomology factors if requested if (bPrintFactors) { uint32_t factor = unique_sorted[dim][i].pUCD->Cohom.nFactor; // Add the number of rational functions if requested if (bPrintRationals) safe_sprintf(buf, sizeof(buf), " factor %3d * %-3d rationals = contribution %3d | factor %3d %-3d dual rationals = contribution %d", (int) factor, (int) rat, (int) (factor * rat), (int) factor, (int) drat, (int) (factor * drat)); else { if (factor != 1) safe_sprintf(buf, sizeof(buf), " factor %3d", (int) factor); } } MSG_OUT(" " << id.Int64ToMonomialPadded(unique_sorted[dim][i].liMonomial).c_str() << buf); } } } // Print out the ambiguous monomials if (ambiguous_monoms.size() < 1) MSG_OUT(" There are no ambiguous contribution monomials to the variety."); else { MSG_OUT(" There are also " << ambiguous_monoms.size() << " ambiguous monomials:"); for (map::const_iterator ita = ambiguous_monoms.begin(); ita != ambiguous_monoms.end(); ita++) { char buf[256]; size_t len = 0; size_t numcohoms = ita->second.vCohoms.size(); for (size_t i=0; ifirst).c_str()); strtmp = buf; len = strtmp.length(); } else { strtmp.assign(len, ' '); } buf[0] = 0; // Add the secondary/remnant cohomology factors if requested if (bPrintFactors) { uint32_t group = ita->second.vCohoms[i].nGroup; uint32_t factor = ita->second.vCohoms[i].nFactor; uint32_t rat = ita->second.nRationals; uint32_t drat = ita->second.nRationalsDual; // Add the number of rational functions if requested if (bPrintRationals) safe_sprintf(buf, sizeof(buf), "factor %3d * %-3d rationals = contribution %3d | %-3d dual rationals = contribution %d --> h^%-2d", (int) factor, (int) rat, (int) (factor * rat), (int) drat, (int) (factor * drat), group); else { if (factor != 1) safe_sprintf(buf, sizeof(buf), "factor %3d --> h^%-2d", (int) factor, (int) group); else safe_sprintf(buf, sizeof(buf), " --> h^%-2d", (int) group); } } MSG_OUT(strtmp << buf << " (complement: " << id.Int64ToMonomial(~ita->first & complete_union) << ")"); } } } } bool CMonomialsList::ReadMonomialsFile(const CInternalData &id, std::string strFileName) { /* Wrapper function to access the reading function of the CMonomialFile class. */ return CMonomialFile::ReadMonomialsFile(id, strFileName, *this); } bool CMonomialsList::WriteMonomialsFile(const CInternalData &id, std::string strFileName) const { /* Wrapper function to access the writing function of the CMonomialFile class. */ return CMonomialFile::WriteMonomialsFile(id, strFileName, *this); }cohomCalg-0.32/source/iohandler.h000066400000000000000000000162061322050713700167550ustar00rootroot00000000000000//////////////////////////////////////////////////////////////////////////////////////////////////// // // // iohandler.h // // =========== // // // // Code: Benjamin Jurke, http://benjaminjurke.net // // // //////////////////////////////////////////////////////////////////////////////////////////////////// // // // File history: // // - 17.04.2010 File created as iohandler.h // // // //////////////////////////////////////////////////////////////////////////////////////////////////// #ifndef INC_IOHANDLER_H #define INC_IOHANDLER_H #include #include #include #include //////////////////////////////////////////////////////////////////////////////////////////////////// // This file handles the translation from the input file or string to the internal data format using // first the tokenizer and then some pretty elementary (read: non-sophisticated) parsing. // // There are several internal data format and due to the quite limited amount of input data several // redundant copies are held by the computation classes. However, the CInternalData class provides // the "common ground" and also contains the output functions to "human readable" format. // // Internally, for most of the program we are working with 64-bit integer variables, because the // usage of bitmasks and bit-wise operators in general is very fast and rather memory efficient. // The usage of those internal variables also puts some limitations on the input data: only up to // 63 coordinates/vertices and Stanley-Reisner ideal generator are supported (the top bit is // reserved!), butat the current state of technology those cases are way out of the league of modern // computers. // For speedup we use some fixed-width arrays of 64 integer variables template class vec64 { public: T x[64]; public: inline void Fill(T val) { for (unsigned int i=0; i<64; i++) x[i]=val; } inline void Clear() { Fill(0); }; }; typedef vec64 i32vec64; typedef vec64 ui32vec64; typedef vec64 i64vec64; typedef vec64 ui64vec64; // For each coordinate/vertex we hold the following data typedef struct { uint64_t liVar; std::string strName; i32vec64 GLSMch; } InternalCoordData; class CInternalData { friend class CInputFile; private: // The input data std::vector vCoords; // The coordinates/vertices std::vector vSRgens; // The Stanley-Reisner ideal generators std::vector vTargetDivisors; // The requested ambient cohomology bundle charges size_t numGLSMch; // For output formatting size_t nMaxMonomWidth; // Some internal data uint64_t liCompleteUnion; private: void Clear(); public: CInternalData(); // Output functions std::string Int64ToCoordProduct(uint64_t liProduct, std::string strSep = "*", std::string strZeroVal = "1") const; std::string Int64ToCoordProductPadded(uint64_t liProduct, std::string strSep = "*", std::string strZeroVal = "1") const; std::string Int64ToMonomial(uint64_t liProduct) const; std::string Int64ToMonomialPadded(uint64_t liProduct) const; void PrintInternalData(); std::string PrintInternalDataAsMathematicaScriptInput(); // Internal data retrival inline size_t GetDimension() const { return vCoords.size() - numGLSMch; }; inline uint64_t GetCompleteUnion() const { return liCompleteUnion; }; inline size_t GetNumGLSMch() const { return numGLSMch; }; inline size_t GetNumCoordinates() const { return vCoords.size(); }; inline size_t GetNumSRgens() const { return vSRgens.size(); }; inline size_t GetNumTargetDivisors() const { return vTargetDivisors.size(); }; inline const std::vector &GetInternalCoordData() const { return vCoords; }; inline const std::vector & GetSRgens() const { return vSRgens; }; inline const std::vector & GetTargetDivisors() const { return vTargetDivisors; }; void GetCanonicalDivisor(i32vec64 &candiv_out) const; // Data input bool ReadAndParseInputFile(std::string strFileName, std::string strAppend); }; //////////////////////////////////////////////////////////////////////////////////////////////////// // The CMonomialsList class contains the data which is ultimately produced by the processes. Encoded // in 64-bit variables, again, it contains the list of all contributing monomials and their respective // factor, which was derived from the secondary/remnant cohomology. Note that the monomials are split // up in two sets: the monomials which have a contribution to an uniquely determined cohomology group // and the ambiguously contributing monomials, whose actual contribution has to be sorted out later. typedef struct { uint32_t nGroup; uint32_t nFactor; } CohomContrib; typedef struct { CohomContrib Cohom; uint32_t nRationals; uint32_t nRationalsDual; } UniqueContribData; typedef struct { std::vector vCohoms; uint32_t nRationals; uint32_t nRationalsDual; } AmbiguousContribData; class CMonomialsList { friend class CSecondaryCohomology; friend class CRationals; friend class CMonomialFile; private: // Associative monomial contribution data std::map unique_monoms; std::map ambiguous_monoms; private: // Adding monomials bool AddUniqueContribution(uint64_t liMonomial, uint32_t nCohomGroup, uint32_t nFactor); bool AddAmbiguousContribution(uint64_t liMonomial, const std::vector &vContributions); public: void Clear(); void ClearRationals(); // Output functions void PrintMonomialList(const CInternalData &id, bool bPrintFactors, bool bPrintRationals, bool bShortList) const; // Intermediate monomial file I/O bool ReadMonomialsFile(const CInternalData &id, std::string strFileName); bool WriteMonomialsFile(const CInternalData &id, std::string strFileName) const; }; bool GetIntSequenceStartEnd(const std::vector &seq, size_t &min_out, size_t &max_out); #endif cohomCalg-0.32/source/main.cpp000066400000000000000000000637731322050713700163020ustar00rootroot00000000000000//////////////////////////////////////////////////////////////////////////////////////////////////// // // // main.cpp +-----------------------+ // // ======== | APPLICATION MAIN FILE | // // +-----------------------+ // // Code: Benjamin Jurke, http://benjaminjurke.net // // // //////////////////////////////////////////////////////////////////////////////////////////////////// // // // File history: // // - 29.03.2010 File created as main.cpp // // Contains a fast implementation of the line bundle cohomology algorithm // // presented in the paper arXiv:1003.5217 [hep-th] // // // //////////////////////////////////////////////////////////////////////////////////////////////////// #include #include #include #include #include "main.h" #include "secondarycohom.h" #include "rationals.h" #include "iohandler.h" #include "platform.h" using namespace std; //////////////////////////////////////////////////////////////////////////////////////////////////// #define APP_NAME "cohomCalg" #define APP_VERSION "0.32" #define APP_AUTHOR "author: Benjamin Jurke (mail@benjaminjurke.com)" << std::endl << " Based on the algorithm detailed in arXiv:1003.5217" #define APP_PLATFORM APP_TARGET_OS << " " << APP_ARCH //////////////////////////////////////////////////////////////////////////////////////////////////// vector CBits::cBitsIn16Bits; void CBits::InitBitCounter() { /* This function initializes the bit counter buffer, by counting the number of bits in all 16-bit variables. (Gosh, who remembers the time, when this was ALL of your available memory...?) */ // Resize the bit buffer cBitsIn16Bits.resize((0x1u << 16), 0); // And count the bits for all 16-bit variables for (unsigned int i=0; i<(0x1u<<16); i++) { unsigned int count = 0; unsigned int n=i; while (n) { count += n & 0x1u; n >>= 1; } cBitsIn16Bits[i] = (char) count; } } string CBits::IntToBinary(uint64_t x, size_t digits) { /* This functions produces a string containing the lower-end bits of a 64-bit variable up to 'digits', which are packed into 8-bit packs to ease readability. */ if ((digits > 0) && (digits <= 64)) { // If we are in range, compute the total length of the output string int32_t offset = digits % 8; size_t stringlen = digits+digits/8 + (offset == 0 ? -1 : 0); string tmp(stringlen, '0'); uint64_t mask = 0x1ull << (digits-1); // Now slide the bit mask over the bits and write a 1 where necessary for (int32_t cnt=1,stringpos=0; cnt<=(int32_t) digits; cnt++, stringpos++) { if (x & mask) tmp[stringpos] = '1'; x <<= 1; if(((cnt-offset) % 8 == 0) && (cnt < (int32_t) digits)) tmp[++stringpos] = ' '; } return tmp; } else { return ""; } } string CBits::IntToBinary(uint64_t x) { /* Returns the bit string containing either 64, 32 or 16 bits depending on numerical value. */ if (x >= (0x1ull << 32)) return IntToBinary(x, 64); if (x >= (0x1ull << 16)) return IntToBinary(x, 32); return IntToBinary(x, 16); } string SecondsToTime(clock_t secs) { /* Converts an integral number of seconds properly into days/hours/minutes/seconds. */ clock_t days = secs / (60*60*24); secs %= 60*60*24; clock_t hours = secs / (60*60); secs %= 60*60; clock_t mins = secs / 60; secs %= 60; string out; char buf[64]; if (days != 0) { if (days==1) out += "1 day "; else { safe_sprintf(buf, sizeof(buf), "%d days ", (int) days); out += buf; } } if (hours != 0) { if (hours==1) out += "1 hour "; else { safe_sprintf(buf, sizeof(buf), "%d hours ", (int) hours); out += buf; } } if (mins != 0) { if (mins==1) out += "1 min "; else { safe_sprintf(buf, sizeof(buf), "%d mins ", (int) mins); out += buf; } } if ((secs != 0) || out.empty()) { if (secs==1) out += "1 sec "; else { safe_sprintf(buf, sizeof(buf), "%d secs ", (int) secs); out += buf; } } out.erase(out.end()-1); return out; } string SecondsToTime(double secs) { /* Converts a floating-point number of seconds properly into days/hours/minutes/seconds while keeping two digits during the first minute. */ char buf[256]; if (secs <= 60.9) { if (secs == 1.0) return "1 second"; else safe_sprintf(buf, sizeof(buf), "%.2f seconds", secs); } else safe_sprintf(buf, sizeof(buf), "%.2f seconds = %s", secs, SecondsToTime((clock_t) secs).c_str()); return buf; } string BytesToReadableSize(uint64_t bytes) { /* Converts a number of bytes to the proper extension string. */ char buf[32]; if (bytes >= (1024ull*1024ull*1024ull*1024ull*1024ull)) safe_sprintf(buf, sizeof(buf), "%.2f PiB", (double) bytes / (1024ull*1024ull*1024ull*1024ull*1024ull)); else if (bytes >= (1024ull*1024ull*1024ull*1024ull)) safe_sprintf(buf, sizeof(buf), "%.2f TiB", (double) bytes / (1024ull*1024ull*1024ull*1024ull)); else if (bytes >= (1024ull*1024ull*1024ull)) safe_sprintf(buf, sizeof(buf), "%.2f GiB", (double) bytes / (1024ull*1024ull*1024ull)); else if (bytes >= (1024*1024)) safe_sprintf(buf, sizeof(buf), "%.2f MiB", (double) bytes / (1024*1024)); else if (bytes >= 10000) safe_sprintf(buf, sizeof(buf), "%.2f KiB", (double) bytes / (1024)); else if (bytes > 1) safe_sprintf(buf, sizeof(buf), "%d bytes", (int) bytes); else return "1 byte"; return buf; } //////////////////////////////////////////////////////////////////////////////////////////////////// string CCmdLineArguments::strCommand; string CCmdLineArguments::strInputFileName; int CCmdLineArguments::iVerboseLevel = 0; bool CCmdLineArguments::bShowTiming = false; bool CCmdLineArguments::bShowBits = false; bool CCmdLineArguments::bCheckSerre = false; bool CCmdLineArguments::bMonomReduction = true; bool CCmdLineArguments::bUseMonomFile = true; bool CCmdLineArguments::bIntegratedRun = false; string CCmdLineArguments::strAppendInput; bool CCmdLineArguments::bMathematicaOutput = false; string CCmdLineArguments::strMonomialFileName; bool CCmdLineArguments::bMaxVertices = false; int CCmdLineArguments::iMaxVertices = -1; bool CCmdLineArguments::bMaxSRgens = false; int CCmdLineArguments::iMaxSRgens = -1; bool CCmdLineArguments::bMaxCohoms = false; int CCmdLineArguments::iMaxCohoms = -1; void CCmdLineArguments::Clear() { strCommand.clear(); strInputFileName.clear(); iVerboseLevel = 0; bShowTiming = false; bCheckSerre = false; bMonomReduction = true; bUseMonomFile = true; strAppendInput.clear(); bMathematicaOutput = false; strMonomialFileName.clear(); } void CCmdLineArguments::PrintHelp() { /* This function shows the help output. */ CONSOLE_MSG_OUT("Syntax: cohomcalg [--option1] [--option2] ... InputFileName [> OutputFileName]"); CONSOLE_MSG_OUT(""); CONSOLE_MSG_OUT("Command line options:"); CONSOLE_MSG_OUT(" --in=\"...