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‎.gitattributes

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articles/data/3cex.html -text
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articles/data/index.html -text
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/back.jpg -text
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/circuits.html -text
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examples/333 -text
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examples/333.mod -text
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examples/334 -text
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examples/s-magic3 -text
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/genmodel.html -text
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/gensymm.html -text
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/graver.html -text
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/groebner.html -text
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/hilbert.html -text
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/markov.html -text
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/minimize.html -text
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/normalform.html -text
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/output.html -text
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/ppi.html -text
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/qsolve.html -text
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/rays.html -text
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version_1.0/4ti2_linux_1.0.tar.gz -text
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version_1.0/4ti2_sun_1.0.tar.gz -text
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version_1.0/graver -text
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version_1.6.2/4ti2-1.6.2.tar.gz -text
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version_1.6.3/4ti2-1.6.3.tar.gz -text
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version_1.6/4ti2-1.6.tar.gz -text
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/walk.html -text
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/zbasis.html -text
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/zsolve.html -text

‎4ti2_manual.pdf

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‎circuits.html

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<pre>
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<!--- Autogenerated, do not edit. -->
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Usage: circuits [options] PROJECT
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Computes the circuits of a cone.
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Input Files:
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PROJECT.mat A matrix (compulsory).
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PROJECT.sign The sign constraints of the variables ('1' means
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non-negative, '0' means a free variable, and '2' means
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both non-negative and non-positive).
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It is optional, and the default is both.
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PROJECT.rel The relations on the matrix rows ('<','>','=').
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It is optional and the default is all '='.
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The mat must be given with this file.
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Output Files:
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PROJECT.cir The circuits of the cone.
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PROJECT.qfree A basis for the linear subspace of the cone.
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If this file does not exist then the linear subspace
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is trivial.
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Options:
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-p, --precision=PREC Select PREC as the integer arithmetic precision.
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PREC is one of the following: `64' (default),
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`32', and `arbitrary' (only `arb` is needed).
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-m, --mat Use the Matrix algorithm (default for 32 and 64).
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-s, --support Use the Support algorithm (default for arbitrary).
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-o, --order=ORDERING Set ORDERING as the ordering in which the columns
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are chosen. The possible orderings are `maxinter',
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`minindex', `maxcutoff' (default), and `mincutoff'.
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-f, --output-freq=n Set the frequency of output (default is 1000).
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-q, --quiet Do not output anything to the screen.
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-h, --help Display this help and exit.
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</pre>

‎examples.html

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</ul>
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The 4ti2 source distribution has many more example files
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in its test suite, which can be found