\" Treats the text between parentheses like additional"); CONSOLE_MSG_OUT(" input data, i.e. like appended content of the input file."); CONSOLE_MSG_OUT(" --nomonomfile Prohibits usage and generation of monomial file."); CONSOLE_MSG_OUT(" --checkserre Computes the Serre dual cohomology for comparison."); CONSOLE_MSG_OUT(" --noreduction Deactivates the Serre self-duality reduction for ambiguous"); CONSOLE_MSG_OUT(" monomials (may increase computation time dramatically!)"); CONSOLE_MSG_OUT(" --hideinput Does not print the input data read from the input file."); CONSOLE_MSG_OUT(" --showtime Shows timing stats even for application runs < 1 second."); CONSOLE_MSG_OUT(" --showbits Prints the internally used bitmasks for debug output."); CONSOLE_MSG_OUT(" --mathematica Gives formattet output for the Mathematica script version."); CONSOLE_MSG_OUT(" --integrated Produces minimalistic output for application integration."); CONSOLE_MSG_OUT(" --verboseN Provides debug output at level N=1..6, e.g. --verbose3."); CONSOLE_MSG_OUT(" --maxX=N Defines limits for X=verts,srgens,cohoms to N."); CONSOLE_MSG_OUT(""); CONSOLE_MSG_OUT("The order of options is irrelevant, but later commands always overwrite"); CONSOLE_MSG_OUT("prior options, e.g. from '--verbose4 --verbose1' only the later one will"); CONSOLE_MSG_OUT("have any effect."); CONSOLE_MSG_OUT(""); CONSOLE_MSG_OUT("The program automatically tries to add the file extension '.in' to the"); CONSOLE_MSG_OUT("InputFileName. See the package manual for further information."); } bool CCmdLineArguments::ParseCmdLineArguments(int argc, char *argv[]) { /* This function parses the C/C++ passed argument lines, which come as an array of strings. Those are translated into the static class variables of CCmdLineArguments. */ Clear(); // There should at least be one argument if (argc < 1) return false; // The first command is always the executable command strCommand = argv[0]; if (argc < 2) { // With no option or anything specified, show the help PrintHelp(); return false; } // Check if someone actually requested the help string strCurArg = argv[1]; if ((strCurArg.compare("--help") == 0) || (strCurArg.compare("-help") == 0) || (strCurArg.compare("/help") == 0) || (strCurArg.compare("--?") == 0) || (strCurArg.compare("-?") == 0) || (strCurArg.compare("/?") == 0)) { PrintHelp(); return false; } // The last argument is expected to be a filename, other than than order is irrelevant bool bCheckForFilename = true; bool bFileRequired = true; for (int i=1; i= -5) MSG_OUT(strAppInfo); // STEP 2: Do all pre-computation initializations CBits::InitBitCounter(); ////////////////////////// // STEP 3: Read in the input file and print the input data CInternalData id; if (!id.ReadAndParseInputFile(CCmdLineArguments::GetInputFileName(), CCmdLineArguments::GetAppendInput())) { if (CCmdLineArguments::GetVerboseLevel() < -5) MSG_OUT_NOENDL("{False,\"Invalid input data\"}"); return 1; } if (CCmdLineArguments::GetVerboseLevel() >= 0) { MSG_OUT("Input data:"); MSG_OUT("==========="); id.PrintInternalData(); } if (CCmdLineArguments::GetVerboseLevel() >= -5) { MSG_OUT(""); MSG_OUT(""); MSG_OUT(""); } ////////////////////////// // STEP 4: Initialize the secondary sequences engine CSecondaryCohomology seccohom; if (!seccohom.Init2ndSequences(id)) { if (CCmdLineArguments::GetVerboseLevel() < -5) MSG_OUT_NOENDL("{False,\"Could not compute secondary sequences\"}"); return 1; } ts.t10SecondarySeqsStart = clock(); // Check if we should use a potentially available monomial file for speedup, if so skip steps 5-6 string strMonomialFileName = CCmdLineArguments::GetMonomialFileName(); if (strMonomialFileName.empty()) CCmdLineArguments::SetUseMonomFile(false); bool bComputeMonoms = true; if (CCmdLineArguments::GetUseMonomFile()) { if (seccohom.GetMonomialsList().ReadMonomialsFile(id, strMonomialFileName)) bComputeMonoms = false; else { CONSOLE_MSG_OUT("Could not open/read in the monomial file '" << strMonomialFileName << "'."); CONSOLE_MSG_OUT(""); } } else { CONSOLE_MSG_OUT("Usage and generation of intermediate monomial files deactivated."); CONSOLE_MSG_OUT(""); } if (bComputeMonoms) { // STEP 5: Start the computation of the secondary sequences CONSOLE_MSG_OUT("Starting computation of secondary sequences..."); if (CCmdLineArguments::GetVerboseLevel() >= 6) MSG_OUT(" - Generating secondary sequences..."); if (!seccohom.TraverseSRpowerset(id)) { if (CCmdLineArguments::GetVerboseLevel() < -5) MSG_OUT_NOENDL("{False,\"Could not traverse SR ideal generator powerset\"}"); return 1; } if (CCmdLineArguments::GetVerboseLevel() >= 4) { MSG_OUT("Verbose Level 4: Full list of monomials with secondary sequences:"); MSG_OUT("-----------------------------------------------------------------"); seccohom.PrintMonomMap(id, false); MSG_OUT(""); MSG_OUT(""); } // STEP 6a: Compute the secondary cohomology / monomial factors from the sequences if (CCmdLineArguments::GetVerboseLevel() >= 6) MSG_OUT(" - Eliminating trivial sequences..."); ts.t20SeqExactnessStart = clock(); if (!seccohom.Compute2ndCohomFromTrivialSequences()) { if (CCmdLineArguments::GetVerboseLevel() < -5) MSG_OUT_NOENDL("{False,\"Could not compute secondary cohomology of trivial sequences\"}"); return 1; } if (CCmdLineArguments::GetVerboseLevel() >= 3) { MSG_OUT("Verbose Level 3: Reduced list of monomials with non-trivial secondary sequences:"); MSG_OUT("--------------------------------------------------------------------------------"); seccohom.PrintMonomMap(id, false); MSG_OUT(""); MSG_OUT(""); } // STEP 6b: Compute the remaining secondary/remnant cohomology elements if (CCmdLineArguments::GetVerboseLevel() >= 6) MSG_OUT(" - Computing cohomology from sequences..."); if (!seccohom.Compute2ndCohomFromSequences(id)) { if (CCmdLineArguments::GetVerboseLevel() < -5) MSG_OUT_NOENDL("{False,\"Could not compute secondary cohomology\"}"); return 1; } // If we are using intermediate monomial files, it is time for storing the computed data to file if (CCmdLineArguments::GetUseMonomFile()) { if (!seccohom.GetMonomialsList().WriteMonomialsFile(id, strMonomialFileName)) { ERR_OUT("Could not write the computed monomials to the file '" << strMonomialFileName << "'. Continuing..."); } } } else { CONSOLE_MSG_OUT("Using monomial file '" << strMonomialFileName << "'. Delete or rename this file"); CONSOLE_MSG_OUT("if you don't want to use it, or use '--nomonomfile' option."); CONSOLE_MSG_OUT("WARNING: Do not change the vertices (order) or Stanley-Reisner ideal in the"); CONSOLE_MSG_OUT("input file without deleting the monomial file - otherwise crashes!"); CONSOLE_MSG_OUT(""); } // STEP 7: Resolve the ambiguous monomials via the "unique complement dualization" technique (unless turned off) if (CCmdLineArguments::GetMonomReduction()) { if (CCmdLineArguments::GetVerboseLevel() >= 2) { MSG_OUT("Verbose Level 2: Preliminary list of contributing monomials with factors (pre-Serre-reduction):"); MSG_OUT("-----------------------------------------------------------------------------------------------"); seccohom.GetMonomialsList().PrintMonomialList(id, true, false, false); MSG_OUT(""); MSG_OUT(""); } if (!seccohom.Perform2ndCohomSerreReduction(id)) { if (CCmdLineArguments::GetVerboseLevel() < -5) MSG_OUT_NOENDL("{False,\"Could not perform Serre duality reduction of contributions\"}"); return 1; } if (CCmdLineArguments::GetVerboseLevel() >= -5) { MSG_OUT(""); MSG_OUT(""); } } else { CONSOLE_MSG_OUT("Serre self-duality reduction for ambiguous monomials deactivated."); } if (CCmdLineArguments::GetVerboseLevel() >= 2) { MSG_OUT("Verbose Level 2: Final list of contributing monomials with factors:"); MSG_OUT("-------------------------------------------------------------------"); seccohom.GetMonomialsList().PrintMonomialList(id, true, false, false); MSG_OUT(""); MSG_OUT(""); } CONSOLE_MSG_OUT("Computation of secondary cohomologies and contributions complete."); ////////////////////////// // STEP 8: Count the number of rational functions for alle monomials ts.t30RationalsCountStart = clock(); vector cohom; if (!CRationals::ComputeCohomologies(id, seccohom.GetMonomialsList(), cohom)) { if (CCmdLineArguments::GetVerboseLevel() < -5) MSG_OUT_NOENDL("{False,\"Internal error while computing the cohomology\"}"); else MSG_OUT("Internal error while computing the cohomology"); return 1; } ts.t90ComputationsDone = clock(); if (CCmdLineArguments::GetVerboseLevel() >= 1) { MSG_OUT("Verbose Level 1: Final list of contributing monomials with factors and rationals:"); MSG_OUT("---------------------------------------------------------------------------------"); for (unsigned int i=0; i= -5) MSG_OUT(""); ////////////////////////// // STEP 9: Provide the final output if (CCmdLineArguments::GetMathematicaOutput()) { MSG_OUT("Preformatted output for Mathematica script version of the algorithm implementation:"); MSG_OUT("-----------------------------------------------------------------------------------"); string tmp; MSG_OUT(id.PrintInternalDataAsMathematicaScriptInput()); CCohomology::GetMathematicaCohomologiesList(cohom, tmp); MSG_OUT(tmp); MSG_OUT(""); MSG_OUT(""); } if (!CCmdLineArguments::GetIntegratedRun()) CCohomology::PrintCohomologies(cohom); else CCohomology::SummarizeCohomologies(cohom); ts.t99AllDone = clock(); // STEP 10: Output timing statistics double totaltime = (ts.t99AllDone-ts.t01ApplicationStart)*ts.dResolution; if (((totaltime > 1.0) || (CCmdLineArguments::GetShowTiming())) && (!CCmdLineArguments::GetIntegratedRun())) { double secondarycohoms = (ts.t30RationalsCountStart - ts.t10SecondarySeqsStart)*ts.dResolution; double rationalscount = (ts.t90ComputationsDone - ts.t30RationalsCountStart)*ts.dResolution; MSG_OUT(""); MSG_OUT(""); MSG_OUT("Application run took " << SecondsToTime(totaltime) << ", more precisely"); MSG_OUT(" " << SecondsToTime(secondarycohoms) << " for the computation of the secondary cohomology"); MSG_OUT(" " << SecondsToTime(rationalscount) << " for the counting of rational functions"); } CONSOLE_MSG_OUT(""); CONSOLE_MSG_OUT(" All done. Program run successfully completed."); CONSOLE_MSG_OUT(""); return 0; } cohomCalg-0.32/source/main.h000066400000000000000000000146011322050713700157310ustar00rootroot00000000000000//////////////////////////////////////////////////////////////////////////////////////////////////// // // // main.h +-----------------------+ // // ====== | APPLICATION MAIN FILE | // // +-----------------------+ // // Code: Benjamin Jurke, http://benjaminjurke.net // // // //////////////////////////////////////////////////////////////////////////////////////////////////// // // // File history: // // - 31.03.2010 File created as main.h // // // //////////////////////////////////////////////////////////////////////////////////////////////////// #ifndef INC_MAIN_H #define INC_MAIN_H #include #include #include #include #include //////////////////////////////////////////////////////////////////////////////////////////////////// // This is the main header file, which is included by all other source files. It contains a couple of // "helper" functions for the conversion of seconds to readable time, for counting and properly printing // of bitmasks. Furthermore, it also contains the CCmdLineArguments class, which allows access to the // command line parameters of the program. This header file also declares the primary output functions // (or rather macros) which are used throughout the program. // A couple of hard internal limits #define HARD_MAX_VERTICES 64 #define HARD_MAX_SRGENS 64 #define HARD_MAX_COHOMS 1024 // Yeah, I know, macros are evil... spare me the lecture #define X_COUNT_BITS16(___n_) (CBits::cBitsIn16Bits[___n_]) #define X_COUNT_BITS32(___n_) (CBits::cBitsIn16Bits[___n_ & 0xffffu] + CBits::cBitsIn16Bits[(___n_ >> 16) & 0xffffu]) #define X_COUNT_BITS64(___n_) (CBits::cBitsIn16Bits[___n_ & 0xffffu] + CBits::cBitsIn16Bits[(___n_ >> 16) & 0xffffu] + CBits::cBitsIn16Bits[(___n_ >> 32) & 0xffffu] + CBits::cBitsIn16Bits[(___n_ >> 48) & 0xffffu]) class CBits { private: // The bit buffer static std::vector cBitsIn16Bits; public: // Initialization static void InitBitCounter(); // Conversion and bit counting static std::string IntToBinary(uint64_t x, size_t digits); static std::string IntToBinary(uint64_t x); static inline unsigned int CountBits(uint16_t x) { return X_COUNT_BITS16(x); } static inline unsigned int CountBits(uint32_t x) { return X_COUNT_BITS32(x); } static inline unsigned int CountBits(uint64_t x) { return X_COUNT_BITS64(x); } }; // A couple of helper functions std::string SecondsToTime(clock_t secs); std::string SecondsToTime(double secs); std::string BytesToReadableSize(uint64_t bytes); //////////////////////////////////////////////////////////////////////////////////////////////////// class CCmdLineArguments { private: // Command line parameter values static std::string strCommand; static std::string strInputFileName; static int iVerboseLevel; static bool bShowTiming; static bool bShowBits; static bool bCheckSerre; static bool bMonomReduction; static bool bUseMonomFile; static bool bIntegratedRun; static std::string strAppendInput; static bool bMathematicaOutput; static std::string strMonomialFileName; static bool bMaxVertices; static int iMaxVertices; static bool bMaxSRgens; static int iMaxSRgens; static bool bMaxCohoms; static int iMaxCohoms; private: static void Clear(); static void PrintHelp(); public: // Primary parsing static bool ParseCmdLineArguments(int argc, char **argv); // Almost all command line variables are read-only static inline std::string GetInputFileName() { return strInputFileName; }; static inline int GetVerboseLevel() { return iVerboseLevel; }; static inline bool GetShowTiming() { return bShowTiming; }; static inline bool GetShowBits() { return bShowBits; }; static inline bool GetCheckSerre() { return bCheckSerre; }; static inline bool GetMonomReduction() { return bMonomReduction; }; static inline bool GetUseMonomFile() { return bUseMonomFile; }; static inline std::string GetAppendInput() { return strAppendInput; }; static inline bool GetMathematicaOutput() { return bMathematicaOutput; }; static inline bool GetIntegratedRun() { return bIntegratedRun; }; static inline std::string GetMonomialFileName() { return strMonomialFileName; }; static inline int GetMaxVertices() { if (bMaxVertices) return iMaxVertices; else return HARD_MAX_VERTICES; } static inline int GetMaxSRgens() { if (bMaxSRgens) return iMaxSRgens; else return HARD_MAX_SRGENS; } static inline int GetMaxCohoms() { if (bMaxCohoms) return iMaxCohoms; else return HARD_MAX_COHOMS; } // Only the monomial filename and usage can be changed static inline void SetMonomialFileName(std::string &filename) { strMonomialFileName = filename; }; static inline void SetUseMonomFile(bool status) { bUseMonomFile = status; }; }; //////////////////////////////////////////////////////////////////////////////////////////////////// // The primary output macros #define CONSOLE_OUT(msg) std::cerr << msg #define CONSOLE_MSG_OUT(msg) CONSOLE_OUT(msg << std::endl) #define STATUS_OUT(msg) CONSOLE_OUT("STATUS: " << msg << "\r") #define ERR_OUT_PLAIN(msg) CONSOLE_OUT(msg << std::endl) #define ERR_OUT(errmsg) ERR_OUT_PLAIN("ERROR: " << errmsg) #define WARN_OUT(errmsg) ERR_OUT_PLAIN("WARNING: " << errmsg) #define MSG_OUT_NOENDL(msg) std::cout << msg #define MSG_OUT(msg) MSG_OUT_NOENDL(msg << std::endl) #endif cohomCalg-0.32/source/platform.h000066400000000000000000000070611322050713700166330ustar00rootroot00000000000000//////////////////////////////////////////////////////////////////////////////////////////////////// // // // platform.h +------------------------+ // // ========== | Cross platform handler | // // +------------------------+ // // Code: Benjamin Jurke, http://benjaminjurke.net // // // //////////////////////////////////////////////////////////////////////////////////////////////////// // // // File history: // // - 27.04.2010 File created as platform.h // // This file takes care of a couple of definitions and environment variables // // which are compiler and/or platform specific. // // // //////////////////////////////////////////////////////////////////////////////////////////////////// #ifndef INC_PLATFORM_H #define INC_PLATFORM_H // NOTE: I've only checked this code on MSVS2010 and Ubuntu/gcc. // We define the command save_sprintf which is the ordinary sprintf string formatting command // but with an additional buffer length check which avoids the buffer overflow errors / security leaks // quite a number of C/C++ programs suffer from. // // Following the C99 standard, a new function snprintf was introduced to take care of this issue. // However, for god-knows-why Microsoft decided to use a different name, so we are using a define to // allow for further ingenious cross-platform problems with this... // // NOTE: You still have to include to use this function... #if defined(_MSC_VER) // MS compiler (Windows) #define safe_sprintf sprintf_s #define string_to_int64(__v_val_) _atoi64(__v_val_) #define WIN32_LEAN_AND_MEAN #include inline void SleepMilliSec(unsigned long ulMilliseconds) { Sleep(ulMilliseconds); } #elif defined (__GNUC__) // gcc compiler (Unix/Linux/MacOS) #define safe_sprintf snprintf #define string_to_int64(__v_val_) atoll(__v_val_) #include inline void SleepMilliSec(unsigned long ulMilliseconds) { struct timespec req = {0}; req.tv_sec = 0; req.tv_nsec = ulMilliseconds * 1000000L; nanosleep(&req, (struct timespec *) NULL); } #else #error Unrecognized compiler. #endif // Next we have a couple of platform variables, which are just for convenience output #if defined(_WIN32) #define APP_TARGET_OS "Windows" #elif defined(__unix__) #define APP_TARGET_OS "Linux/Unix" #elif (defined(__APPLE__) && defined(__MACH__)) #define APP_TARGET_OS "MacOS X" #else #define APP_TARGET_OS "Unrecognized OS" #endif #if (defined(_M_X64) || defined(__amd64__)) #define APP_ARCH "x86-64 / 64 bit" #elif (defined(_M_IA64)) #define APP_ARCH "ia64 (Itanium) / 64 bit" #elif (defined(_M_IX86) || defined (__i386__)) #define APP_ARCH "i386 / 32 bit" #else #define APP_ARCH "Unrecognized" #endif #endif cohomCalg-0.32/source/rationals.cpp000066400000000000000000001205671322050713700173450ustar00rootroot00000000000000//////////////////////////////////////////////////////////////////////////////////////////////////// // // // rationals.cpp // // ============= // // // // Code: Benjamin Jurke, http://benjaminjurke.net // // // //////////////////////////////////////////////////////////////////////////////////////////////////// // // // File history: // // - 08.04.2010 File created as rationals.cpp // // Handles the counting of the rational functionsmology which ultimately // // yields a list of the relevant denominator monomials and their respective // // multiplicities. // // - 23.02.2010 Added multi-threading support for the computation of secondary sequences. // // // //////////////////////////////////////////////////////////////////////////////////////////////////// #include #include #include #include #include #include #include "rationals.h" #include "main.h" #include "platform.h" extern "C" { #include "polylib/polylib64.h" } using namespace std; //////////////////////////////////////////////////////////////////////////////////////////////////// string CCohomology::GetCohomologyGroupString(const vector &BundleGLSMcharges) { /* This static output function produces the string "H^i(A; O(2,3,2,4))" with the line bundle's divisor charges. */ char buf[32]; string strLine = "H^i(A; O("; for (size_t j=0; j 0) safe_sprintf(buf, sizeof(buf), ",%4d", (int) BundleGLSMcharges[j]); else safe_sprintf(buf, sizeof(buf), "%4d", (int) BundleGLSMcharges[0]); strLine += buf; } strLine += " ))"; return strLine; } string CCohomology::GetGroupDimensionsString(const std::vector &CohomologyDimensions) { /* This static output function produces the string "( 3, 2, 4, 5, 2)" of the cohomology group dimensions. */ char buf[32]; string strLine = "("; for (size_t i=0; i 0) safe_sprintf(buf, sizeof(buf), ",%4d", (int) CohomologyDimensions[i]); else safe_sprintf(buf, sizeof(buf), "%4d", (int) CohomologyDimensions[i]); strLine += buf; } strLine += " )"; return strLine; } string CCohomology::GetGroupDimensionsStringNoPadding(const std::vector &CohomologyDimensions) { /* This static output function produces the string "3,2,4,5,2" of the cohomology group dimensions without any padding as a comma-seperated list. */ char buf[32]; string strLine = ""; for (size_t i=0; i 0) safe_sprintf(buf, sizeof(buf), ",%d", (int) CohomologyDimensions[i]); else safe_sprintf(buf, sizeof(buf), "%d", (int) CohomologyDimensions[i]); strLine += buf; } return strLine; } string CCohomology::GetCohomologyString(const vector &BundleGLSMcharges, const vector &CohomologyDimensions) { /* This static output function naively connects the cohomology group string the cohomology group dimension string, yielding "H^i(A; O(2,3,2,4)) = (3,2,4,5,2)" */ return GetCohomologyGroupString(BundleGLSMcharges) + " = " + GetGroupDimensionsString(CohomologyDimensions); } string CCohomology::GetCohomologyString() const { /* This member function checks if the number of possible cohomology group dimensions is ambiguous or could not be determined at all and yields the appropiate output. */ if (IsAmbiguous()) { if (IsNotDetermined()) return CCohomology::GetCohomologyGroupString(BundleGLSMch) + " could not be determined"; else { char buf[64]; safe_sprintf(buf, sizeof(buf), " has %d ambiguous solutions", (int) CohomologyDims.size()); return CCohomology::GetCohomologyGroupString(BundleGLSMch) + buf; } } else return CCohomology::GetCohomologyString(BundleGLSMch, CohomologyDims[0]); } void CCohomology::PrintFullCohomologyMonomialMap(const CInternalData &id, bool ShortList) const { /* This wrapper function outputs the full list of contributing monomials, including the secondary/remnant cohomology factors and computed numbers rational functions. Basically, it completely shows the individual contributions to the cohomology group dimensions. */ MSG_OUT("Monomials, cohomology factors and rational functions of " << GetCohomologyString()); monoms.PrintMonomialList(id, true, true, ShortList); } void CCohomology::PrintCohomologies(const vector &cohomologies) { /* This function outputs a list of all cohomology group dimensions supplied by the argument vector. In case of ambiguous results, each possibility is listed. */ MSG_OUT("Cohomology dimensions:"); MSG_OUT("======================"); // Run through the entire argument vector size_t nCohoms = cohomologies.size(); for (size_t k=0; k 0) line = string(offset.length(), ' '); else line.assign(offset); MSG_OUT(line << " = " << GetGroupDimensionsString(cohomologies[k].CohomologyDims[i])); } } MSG_OUT(""); } } void CCohomology::SummarizeCohomologies(const vector &cohomologies) { /* This function outputs a list of lists of all cohomology group dimensions supplied by the argument vector. In case of ambiguous results an error message is places, i.e. it only treats non-ambiguous cohomology groups as "valid" output. */ // Run through the entire argument vector size_t nCohoms = cohomologies.size(); bool bAllRight = true; string out = ""; for (size_t k=0; k0) out.append(","); out.append("{{"); out.append(GetGroupDimensionsStringNoPadding(cohomologies[k].CohomologyDims[0])); out.append("},{"); size_t nContribDemons = cohomologies[k].ContributingDenoms.size(); for (size_t r=0; r 0) out.append(","); out.append(cohomologies[k].ContributingDenoms[r]); } out.append("}}"); } // Produce output if (bAllRight) MSG_OUT_NOENDL("{True," << out << "}"); else MSG_OUT_NOENDL("{False,\"Ambiguous cohomologies\""); } void CCohomology::GetMathematicaCohomologiesList(const vector &cohomologies, string &out) { /* This function translates the results of the computations, i.e. the dimensions of the line bundle sheaf cohomology groups into a form easily comparable to the condensed output of the legacy Mathematica 7 script. */ // First put out the 'LinebundleCohomologyOf' commands, which basically correspond to our // 'ambientcohom' commands and specify the line bundle divisor's charges. out = " (*Requested cohomology commands:*)\n"; char buf[64]; size_t nCohoms = cohomologies.size(); for (size_t k=0; k0) out += ","; safe_sprintf(buf, sizeof(buf), "%d", (int) cohomologies[k].BundleGLSMch[i]); out += buf; } out += "}];\n"; } // Next a list of lists containing the computed cohomology dimensions out += " ResultingCohomologies = {"; for (size_t k=0; k0) out += ","; out += "{"; if (cohomologies[k].IsAmbiguous()) { if (cohomologies[k].IsNotDetermined()) out += "-1 (*not determined*)"; else out += "-1 (*ambiguous*)"; } else { for (size_t i=0; i0) out += ","; safe_sprintf(buf, sizeof(buf), "%d", (int) cohomologies[k].CohomologyDims[0][i]); out += buf; } } out += "}"; } out += "}"; } //////////////////////////////////////////////////////////////////////////////////////////////////// void StringRemoveSpaces(string &stringIn) { size_t pos = 0; bool spacesLeft = true; while (spacesLeft) { pos = stringIn.find(" "); if(pos != string::npos) stringIn.erase(pos, 1); else spacesLeft = false; } } void CRationals::PrintPolyLibConstraintMatrix(const CInternalData &id, void *m) { /* This function prints the equalities and inequalities encoded in a PolyLib matrix structure, which is used in the debug output at the highest verbose level. */ Matrix *Mat = (Matrix *) m; char buf[128]; string tmp, cureqn, mathematica; MSG_OUT(" Condition matrix has " << Mat->NbRows << " rows x " << Mat->NbColumns << " columns"); if ((Mat->NbRows > 0) && (Mat->NbColumns > 0)) { // Run through all rows of the matrix for (unsigned int i=0; iNbRows; i++) { safe_sprintf(buf, sizeof(buf), " line %2d: ", (int) i+1); tmp = buf; // Clear the current equation buffer cureqn.clear(); if (i>0) mathematica += ","; // Check if we have an equality or inequality if (Mat->p[i][0] == 0) { // equality tmp += "eq: "; for (unsigned int j=1; jNbColumns-1; j++) { if (Mat->p[i][j] == 0) safe_sprintf(buf, sizeof(buf), " "); else { if (Mat->p[i][j] == 1) safe_sprintf(buf, sizeof(buf), "+ %-7s ", id.GetInternalCoordData()[j-1].strName.c_str()); else if (Mat->p[i][j] == -1) safe_sprintf(buf, sizeof(buf), "- %-7s ", id.GetInternalCoordData()[j-1].strName.c_str()); else if (Mat->p[i][j] < 0) safe_sprintf(buf, sizeof(buf), "- %3ld*%-3s ", (long int) -Mat->p[i][j], id.GetInternalCoordData()[j-1].strName.c_str()); else safe_sprintf(buf, sizeof(buf), "+ %3ld*%-3s ", (long int) Mat->p[i][j], id.GetInternalCoordData()[j-1].strName.c_str()); } cureqn += buf; } safe_sprintf(buf, sizeof(buf), " == %3ld", -(long int) Mat->p[i][Mat->NbColumns-1]); cureqn += buf; } else { // inquality tmp += "ineq: "; for (unsigned int j=1; jNbColumns-1; j++) { if (Mat->p[i][j] == 0) safe_sprintf(buf, sizeof(buf), " "); else { if (Mat->p[i][j] == 1) safe_sprintf(buf, sizeof(buf), "+ %-7s ", id.GetInternalCoordData()[j-1].strName.c_str()); else if (Mat->p[i][j] == -1) safe_sprintf(buf, sizeof(buf), "- %-7s ", id.GetInternalCoordData()[j-1].strName.c_str()); else if (Mat->p[i][j] < 0) safe_sprintf(buf, sizeof(buf), "- %3ld*%-3s ", (long int) -Mat->p[i][j], id.GetInternalCoordData()[j-1].strName.c_str()); else safe_sprintf(buf, sizeof(buf), "+ %3ld*%-3s ", (long int) Mat->p[i][j], id.GetInternalCoordData()[j-1].strName.c_str()); } cureqn += buf; } safe_sprintf(buf, sizeof(buf), " >= %3ld", -(long int) Mat->p[i][Mat->NbColumns-1]); cureqn += buf; } tmp += cureqn; StringRemoveSpaces(cureqn); mathematica += cureqn; MSG_OUT(tmp); } tmp = "Reduce[{"; tmp += mathematica; tmp += "},Integers]"; MSG_OUT(" Mathematica cmd: " << tmp << ""); } } struct CountRationalsData { const CInternalData &id; //const vector &coords; const i32vec64 &TargetDivisor; uint32_t &out; uint64_t monomial; //size_t numCoords; //size_t numGLSMch; bool bReturn; size_t worker_id; CountRationalsData(const CInternalData &init_InternalData, uint64_t init_monomial, const i32vec64 &init_TargetDivisor, uint32_t &init_out, size_t init_numCoords, size_t init_numGLSMch, size_t init_worker_id) : id(init_InternalData), TargetDivisor(init_TargetDivisor), out(init_out) { monomial = init_monomial; //numCoords = init_numCoords; //numGLSMch = init_numGLSMch; worker_id = init_worker_id; bReturn = false; } }; void CountRationalFunctionsWorker(void *p_dat) { /* This is the main function for the counting of rational functions. If practically serves as the wrapper from our data format to the matrix input format required by the PolyLib. */ CountRationalsData *crd = (CountRationalsData *) p_dat; if (!crd) { ERR_OUT("Internet pointer error in monomial counting worker."); return; } const vector &coords = crd->id.GetInternalCoordData(); size_t numCoords = crd->id.GetNumCoordinates(); size_t numGLSMch = crd->id.GetNumGLSMch(); // First we need to create a matrix in the PolyLib format Matrix *P = Matrix_Alloc((unsigned int) (numCoords + numGLSMch), (unsigned int) (numCoords + 2)); if (!P) { crd->bReturn = false; ERR_OUT("Internal allocation error in monomial counting worker."); return; } const size_t lastcol = numCoords + 2 - 1; i32vec64 constraint_vals; constraint_vals.Clear(); for (size_t j=0; jTargetDivisor.x[j]; // Now insert the appropiate values and signs into the matrix elements for (size_t i=0; imonomial & coords[i].liVar) { // Coordinate is in denominator for (size_t j=0; jp[j][i+1], - coords[i].GLSMch.x[j]); constraint_vals.x[j] += coords[i].GLSMch.x[j]; } } else { // Coordinate is in nominator for (size_t j=0; jp[j][i+1], coords[i].GLSMch.x[j]); } } // The first column of the matrix selects the type of the condition for (size_t j=0; jp[j][0], 0); // Put the final target charges in last column value_set_si(P->p[j][lastcol], -constraint_vals.x[j]); } // And finally we require the positivity condition on all variables for (size_t i=0; ip[numGLSMch+i][0], 1); value_set_si(P->p[numGLSMch+i][i+1], 1); } // The "universe matrix" is required by PolyLib (no idea what for....) Matrix *C = Matrix_Alloc(1, 2); value_set_si(C->p[0][0],1); value_set_si(C->p[0][1],1); /* THIS VERBOSE OUTPUT WAS SHIFTED BEHIND THE COMPUTATION if (ccmdlinearguments::getverboselevel() >= 5) { string tmp = "verbose level 6: rationals counting condition matrix for " + id.int64tomonomial(monomial) + ":"; msg_out(tmp); string tmp2(tmp.length(), '-'); msg_out(tmp2); printpolylibconstraintmatrix(id, p); } */ // Compute a polynomial approximation of the Ehrhart polynomial and evaluate Matrix *Validity_Lattice = 0; Enumeration *e = Ehrhart_Quick_Apx(P, C, &Validity_Lattice, 0); // Now we need to retrieve the actually interesting data, which is at the moment completely // idiotically 'solved'. Why is there no function to simply extract the constant part of an e_value? // Furtunately, this does not present a bottleneck to the computational speed, but it's ugly like hell... long long int val = 0; if (e) { // Brrr.... temporary files for data retrieval... Oh - and we can't use tmpfile() because // Microsoft in their infinite wisdom "broke" the command in Windows Vista / 7, as the default // destination is only accessible in Administrator-mode... char tmpfilename[64]; safe_sprintf(tmpfilename, sizeof(tmpfilename), "__x_TMP_polylib_file_%dy.tmp", (int) crd->worker_id); //const char *tmpfilename = "__x_TMP_polylib_file_y.tmp"; FILE *points_val = fopen(tmpfilename, "w+"); if (!points_val) { ERR_OUT("Could not open temporary file for computation."); crd->bReturn = false; return; } for (Enumeration *en=e; en; en = en->next) print_evalue(points_val, &en->EP, NULL); rewind(points_val); char buf[16]; int readres = fscanf(points_val, "%c %lld", buf, &val); fclose(points_val); remove(tmpfilename); if (readres < 2) { ERR_OUT("INTERNAL: Failed to scan the PolyLib result."); crd->bReturn = false; return; } } else { WARN_OUT("Counting of the rationals erroneous - is your input geometry valid?"); // During a normal program run, we have the warning output, but in integration mode we treat this as a serious error if (CCmdLineArguments::GetVerboseLevel() < -5) crd->bReturn = false; return; } // The variable 'val' now holds our precious number of rational functions // A result -1 indicates some serious error in the constraints and therefore in // the counting of the rational functions / points in the corresponding polyhedron if (val < 0) { ERR_OUT("INTERNAL: Invalid number of rational functions computed."); crd->bReturn = false; return; } // Debug Output /* if (CCmdLineArguments::GetVerboseLevel() >= 5) { string tmp; bool bPrint = true; if (val != 0) tmp = "verbose level 5: rationals counting condition matrix for " + crd->id.Int64ToMonomial(monomial) + ":"; else if (CCmdLineArguments::GetVerboseLevel() >= 6) tmp = "verbose level 6: rationals counting condition matrix for " + id.Int64ToMonomial(monomial) + ":"; else bPrint = false; if (bPrint) { MSG_OUT(tmp); string tmp2(tmp.length(), '-'); MSG_OUT(tmp2); PrintPolyLibConstraintMatrix(id, P); MSG_OUT(" Yields value: " << val); MSG_OUT(""); } }*/ // Clean up stuff Matrix_Free(C); Matrix_Free(P); while (e) { free_evalue_refs(&(e->EP)); Polyhedron_Free(e->ValidityDomain); Enumeration *en = e->next; free(e); e = en; } // Store the computed value crd->out = (uint32_t) val; crd->bReturn = true; } std::vector< std::pair > CRationals::WorkersList; //#define USE_MULTITHREADED_MONOMIAL_COUNTING // It appears that the PolyLib is NOT thread-safe (causing a weird kind of heap corruption), therefore for the moment we are stuck with a single-threaded evaluation of the rational counting... :-( #ifdef USE_MULTITHREADED_MONOMIAL_COUNTING bool CRationals::CountRationalFctns(const CInternalData &id, uint64_t monomial, const i32vec64 &TargetDivisor, uint32_t &out) { CountRationalsData *crd = new CountRationalsData(id, monomial, TargetDivisor, out, id.GetInternalCoordData().size(), id.GetNumGLSMch(), WorkersList.size()); if (!crd) return false; tthread::thread *t = new tthread::thread(CountRationalFunctionsWorker, (void*) crd); WorkersList.push_back(make_pair(t, crd)); return true; } bool CRationals::WaitForAllWorkersFinish() { while (WorkersList.size() > 0) { WorkersList[0].first->join(); if (!(((CountRationalsData *) WorkersList[0].second)->bReturn)) return false; delete WorkersList[0].second; // free the thread data memory delete WorkersList[0].first; // delete the thread WorkersList.erase(WorkersList.begin()); } return true; } #else bool CRationals::CountRationalFctns(const CInternalData &id, uint64_t monomial, const i32vec64 &TargetDivisor, uint32_t &out) { CountRationalsData crd = CountRationalsData(id, monomial, TargetDivisor, out, id.GetInternalCoordData().size(), id.GetNumGLSMch(), 0); CountRationalFunctionsWorker(&crd); return crd.bReturn; } bool CRationals::WaitForAllWorkersFinish() { return true; } #endif void SplitAddToCohomVector(vector &inout, const vector &split, uint32_t rational, size_t dim) { /* This internal helper functions carries out the branching required for the ultimate attempt to resolve the ambiguous contribution. It takes a vector of possible cohomology group dimensions and a vector of fixes for a particular contribution. Then all those different candidates are applied to all possibilities, which lets the list of all possibilities grow pretty fast. Currently, this is a somewhat of a big problem, as it represents the only real "memory hole" in the entire program. */ size_t inoutlen = inout.size(); size_t splitlen = split.size(); ui32vec64 newcohom; newcohom.Clear(); for (size_t i=0; i &out_cohomology, vector &out_contribcohoms) { /* Now, this is the big fat mama of all functions. It takes the monomial list and the line bundle's divisor charges as input and computes the corresponding dimensions of the cohomology. Now, we have to keep in mind that there still may be ambiguous contributions left over. First we simple count the number of rational functions for all those ambiguous cases. If all goes well, none of these troublesome monomials actually contributes for real - we can then compute the uniquely determined contributions and are all done. This is the nice case. The second attempt is to compute the ambiguous contributions for the Serre-dual divisor and hope that all of these are actually zero - then we can simply take the dimensions from the Serre-dual and are done. In the worst case, neither the "normal" nor "Serre-dual" ambiguities vanish all at the same time. Then we have to take the ugly branch approach, where we compute the set of ALL possible cohomology group configurations both for the "normal" and Serre-dual case and check if there are compatible pairs. This may ultimately lead to the ambiguous or undeterminant cases. Luckily, this does not happen very often.... */ size_t dim = id.GetDimension(); out_cohomology.clear(); out_cohomology.resize(dim+1); out_contribcohoms.clear(); // Now compute the ambiguous contributions - if any is non-zero we have to take more involved steps bool bIsUnique = true; for (map::iterator it = ml.ambiguous_monoms.begin(); it != ml.ambiguous_monoms.end(); it++) if (!CountRationalFctns(id, it->first, TargetDivisor, it->second.nRationals)) return false; if (!WaitForAllWorkersFinish()) return false; for (map::iterator it = ml.ambiguous_monoms.begin(); it != ml.ambiguous_monoms.end(); it++) { if (it->second.nRationals != 0) bIsUnique = false; } if (bIsUnique) { // So, there a no contributing non-ambiguous factors - Whohoo! // Then compute the unique ones and output for (map::iterator it = ml.unique_monoms.begin(); it != ml.unique_monoms.end(); it++) if (!CountRationalFctns(id, it->first, TargetDivisor, it->second.nRationals)) return false; if (!WaitForAllWorkersFinish()) return false; for (map::iterator it = ml.unique_monoms.begin(); it != ml.unique_monoms.end(); it++) { out_cohomology[it->second.Cohom.nGroup] += it->second.Cohom.nFactor * it->second.nRationals; if (it->second.nRationals != 0) { char buf[32]; string tmp = "{"; safe_sprintf(buf, sizeof(buf), "%d,", it->second.Cohom.nGroup); tmp += buf; safe_sprintf(buf, sizeof(buf), "%d*", it->second.Cohom.nFactor); tmp += buf; tmp += id.Int64ToCoordProduct(it->first); tmp += "}"; out_contribcohoms.push_back(tmp); } } return true; } ///////////////////////////////////////////////////////// // If we have a non-unique situation, compute the rationals for the Serre dual target divisor i32vec64 vDualCharges; id.GetCanonicalDivisor(vDualCharges); size_t numGLSMch = id.GetNumGLSMch(); for (size_t i=0; i::iterator it = ml.unique_monoms.begin(); it != ml.unique_monoms.end(); it++) if (!CountRationalFctns(id, it->first, vDualCharges, it->second.nRationalsDual)) return false; if (!WaitForAllWorkersFinish()) return false; bool bDualIsUnique = true; for (map::iterator it = ml.ambiguous_monoms.begin(); it != ml.ambiguous_monoms.end(); it++) if (!CountRationalFctns(id, it->first, vDualCharges, it->second.nRationalsDual)) return false; if (!WaitForAllWorkersFinish()) return false; for (map::iterator it = ml.ambiguous_monoms.begin(); it != ml.ambiguous_monoms.end(); it++) { if (it->second.nRationalsDual != 0) bDualIsUnique = false; } if (bDualIsUnique) { // So, there a no contributing non-ambiguous factors in the Serre dual - (little Whohoo!) // Compute the unique cases of the Serre-dual, and translate to the "normal" case for output for (map::iterator it = ml.unique_monoms.begin(); it != ml.unique_monoms.end(); it++) { out_cohomology[dim-it->second.Cohom.nGroup] += it->second.Cohom.nFactor * it->second.nRationalsDual; if (it->second.nRationalsDual != 0) { char buf[32]; safe_sprintf(buf, sizeof(buf), "%d*", it->second.Cohom.nFactor); string tmp = buf; tmp += id.Int64ToCoordProduct(it->first); out_contribcohoms.push_back(tmp); } } return true; } ///////////////////////////////////////////////////////// // At this point, it'll get complicated - BOTH the "normal" and "dual" cases are NOT unique... // First compute the needed unique normal rationals (those are still left open, when we reach here) for (map::iterator it = ml.unique_monoms.begin(); it != ml.unique_monoms.end(); it++) if (!CountRationalFctns(id, it->first, TargetDivisor, it->second.nRationals)) return false; if (!WaitForAllWorkersFinish()) return false; // Now everything is computed (unique/ambiguous contribution for the "normal" and Serre-dual), so we have to // figure out how it all fits together. // The basic idea is to compute ALL potential output cohomologies, which arise from the ambiguos contributions // both on the "normal" and "dual" side and then consider the "intersection" of those cohomologies. Yes, this is // very ugly, but at the moment, it seems to be the best we can do... // Compute the unique part of all cohomologies, this is basically the starting point for our "ambiguity branching". // For speedup, we now use fixed width array of integers... it's somewhat memory wasteful, but considerably faster ui32vec64 cohom_dummy, dualcohom_dummy; cohom_dummy.Clear(); dualcohom_dummy.Clear(); for (map::iterator it = ml.unique_monoms.begin(); it != ml.unique_monoms.end(); it++) { cohom_dummy.x[it->second.Cohom.nGroup] += it->second.Cohom.nFactor * it->second.nRationals; dualcohom_dummy.x[it->second.Cohom.nGroup] += it->second.Cohom.nFactor * it->second.nRationalsDual; } vector cohoms(1, cohom_dummy); vector dualcohoms(1, dualcohom_dummy); // Now loop through the ambiguous part and branch to all possibilities // ############################################## // ### THIS IS EXTREMELY MEMORY EXPENSIVE!!!! ### ...and a potential memory hole! IMPROVE! // ############################################## for (map::iterator it = ml.ambiguous_monoms.begin(); it != ml.ambiguous_monoms.end(); it++) { size_t curCohomsSize = cohoms.size(); size_t curDualCohomsSize = dualcohoms.size(); // We put the actual branching and check for the looming std::bad_alloc exception, which comes up when we run // out of memory. Least we can do in this case is to provide some output of how far we got, but unfortunately, // this ends our business... try { if (it->second.nRationals != 0) { SplitAddToCohomVector(cohoms, it->second.vCohoms, it->second.nRationals, dim); // Is this safe? ###################### //char buf[32]; //safe_sprintf(buf, "%ud*", it->second.Cohom.nFactor); string tmp = "(*Ambiguous*)"; tmp += id.Int64ToCoordProduct(it->first); out_contribcohoms.push_back(tmp); } curCohomsSize = cohoms.size(); if (it->second.nRationalsDual != 0) SplitAddToCohomVector(dualcohoms, it->second.vCohoms, it->second.nRationalsDual, dim); } catch(std::bad_alloc &er) { ERR_OUT("RUNTIME: " << er.what()); ERR_OUT_PLAIN("Due to the ambiguity branching there are at least " << curCohomsSize << " \"normal\" cohomologies"); ERR_OUT_PLAIN("and " << curDualCohomsSize << " Serre-dual cohomologies, consuming " << BytesToReadableSize((curCohomsSize + curDualCohomsSize) * sizeof(ui32vec64)) << " memory."); ERR_OUT_PLAIN(""); if (sizeof(void *) < 8) { ERR_OUT_PLAIN("You could try the same computation again using the 64-bit version of the program."); ERR_OUT_PLAIN(""); } return false; } } // OK, the hard part is now done, apparently, we did not run out of memory... size_t numcohoms = cohoms.size(); size_t numdualcohoms = dualcohoms.size(); if (CCmdLineArguments::GetVerboseLevel() >= 2) { MSG_OUT("Verbose level 2: Serre dualization information:"); MSG_OUT("-----------------------------------------------"); MSG_OUT(" Due to the ambiguous contributions to the requested cohomologies the following branching occurred:"); MSG_OUT(" - \"normal\" configurations: " << numcohoms << " (" << BytesToReadableSize(numcohoms * sizeof(ui32vec64)) << " memory)"); MSG_OUT(" - Serre-dual configurations: " << numdualcohoms << " (" << BytesToReadableSize(numdualcohoms * sizeof(ui32vec64)) << " memory)"); MSG_OUT(""); } // Now find the "Serre-dual intersection" of the computed branching sets vector stablecohoms; for (size_t i=0; i &out_cohomology, vector &out_contribcohoms) { /* This funcion takes care of the optional Serre-duality check, which is however only carried out in case that the results from the "normal" cohomology are unique. Otherwise the Serre-duality is already used in the determination of the result cohomologies. */ if (!ComputeCohomology(id, ml, TargetDivisor, out_cohomology, out_contribcohoms)) return false; // Check if the Serre-duality check is activated... if (CCmdLineArguments::GetCheckSerre()) { size_t dim = id.GetDimension(); if (out_cohomology.size() == dim+1) { // A unique cohomology was identified, so consider the Serre-dual divisor i32vec64 SerreDualDivisor; id.GetCanonicalDivisor(SerreDualDivisor); size_t numGLSMch = id.GetNumGLSMch(); for (size_t i=0; i dual_cohom; vector dual_contribcohoms; if (!ComputeCohomology(id, ml, SerreDualDivisor, dual_cohom, dual_contribcohoms)) return false; if (dual_cohom.size() == dim+1) { // If the Serre-dual cohomology could also be determined uniquely, compare for (size_t i=0; i<=dim; i++) { if (out_cohomology[i] != dual_cohom[dim-i]) { // Print a message, if the cohomology does not correspond properly.. vector div; div.assign(TargetDivisor.x, TargetDivisor.x + numGLSMch); MSG_OUT("WARNING: The req. cohomology " << CCohomology::GetCohomologyString(div, out_cohomology) << " does not correspond"); div.assign(SerreDualDivisor.x, SerreDualDivisor.x + numGLSMch); MSG_OUT("to the Serre dual cohomology " << CCohomology::GetCohomologyString(div, dual_cohom) << "."); return false; } } } else { vector div; div.assign(SerreDualDivisor.x, SerreDualDivisor.x + numGLSMch); MSG_OUT("WARNING: The Serre dual cohomology " << CCohomology::GetCohomologyGroupString(div) << " could not"); MSG_OUT("uniquely be determined. Please check this case manually."); return false; } } else { vector div; div.assign(TargetDivisor.x, TargetDivisor.x + id.GetNumGLSMch()); MSG_OUT("WARNING: The cohomology " << CCohomology::GetCohomologyGroupString(div) << " could not"); MSG_OUT("uniquely be determined. Please check this case manually."); return false; } } return true; } bool CRationals::ComputeCohomologies(const CInternalData &id, const CMonomialsList &ml, vector &out_cohomologies) { /* This function makes a batch run through all the requested line bundle divisors specified by the input data. The computed data is then stored in an output vector of CCohomology classes. */ // Clear the output vector out_cohomologies.clear(); size_t numGLSMch = id.GetNumGLSMch(); size_t numCohoms = id.GetNumTargetDivisors(); // Run through all the requested line bundle divisors for (size_t i=0; i cohomdims; if (!ComputeCohomologyAndSerreDual(id, curcohom.monoms, curtargetdiv, cohomdims, curcohom.ContributingDenoms)) return false; // Sort the data properly into the CCohomology structure size_t numentries = cohomdims.size(); size_t dim = id.GetDimension(); if (numentries == dim+1) { // This indicates a non-ambiguous result curcohom.CohomologyDims.push_back(cohomdims); } else if (numentries >= dim+2) { if (numentries == (cohomdims[dim+1] * (dim+1) + 1)) { // So we have cohomdims[dim+1] results vector tmp(cohomdims.begin(), cohomdims.begin() + dim + 1); curcohom.CohomologyDims.push_back(tmp); for (size_t j=1; j #include #include #include #include "iohandler.h" #include "secondarycohom.h" //////////////////////////////////////////////////////////////////////////////////////////////////// // In this file we take the list of monomials and secondary cohomology factors determined earlier // and count the number of rational functions with the appropiate variables in the numerator and // denominator. More precisely, this problem can be reformulated as a underdetermined linear system // of equations, which is solved over the positive integers. Therefore the counting of rational // functions is equivalent to counting the number of integer lattice points inside a corresponding // polyhedron determined by those constraints. We rely on the freely available PolyLib library for // the task of counting those integers, which makes use of the theory of Ehrhard polynomials. // // As for the data structures used in this class: The class CCohomology is the "result" class, which // contains the requested charges of the divisor determining the line bundle O(D) again and of // course the computed dimensions of the cohomology classes H^i(X;O(D)). // // The actual computations are carried out in the CRationals class, which basically serves as a // wrapper for the PolyLib and translates our data format appropiately. class CCohomology { friend class CRationals; private: // The output data std::vector BundleGLSMch; // determines divisor D of line bundle O(D) std::vector > CohomologyDims; // contains (candidate) dimensions of H^i(X;O(D)) std::vector ContributingDenoms; // contains a vector of contributing denominator monomials CMonomialsList monoms; // contains all monomials and their contributions to the results public: // Output functions static std::string GetCohomologyGroupString(const std::vector &BundleGLSMcharges); static std::string GetGroupDimensionsString(const std::vector &CohomologyDimensions); static std::string GetGroupDimensionsStringNoPadding(const std::vector &CohomologyDimensions); static std::string GetCohomologyString(const std::vector &BundleGLSMcharges, const std::vector &CohomologyDimensions); std::string GetCohomologyString() const; void PrintFullCohomologyMonomialMap(const CInternalData &id, bool ShortList) const; static void PrintCohomologies(const std::vector &cohomologies); static void SummarizeCohomologies(const std::vector &cohomologies); static void GetMathematicaCohomologiesList(const std::vector &cohomologies, std::string &out); // Data retrieval inline bool IsAmbiguous() const { return (CohomologyDims.size() != 1); }; inline bool IsNotDetermined() const { return (CohomologyDims.size() < 1); }; }; class CRationals { private: static std::vector< std::pair > WorkersList; // contains the list of worker threads; static bool WaitForAllWorkersFinish(); private: static void PrintPolyLibConstraintMatrix(const CInternalData &id, void *m); static bool CountRationalFctns(const CInternalData &id, uint64_t monomial, const i32vec64 &TargetDivisor, uint32_t &out); static bool ComputeCohomology(const CInternalData &id, CMonomialsList &ml, const i32vec64 &TargetDivisor, std::vector &out_cohomology, std::vector &out_contribcohoms); static bool ComputeCohomologyAndSerreDual(const CInternalData &id, CMonomialsList &ml, const i32vec64 &TargetDivisor, std::vector &out_cohomology, std::vector &out_contribcohoms); public: static bool ComputeCohomologies(const CInternalData &id, const CMonomialsList &ml, std::vector &out_cohomologies); }; #endifcohomCalg-0.32/source/secondarycohom.cpp000066400000000000000000000743561322050713700203720ustar00rootroot00000000000000//////////////////////////////////////////////////////////////////////////////////////////////////// // // // secondarycohom.cpp // // ================== // // // // Code: Benjamin Jurke, http://benjaminjurke.net // // // //////////////////////////////////////////////////////////////////////////////////////////////////// // // // File history: // // - 04.04.2010 File created as secondarycohom.cpp // // Handles the computations of the secondary cohomology which ultimately // // yields a list of the relevant denominator monomials and their respective // // multiplicities. // // // //////////////////////////////////////////////////////////////////////////////////////////////////// #include #include #include #include #include #include "secondarycohom.h" #include "main.h" #include "platform.h" using namespace std; //////////////////////////////////////////////////////////////////////////////////////////////////// #define TRAVERSE_SMP_THRESHOLD 8192 #define INSERTION_BUFFERSIZE (1024*1024) // Size of the insertion buffer window length #define MONOMIAL_MAP_MAX_FULL_OUTPUT 250 // Max. number of monomials printed with shorten_output //////////////////////////////////////////////////////////////////////////////////////////////////// void CSecondaryCohomology::Clear() { insertion_prototype.Clear(0); unique_monoms.clear(); min_c_deg = 0; max_c_deg = 0; len_c_deg = 0; monoms.Clear(); } CSecondaryCohomology::CSecondaryCohomology() { Clear(); } string CSecondaryCohomology::Print2ndSeq(const MonomData &mondat, int32_t min_out, int32_t max_out) { /* This output function prints the C-degrees of a secondary/remnant sequence in the range C^min_out to C^max_out. The output range values are checked for validity. Zero C-degrees in this list are replaced by spaces to make tabular output possible. */ string strTmp; char buf[64]; // Check the C-degree range if (min_out < min_c_deg) min_out = min_c_deg; if (max_out > max_c_deg) max_out = max_c_deg; // Loop through the range and print any non-zero C-degree, otherwise spaces for (int32_t j=min_out; j<=max_out; j++) { safe_sprintf(buf, sizeof(buf), "C^%d=%lld ", (int) j, (long long int) mondat.c[j-min_c_deg]); if (mondat.c[j-min_c_deg] != 0) strTmp += buf; else strTmp += string(strlen(buf), ' '); } return strTmp; } string CSecondaryCohomology::Print2ndSeq(const MonomData &mondat) { /* This output functions prints the C-degrees of the secondary/remnant sequence starting with the first and ending with the last non-zero C-degree. Note that this is NOT suitable for tabular output. */ size_t seq_start, seq_end; if (GetIntSequenceStartEnd(mondat.c, seq_start, seq_end)) return Print2ndSeq(mondat, (int32_t) seq_start+min_c_deg, (int32_t) seq_end+min_c_deg); else return "zero sequence"; } string CSecondaryCohomology::PrintMonomialWith2ndSeq(const CInternalData &id, MonomMap::const_iterator monom, int32_t min_out, int32_t max_out) { /* This output function prints the monomial (and potentially the internal bit-mask), determines the length of the non-zero part of the C-degrees and prints the range of C-degrees from min_out to max_out. */ char buf[64]; size_t seq_start = 0, seq_end = 0; safe_sprintf(buf, sizeof(buf), " with %4ld total (len %2d): ", (long int) monom->second.num, (int) (seq_end - seq_start + 1)); // Check if we have a zero sequence if (GetIntSequenceStartEnd(monom->second.c, seq_start, seq_end)) return id.Int64ToMonomialPadded(monom->first) + buf + Print2ndSeq(monom->second, min_out, max_out); else return id.Int64ToMonomialPadded(monom->first) + buf + "zero sequence"; } void CSecondaryCohomology::PrintMonomMap(const CInternalData &id, bool shorten_output) { /* This output function prints the entire monomial map in tabular form. Only the necessary part of the secondary/remnant sequences is printed. Furthermore an automatic shortening of excessive large outputs can be activated. */ // Determine the smallest and highest non-trivial c-degree in the entire list int32_t min_deg = len_c_deg; int32_t max_deg = 0; for (MonomMap::const_iterator set_iter = unique_monoms.begin(); set_iter != unique_monoms.end(); set_iter++) { int32_t i; // Check FORWARDS from the beginning for (i = 0; isecond.c[i] != 0) { min_deg = i; break; } } // Check BACKWARDS from the end for (i = len_c_deg-1; i >= max_deg; i--) { if (set_iter->second.c[i] != 0) { max_deg = i+1; break; } } } min_deg += min_c_deg; max_deg += min_c_deg; // Now print the monomials size_t numelems = unique_monoms.size(); MonomMap::const_iterator set_iter = unique_monoms.begin(); MSG_OUT("There are " << numelems << " elements in the monomial map (using " << (len_c_deg * sizeof(int64_t) * numelems + sizeof(int64_t) + sizeof(uint64_t)) << " bytes of memory):"); for (size_t i=0; i MONOMIAL_MAP_MAX_FULL_OUTPUT) { if ((i >= 50) && (i < numelems - 50)) { MSG_OUT("(.....)"); i = numelems - 50; } } } } } bool CSecondaryCohomology::IsSequenceExact(const vector &seq, size_t &pos_out) const { /* This computational helper function checks a arbitrary length sequence for naive exactness. It also computes the naive kernel via the alternating sum method from the end and put out a potential repair position in case of non-exactness. */ size_t seqlen = seq.size(); if (seqlen > 0) { int64_t kernel = seq[seqlen-1]; for (size_t i=0; i &buffer, MonomMap &unique_monoms, size_t max_run, MonomData &insertion_prototype, int min_c_deg) { /* This internal helper function flushes the monomial insertion buffer. As the monomials are kept in an associate list, it helps to presort the monomials, such that the number of look-ups in the associative index is minimized. */ if (max_run > 0) { // Sort the insertion buffer sort(buffer.begin(), buffer.begin()+max_run); // The first one we have to get by hand pair ret = unique_monoms.insert(pair(buffer[0].monomial, insertion_prototype)); ret.first->second.num++; ret.first->second.c[buffer[0].nka - min_c_deg]++; // Now loop through the buffer for (size_t i=1; ifirst != buffer[i].monomial) ret = unique_monoms.insert(pair(buffer[i].monomial, insertion_prototype)); // Increase data ret.first->second.num++; ret.first->second.c[buffer[i].nka - min_c_deg]++; } } } struct TraverseWorkerData { unsigned int worker_id; MonomMap unique_monoms; vector vBuffer; uint64_t window_start, window_end, window_width, buffer_runs; MonomData *insertion_prototype; int32_t min_c_deg; vector SRunion[4]; vector *Status; }; void TraverseWorkerFunction(void *p_dat) { TraverseWorkerData *wd = (TraverseWorkerData *) p_dat; FastMonomialData *pbuf; // This is the expensive main loop for (uint64_t buffer_loop = 0; buffer_loop < wd->buffer_runs; buffer_loop++) { uint64_t window_start = wd->window_start + buffer_loop * INSERTION_BUFFERSIZE; uint64_t window_end = window_start + INSERTION_BUFFERSIZE - 1; if (window_end > wd->window_end) window_end = wd->window_end; pbuf = &wd->vBuffer[0]; for (uint64_t sr_combi=window_start; sr_combi<=window_end; sr_combi++, pbuf++) { uint64_t genunion = wd->SRunion[0][sr_combi & 0xffffu] | wd->SRunion[1][(sr_combi >> 16) & 0xffffu] | wd->SRunion[2][(sr_combi >> 32) & 0xffffu] | wd->SRunion[3][(sr_combi >> 48) & 0xffffu]; pbuf->monomial = genunion; pbuf->nka = CBits::CountBits(genunion) - CBits::CountBits(sr_combi); } SortAndFlushBuffer(wd->vBuffer, wd->unique_monoms, (size_t) (window_end-window_start + 1), *wd->insertion_prototype, wd->min_c_deg); // Show some progress status output (*wd->Status)[wd->worker_id] = (double) (window_end - wd->window_start) / wd->window_width; } } struct StatusWorkerData { vector *status; clock_t start; bool Run; }; void StatusOutputWorker(void *p_dat) { StatusWorkerData *wstat = (StatusWorkerData *) p_dat; if (!wstat) return; while (wstat->Run) { double dTotal = 0.0; for (size_t i=0; istatus->size(); i++) dTotal += (*wstat->status)[i]; dTotal /= wstat->status->size(); double dSecElapsed = (double) (clock() - wstat->start) / CLOCKS_PER_SEC; double dSecRemaining = (dTotal > 0.0) ? ((1.0 - dTotal) / dTotal) * dSecElapsed : 1.0; dTotal *= 100; char buf[64]; safe_sprintf(buf, sizeof(buf), "%.2f", dTotal); CONSOLE_OUT(" " << buf << "% completed (" << SecondsToTime((clock_t) dSecRemaining) << " remaining)..."); CONSOLE_OUT(" \r"); SleepMilliSec(100); } delete wstat; } bool CSecondaryCohomology::TraverseSRpowerset(const CInternalData &id) { /* This is the main powerset traverse function, which loops through the entire range of subsets of the Stanley-Reisner generators and computes the corresponding monomial unions as well as the secondary/remnant sequences. */ // As an enormous speedup, we are using a union buffer analogous to the counting of the bits // Since we are dealing with 64 bit variables, we are using 4 bit buffer for 16-bit blocks, such // that the buffer size is 4*8*64 KB = 2 MBr. Note that this buffer has to be allocated // dynamically, otherwise the MS VS compiler throws a stack overflow in debug mode. // Prepare and setup the worker threads unsigned int numWorkers = thread::hardware_concurrency(); if (numWorkers == 0) numWorkers = 4; // Compute the maximal SR bitmask value and the number of buffer runs size_t number_of_srgens = id.GetNumSRgens(); uint64_t sr_powerset_max = (0x1ull << number_of_srgens); if (sr_powerset_max < TRAVERSE_SMP_THRESHOLD) numWorkers = 1; uint64_t sr_powerset_max_per_worker = sr_powerset_max / numWorkers; // Allocate the insertion buffer (typically around 12-16 MB) TraverseWorkerData *workerdat = new TraverseWorkerData[numWorkers]; vector paddedSRvec(id.GetSRgens()); paddedSRvec.resize(64, 0); vector WorkerStatus; WorkerStatus.resize(numWorkers, 0.0); for (unsigned int k = 0; k < numWorkers; k++) { workerdat[k].vBuffer.resize(INSERTION_BUFFERSIZE); workerdat[k].window_start = k*sr_powerset_max_per_worker; workerdat[k].worker_id = k; workerdat[k].window_end = (k+1)*sr_powerset_max_per_worker - 1; if (k==numWorkers-1) workerdat[k].window_end = sr_powerset_max - 1; workerdat[k].window_width = workerdat[k].window_end - workerdat[k].window_start + 1; workerdat[k].buffer_runs = workerdat[k].window_width / INSERTION_BUFFERSIZE; if (workerdat[k].window_width % INSERTION_BUFFERSIZE != 0) workerdat[k].buffer_runs++; workerdat[k].insertion_prototype = &insertion_prototype; workerdat[k].min_c_deg = min_c_deg; workerdat[k].Status = &WorkerStatus; // Init the worker buffer for (size_t i=0; i<4; i++) { workerdat[k].SRunion[i].resize(0x1u << 16); for (size_t j=0; j<(0x1u << 16); j++) { uint64_t combi = j << (i*16); uint64_t genunion = 0; for (size_t k=0; k<16; k++) { if (combi & (0x1ull << (k + i*16))) genunion |= paddedSRvec[k + i*16]; } workerdat[k].SRunion[i][j] = genunion; } } } paddedSRvec.clear(); // Start the workers vector worker_threads; for (size_t k = 0; kRun = true; wstat->status = &WorkerStatus; wstat->start = clock(); thread *stat = new thread(StatusOutputWorker, wstat); // Wait for the threads to complete... for (size_t k = 0; kjoin(); delete worker_threads[k]; } wstat->Run = false; // Piece together the individually generated data unique_monoms.clear(); for (size_t k = 0; k ret = unique_monoms.insert(pair(it->first, it->second)); if (ret.second==false) { size_t chain_len = it->second.c.size(); ret.first->second.num += it->second.num; for (size_t r = 0; r < chain_len; r++) ret.first->second.c[r] += it->second.c[r]; } it++; } } CONSOLE_OUT(string(75, ' ') << "\r"); return true; } bool CSecondaryCohomology::Compute2ndCohomFromTrivialSequences() { /* After generating the secondary/remnant sequences, the secondary/remnant "cohomology" has to be computed from this data. However, lacking a proper description of the mappings one has to take a couple of assumptions and employ the Serre-duality to resolve a couple of ambiguities. For now, we are taking a two-step scan through the entire range of the computed monomials, where in the first one we are simply removing the trivial cases: If only a single number is not equal to 0, the sequence is non-exact, but the remnant cohomology is obvious. Furthermore, we remove all obviously exact sequence, which is quickly checked by computing the alternating sum. */ MonomMap::iterator cur = unique_monoms.begin(); while (cur != unique_monoms.end()) { if (cur->second.num == 1) { // Take care of a sequence containing just a single value 1 for (size_t i=0; isecond.c[i] != 0) { if (!monoms.AddUniqueContribution(cur->first, (int32_t) i+min_c_deg, 1)) return false; break; } } unique_monoms.erase(cur++); } else { // Compute the alternating sum of the secondary/remnant sequence int64_t altersum = 0; for (size_t i=0; isecond.c[i]; else altersum -= cur->second.c[i]; } if (altersum == 0) { // Sequence is exact, so discard unique_monoms.erase(cur++); } else { // Sequence is non-exact & non-trivial, so keep the altersum value AND compute the sequence length uint32_t seq_start = len_c_deg; for (uint32_t i=0; isecond.c[i] != 0) { seq_start = i; break; } } uint32_t seq_end = 0; for (uint32_t i=len_c_deg-1; i>=0; i--) { if (cur->second.c[i] != 0) { seq_end = i; break; } } uint32_t seq_len = seq_end - seq_start + 1; if (seq_len < 1) { // This would imply a complete zero sequence! ERR_OUT("Internal error while computing secondary cohomology."); return false; } // Take care of special length switch (seq_len) { case 1: // Sequence has a single non-zero value if (!monoms.AddUniqueContribution(cur->first, seq_start+min_c_deg, (uint32_t) cur->second.c[seq_start])) return false; break; default: // Otherwise, store the alternating sum value cur->second.altersum = altersum; cur++; } } } } return true; } bool CSecondaryCohomology::Compute2ndCohomFromSequences(const CInternalData &id) { /* In the second part of the secondary/remnant cohomology computation, we are taking care of the non-trivial cases remaining. In principle this procedure is suitable for all cases, however, it is somewhat more expensive, therefore the first run to remove the "obvious" secondary/remnant sequences. The basic idea is to "repair" the secondary sequence in the C-degree range of 0...dim in order to make it exact again. The repair value and its possible positions then yield the cohomology of this sequence. On the other hand, this is ultimately the origin of the troublesome ambiguities, which can only be properly removed by understanding the mappings between the C-degrees. */ // The temporary "repair" storage vector fixes; // Loop through all remaining monomials in the list size_t variety_dim = id.GetDimension(); MonomMap::iterator cur = unique_monoms.begin(); while (cur != unique_monoms.end()) { if (cur->second.altersum != 0) { uint64_t absaltersum = abs(cur->second.altersum); fixes.clear(); // Search for the the C-degrees in range, which is >= the absolute value of the // alternating sum of the sequence, which measures the "total failure" exactness for (unsigned int j=0; j<=variety_dim; j++) { if (cur->second.c[j-min_c_deg] >= absaltersum) { // Now descrease the value of this position by the absolute value of the // alternating sum and check, if this makes the sequence exact vector tempseq(cur->second.c); tempseq[j-min_c_deg] -= absaltersum; size_t dummy; if (IsSequenceExact(tempseq, dummy)) { // If exactness can be restored this way, the cohomology group at the // respective repair position has the dimension of the absolute value // of the alternating sum - we therefore store this fix as a candidate CohomContrib newfix; newfix.nGroup = j; newfix.nFactor = (uint32_t) absaltersum; fixes.push_back(newfix); } } } // Check if we have obtained at least one "repair" value / secondary cohomology group size_t num_fixes = fixes.size(); if (num_fixes < 1) { // This should NEVER happen, but is potentially possible, as the // repair range is restricted to 0...dim instead of the total sequence ERR_OUT("FATAL: Could no properly resolve the exactness of a secondary sequence"); MSG_OUT(Print2ndSeq(cur->second)); return false; } // Now, do we have multi-contributions or not? if (num_fixes > 1) { // Ambiguous contribution we have to take care of lateron if (!monoms.AddAmbiguousContribution(cur->first, fixes)) return false; } else { // Unique contribution... that's fine if (!monoms.AddUniqueContribution(cur->first, fixes[0].nGroup, fixes[0].nFactor)) return false; } } unique_monoms.erase(cur++); } // At this point there should be no more monomials left, but check anyway if (unique_monoms.size() > 0) { ERR_OUT("Some monomials could not be properly processed."); return false; } // Clear up allocated buffer space of the monomials (should not be too much...) unique_monoms.clear(); return true; } bool CSecondaryCohomology::Perform2ndCohomSerreReduction(const CInternalData &id) { /* Now we have to take care of the ambiguos contributions derive from from restoring the exactness of the secondary/remnant sequence. The idea is to check if the complement monomial can already be found in the list of unique contributions, because this would obviously correspond to a Serre-dual contribution. If so, we can turn the ambiguous contribution in an unique one. However, this does not solve every case. In the second scan, we check if from the remaining ambiguous contributions an ambiguous complement monomial can be found, whose ambiguous contributions might be just right to identify a unique one. Unfortunately, this still leaves some cases behind, which we have to deal with in the actual computation of the cohomology dimensions. */ size_t num_ambiguous_before = monoms.ambiguous_monoms.size(); uint64_t complete_union = id.GetCompleteUnion(); uint32_t variety_dim = (uint32_t) id.GetDimension(); // Scan through all ambiguous contributions and check if the complement monomial is unique for (map::iterator ita = monoms.ambiguous_monoms.begin(); ita != monoms.ambiguous_monoms.end(); ) { uint64_t monomial = ita->first; uint64_t complement = (~monomial) & complete_union; // First try to find a UNIQUE complement partner map::const_iterator uc = monoms.unique_monoms.find(complement); if (uc != monoms.unique_monoms.end()) { // Check if this complement partner has a compatible contribution, which would identify // a correct contribution of our ambiguous case uint32_t group_suggestion = variety_dim - uc->second.Cohom.nGroup; size_t numcandidates = ita->second.vCohoms.size(); bool bFoundCandidate = false; size_t candidate = 0; for (size_t i=0; isecond.vCohoms[i].nGroup == group_suggestion) { bFoundCandidate = true; candidate = i; break; } } if (bFoundCandidate) { // So the unique complement monomial exists and identifies the correct contribution UniqueContribData newunique; newunique.Cohom.nGroup = group_suggestion; newunique.Cohom.nFactor = ita->second.vCohoms[candidate].nFactor; newunique.nRationals = ita->second.nRationals; newunique.nRationalsDual = ita->second.nRationalsDual; // Now add the identified unique one pair::iterator, bool> nu = monoms.unique_monoms.insert(pair(monomial, newunique)); if (nu.second == false) { ERR_OUT("The monomial " << id.Int64ToMonomial(monomial) << " already exists in the unique monomials list!"); return false; } // Remove the ambiguous contribution and start the scan again at the beginning monoms.ambiguous_monoms.erase(ita); ita = monoms.ambiguous_monoms.begin(); } else ita++; } else { // If no UNIQUE partner can be found, try to find an ambiguous partner... map::iterator ita2 = monoms.ambiguous_monoms.find(complement); if (ita2 != monoms.ambiguous_monoms.end()) { // OK, we have a partner. Then try to find a "Serre-dual" intersection of the potential contributions vector intersection; size_t cohoms_ita = ita->second.vCohoms.size(); size_t cohoms_ita2 = ita2->second.vCohoms.size(); intersection.clear(); for (size_t i=0; isecond.vCohoms[i].nGroup == (variety_dim - ita2->second.vCohoms[j].nGroup)) { // Store each such intersection of complement contributions intersection.push_back(ita->second.vCohoms[i]); intersection.push_back(ita2->second.vCohoms[j]); } } } // Check if the intersection was able to uniquely identify a contribution cohomology group if (intersection.size() == 2) { // Apparently, we could uniquely resolve the issue // Add the "normal" monomial to the list of unique ones UniqueContribData newunique; newunique.Cohom.nGroup = intersection[0].nGroup; newunique.Cohom.nFactor = intersection[0].nFactor; newunique.nRationals = ita->second.nRationals; newunique.nRationalsDual = ita->second.nRationalsDual; pair::iterator, bool> ret = monoms.unique_monoms.insert(std::pair(monomial, newunique)); // Add the "complement" partner monomial to the list of unique ones newunique.Cohom.nGroup = intersection[1].nGroup; newunique.Cohom.nFactor = intersection[1].nFactor; newunique.nRationals = ita2->second.nRationals; newunique.nRationalsDual = ita2->second.nRationalsDual; pair::iterator, bool> ret2 = monoms.unique_monoms.insert(pair(complement, newunique)); if ((ret.second == false) || (ret2.second == false)) { ERR_OUT("INTERNAL: Could not add resolved ambiguous monomials to unique monomials list."); return false; } // Delete both ambiguous cases from the ambiguous list & start the scan from the beginning monoms.ambiguous_monoms.erase(monomial); monoms.ambiguous_monoms.erase(complement); ita = monoms.ambiguous_monoms.begin(); } else ita++; } else { // CONSOLE_MSG_OUT("WARNING: The Serre duality check could not entirely resolve all monomials."); ita++; } } } // In the best case scenario, we could resolve all ambiguous cases and turn them into // uniques. Unfortunately, this is not always the case. size_t num_ambiguous_after = monoms.ambiguous_monoms.size(); if (num_ambiguous_after > 0) { WARN_OUT("The Serre dualization reduction was unable to uniquely resolve " << num_ambiguous_after << " of the original " << num_ambiguous_before << " ambiguous monoms."); } return true; } cohomCalg-0.32/source/secondarycohom.h000066400000000000000000000075451322050713700200330ustar00rootroot00000000000000//////////////////////////////////////////////////////////////////////////////////////////////////// // // // secondarycohom.h // // ================ // // // // Code: Benjamin Jurke, http://benjaminjurke.net // // // //////////////////////////////////////////////////////////////////////////////////////////////////// // // // File history: // // - 04.04.2010 File created as secondarycohom.cpp // // // //////////////////////////////////////////////////////////////////////////////////////////////////// #ifndef INC_SECONDARYCOHOM_H #define INC_SECONDARYCOHOM_H #include #include #include #include #include #include #include #include "iohandler.h" //////////////////////////////////////////////////////////////////////////////////////////////////// // This first computational part of the program houses the engine that traverses the powerset of the // Stanley-Reisner ideal generators. Using 64-bit integer bit-masks, which are specified in the // CInternalData handler, is basically runs a loop through all possible combinations and successively // builds up the secondary/remnant sequences. After the loop, the cohomology of those sequences is // determined by considering the alternating sum - which is a quick exactness test - and attempting // exactness repairs in the range of C^0 to C^dim of the variety, which ultimately determine the // secondary cohomology. All those steps are handled by the CSecondaryCohomology class. typedef struct { uint64_t num; int64_t altersum; std::vector c; public: inline void Clear(size_t len) { num = 0; altersum = 0; c.clear(); if (len>0) c.resize(len, 0); }; } MonomData; typedef std::map MonomMap; class CSecondaryCohomology { private: // Secondary sequences data MonomData insertion_prototype; MonomMap unique_monoms; int32_t min_c_deg; int32_t max_c_deg; uint32_t len_c_deg; CMonomialsList monoms; private: // Internal computations bool IsSequenceExact(const std::vector &seq, size_t &pos_out) const; // Internal output functions std::string Print2ndSeq(const MonomData &mondat, int32_t min_out, int32_t max_out); std::string Print2ndSeq(const MonomData &mondat); std::string PrintMonomialWith2ndSeq(const CInternalData &id, MonomMap::const_iterator monom, int min_out, int max_out); void Clear(); public: CSecondaryCohomology(); // The primary SR powerset traverse functions (EXECUTE IN ORDER!) bool Init2ndSequences(const CInternalData &id); // STEP 1 bool TraverseSRpowerset(const CInternalData &id); // STEP 2 bool Compute2ndCohomFromTrivialSequences(); // STEP 3 bool Compute2ndCohomFromSequences(const CInternalData &id); // STEP 4 bool Perform2ndCohomSerreReduction(const CInternalData &id); // STEP 5 // Monomial list access inline CMonomialsList &GetMonomialsList() { return monoms; }; // Output function void PrintMonomMap(const CInternalData &id, bool shorten_output); }; #endif cohomCalg-0.32/source/tokenizer.cpp000066400000000000000000000317141322050713700173560ustar00rootroot00000000000000//////////////////////////////////////////////////////////////////////////////////////////////////// // // // tokenizer.cpp +----------------------+ // // ============= | generic TOKENIZER | // // +----------------------+ // // Code: Benjamin Jurke, http://benjaminjurke.net // // // //////////////////////////////////////////////////////////////////////////////////////////////////// // // // File history: // // - 04.06.2009 File created as tokenizer.cpp // // Contains a simple generic tokenizer class to read in a string and break // // it down to its tokens for further parsing. // // - 17.04.2010 Changed WORD tokens from alpha to alphanums // // // //////////////////////////////////////////////////////////////////////////////////////////////////// #include #include #include #include #include #include #include "platform.h" #include "tokenizer.h" #include "main.h" using namespace std; //////////////////////////////////////////////////////////////////////////////////////////////////// // This macro (yeah, I know... spare me the lecture...) determines which characters we interpret as // whitespaces, i.e. spaces, tabs, newline and carriage returns #define IS_WHITESPACE(__x_) ((__x_ == ' ') || (__x_ == '\t') || (__x_ == '\n') || (__x_ == '\r')) //////////////////////////////////////////////////////////////////////////////////////////////////// bool operator!=(const CToken &lhs, const CToken &rhs) { /* The operator function handles the comparison of two tokens. We do NOT compare the InputOffset, i.e. just the data and type of the tokens has to be equal. */ if (lhs.tkType != rhs.tkType) return true; // Have same type, but do they have same data? switch (lhs.tkType) { case TOKEN_SYMBOL: return (lhs.symbol != rhs.symbol); case TOKEN_INTEGER: return (lhs.integer != rhs.integer); case TOKEN_STRING: case TOKEN_WORD: return (lhs.str.compare(rhs.str) != 0); case TOKEN_END: case TOKEN_ERR: return false; } // We should never reach here... return false; } bool CToken::GetBool(bool &bBool) const { /* As there is no fundamental boolean token, we try to interpret the current token as boolean. Therefore, we consider the following values: true --> WORD: true (case-inv.) false --> WORD: false (case-inv.) STRING: true (case-inv.) --> STRING: false (case-inv.) INTEGER: non-zero value --> INTEGER: zero value Tokens of any other type cannot be converted to a boolean value and therefore return false. */ switch (tkType) { case TOKEN_WORD: case TOKEN_STRING: // We try to recognize either 'true' or 'false' from the string-like tokens { if (str.length() > 5) return false; string strTemp = str; transform(strTemp.begin(), strTemp.end(), strTemp.begin(), (int (*) (int)) tolower); if ((strTemp.compare("false") == 0) || (strTemp.compare("0") == 0)) { bBool = false; return true; } else if ((strTemp.compare("true") == 0) || (strTemp.compare("1") == 0)) { bBool = true; return true; } return false; } case TOKEN_INTEGER: // From numerical tokens, we recognize the non-zero values as true bBool = (integer != 0); return true; case TOKEN_SYMBOL: case TOKEN_END: case TOKEN_ERR: // All other tokens cannot be converted to boolean value return false; } return false; } string CToken::GetTokenString() const { /* This function converts a token into human readable form, i.e. it prints the token type and the token value. */ char buf[128]; switch (tkType) { case TOKEN_SYMBOL: safe_sprintf(buf, sizeof(buf), "SYMBOL: %c (0x%x)", symbol, (int) symbol); break; case TOKEN_WORD: safe_sprintf(buf, sizeof(buf), "WORD: %s", str.c_str()); break; case TOKEN_INTEGER: safe_sprintf(buf, sizeof(buf), "INTEGER: %ld", (long int) integer); break; case TOKEN_STRING: safe_sprintf(buf, sizeof(buf), "STRING: %s", str.c_str()); break; case TOKEN_END: safe_sprintf(buf, sizeof(buf), "END"); break; case TOKEN_ERR: safe_sprintf(buf, sizeof(buf), "ERR"); break; default: safe_sprintf(buf, sizeof(buf), "--INVALID TOKEN--"); break; } return buf; } //////////////////////////////////////////////////////////////////////////////////////////////////// CTokenizer::CTokenizer() { Clear(); } void CTokenizer::Clear() { pInputLine = NULL; pCurChar = NULL; iCurToken = 0; vTokens.clear(); } bool CTokenizer::ReadWord() { /* This internal function tries to read a WORD type token at the current position of the input data. A WORD token is specified to be any non-seperated alphanumeric sequence of characters not starting with a number. */ // Determine the length of the alphanumeric sequence if (!isalpha(pCurChar[0])) return false; ptrdiff_t len=1; while (isalnum(pCurChar[len])) len++; // Create a duplicate of the WORD token string string strTmp; strTmp.assign(pCurChar, len); // Create a new token and add to token list CToken TmpToken; TmpToken.StoreWord(strTmp.c_str(), pCurChar - pInputLine); vTokens.push_back(TmpToken); pCurChar += len; return true; } bool CTokenizer::ReadInteger() { /* This internal function tries to read a non-negative INTEGER type token at the current position of the input data. Note that the calling function has to take care of a potential minus sign in from of this number. If the number does not fit into signed 64-bit variable, the return value is false. */ // We determine the length of the numeric sequence if (!isdigit(pCurChar[0])) return false; ptrdiff_t len=1; while (isdigit(pCurChar[len])) len++; // Convert the number int64_t iTmp = string_to_int64(pCurChar); if (errno == ERANGE) { // In case the number is larger than 64 bit return false; } // Create a new token and add to the token list CToken TmpToken; TmpToken.StoreInteger(iTmp, pCurChar - pInputLine); vTokens.push_back(TmpToken); pCurChar += len; return true; } bool CTokenizer::ReadString() { /* This internal function tries to read a STRING type token, which is any sequence starting and ending with a '"'. Therefore it currently not possible to have a '"' character in the string. */ // Determine the length of the string if (pCurChar[0] != '"') return false; int i=1; while ((pCurChar[i] != 0) && (pCurChar[i] != '"')) i++; if (pCurChar[i] != '"') return false; // Create a duplicate of the string string strTmp; strTmp.assign(pCurChar, 1, i-1); // Create a new token and add to the token list CToken TmpToken; TmpToken.StoreString(strTmp.c_str(), pCurChar - pInputLine); vTokens.push_back(TmpToken); pCurChar += i+1; return true; } bool CTokenizer::ReadSymbol() { /* This function tries to read in a symbol character. If a '-' character is found it tries to read in a subsequent integer and applies the sign. Otherwise the character is simply stored as a symbol. Note that this function does NOT check if the character is of alphanumeric type, which may allow for a different interpretation. Therefore, this function should be the fallback option wenn determining the token type. */ const char c = pCurChar[0]; pCurChar++; switch (c) { case '-': // If we have a minus sign, look for an integer if (ReadInteger()) { // If there is indeed an integer (which is now stored at the last position of // the token list) flip the sign const size_t numTokens = GetNumberOfTokens(); int64_t num = 0; vTokens[numTokens-1].GetInteger(num); vTokens[numTokens-1].StoreInteger(-num, pCurChar - pInputLine - 1); break; } default: // If we have no minus sign or cannot find an integer, simply store the character // as a SYMBOL token CToken TmpToken; TmpToken.StoreSymbol(c, pCurChar - pInputLine - 1); vTokens.push_back(TmpToken); } return true; } bool CTokenizer::ReadNextToken() { /* This function advances the current character position to the next value which is not considered to be a whitespace and then calls the indivual Read*** functions in order to properly recognize the token. */ // First skip all whitespace SkipWhitespaces(); // End of string? if (pCurChar[0] == 0) return true; // Then we read the next token if (pCurChar[0] == '"') return ReadString(); if (isdigit(pCurChar[0])) return ReadInteger(); if (isalpha(pCurChar[0])) return ReadWord(); // Note that the ReadSymbol must come last, because everything can be interpreted as an // ordinary SYMBOL, which is simply a character. return ReadSymbol(); } void CTokenizer::SkipWhitespaces() { /* Skips whitespace characters (as defined by the macro at the top of the file) until either the end of the string of a non-whitespace character is reached. */ while ((pCurChar[0] != 0) && IS_WHITESPACE(pCurChar[0])) pCurChar++; } bool CTokenizer::TokenizeInputString(const string &input) { /* This function clears the tokenizer of all prior data and starts the process of breaking up the input string into individual tokens. Note that the input string is not changed, nor is copy of the original string kept. */ // Note that the usage of the STL class string ensures that we truly have terminating // zero character, i.e. this class is reasonably safe pInputLine = input.c_str(); pCurChar = pInputLine; // Read tokens until we hit the end of the string while (pCurChar[0] != 0) { if (!ReadNextToken()) return false; } // Add and END token CToken EndToken; EndToken.SetEndToken(pCurChar - pInputLine); vTokens.push_back(EndToken); // Set the current token to start iCurToken = 0; // Clear the "critical" variables for safety pInputLine = NULL; pCurChar = NULL; // OutputTokenList(); // Just for debugging return true; } void CTokenizer::OutputTokenList() const // Just for debugging { /* This output function prints a full list of all tokens, which might be useful for debugging or writing parsing functions. */ const size_t numTokens = GetNumberOfTokens(); MSG_OUT("There are " << numTokens << " tokens in the input string:"); for (size_t i=0; i &out_list, char cBeginDelim, char cSeperator, char cEndDelim) { /* This function is a semi-parser function, which simplifies the recurring task of reading in symbol-seperated integer lists like e.g. comma-seperated bracket-delimited vectors (2,3,1). */ char c; int64_t integer; // First we expect a SYMBOL containing the cBeginDelim character if (!GetNextToken().GetSymbol(c)) return false; if (c != cBeginDelim) return false; // The we loop as long as we find and INTEGER followed by the cSeperator character SYMBOL while (GetNextToken().GetInteger(integer)) { out_list.push_back(integer); if (!GetNextToken().GetSymbol(c)) return false; if (c == cEndDelim) break; if (c != cSeperator) return false; } // Finally, there should be a SYMBOL containing the cEndDelim character if (c != cEndDelim) return false; return true; } cohomCalg-0.32/source/tokenizer.h000066400000000000000000000132271322050713700170220ustar00rootroot00000000000000//////////////////////////////////////////////////////////////////////////////////////////////////// // // // tokenizer.h +----------------------+ // // =========== | generic TOKENIZER | // // +----------------------+ // // Code: Benjamin Jurke, http://benjaminjurke.net // // // //////////////////////////////////////////////////////////////////////////////////////////////////// // // // File history: // // - 10.06.2009 File created as tokenizer.h // // // //////////////////////////////////////////////////////////////////////////////////////////////////// #ifndef INC_TOKENIZER_H #define INC_TOKENIZER_H #include #include #include #include //////////////////////////////////////////////////////////////////////////////////////////////////// // The basic goal of a tokenizer is to break down some input string (i.e. a simple series of characters) // down into individual tokens (like strings, numbers, special symbols), which can then be easily used // for further processing. // // The CToken class corresponds to the individual "tokens" to which the tokenizer breaks down the input // string. enum MyTokenType { // Data content TOKEN_SYMBOL = 1, TOKEN_WORD = 2, TOKEN_INTEGER = 3, TOKEN_STRING = 4, // Control tokens TOKEN_END = 0, TOKEN_ERR = -1 }; class CToken { friend class CTokenizer; private: MyTokenType tkType; ptrdiff_t iInputOffset; // Data variables char symbol; int64_t integer; std::string str; private: inline CToken() { tkType = TOKEN_ERR; iInputOffset = 0; symbol = 0; integer = 0; }; // Data storage/insertion inline void StoreSymbol(char cSymbol, ptrdiff_t offset) { symbol = cSymbol; tkType = TOKEN_SYMBOL; iInputOffset = offset; }; inline void StoreWord(const char *strWord, ptrdiff_t offset) { str = strWord; tkType = TOKEN_WORD; iInputOffset = offset; }; inline void StoreInteger(int64_t iInteger, ptrdiff_t offset) { integer = iInteger; tkType = TOKEN_INTEGER; iInputOffset = offset; }; inline void StoreString(const char *strString, ptrdiff_t offset) { str = strString; tkType = TOKEN_STRING; iInputOffset = offset; }; inline void SetEndToken(ptrdiff_t offset) { tkType = TOKEN_END; iInputOffset = offset; }; public: // Comparision operator friend bool operator!=(const CToken &lhs, const CToken &rhs); friend inline bool operator==(const CToken &lhs, const CToken &rhs) { return (!(lhs != rhs)); }; // Type and control structures retrival inline MyTokenType WhatType() const { return tkType; }; inline bool IsEndToken() const { return (WhatType() == TOKEN_END); } inline ptrdiff_t GetInputOffset() const { return iInputOffset; } // Data retrival inline bool GetSymbol(char &cSymbol) const { if (tkType == TOKEN_SYMBOL) { cSymbol = symbol; return true; } return false; }; inline bool GetWord(std::string &strWord) const { if (tkType == TOKEN_WORD) { strWord = str; return true; } return false; }; inline bool GetInteger(int64_t &iInteger) const { if (tkType == TOKEN_INTEGER) { iInteger = integer; return true; } return false; }; inline bool GetString(std::string &strString) const { if (tkType == TOKEN_STRING) { strString = str; return true; } return false; }; bool GetBool(bool &bBool) const; // For debugging purposes std::string GetTokenString() const; }; //////////////////////////////////////////////////////////////////////////////////////////////////// class CTokenizer { private: // Data variables const char *pInputLine; const char *pCurChar; std::vector vTokens; size_t iCurToken; private: // Internal functions for reading tokens bool ReadWord(); bool ReadInteger(); bool ReadString(); bool ReadSymbol(); bool ReadNextToken(); void SkipWhitespaces(); public: CTokenizer(); void Clear(); // Data retrieval inline size_t GetNumberOfTokens() const { return vTokens.size(); }; inline size_t GetCurTokenIndex() const { return iCurToken; }; inline const CToken &GetToken(size_t index) const { return vTokens.at(index); }; inline const CToken &GetCurToken() const { return GetToken(iCurToken); }; inline const CToken &GetNextToken() { return GetToken(iCurToken++); }; // Note that GetNextToken POST-increments, inline const CToken &GetPrevToken() { return GetToken(--iCurToken); }; // whereas GetPrevToken PRE-decrements! bool GetIntegerList(std::vector &out_list, char cBeginDelim = '(', char cSeperator = ',', char cEndDelim = ')'); // Output functions void OutputTokenList() const; // Main function to initialize the tokenizer bool TokenizeInputString(const std::string &input); }; #endif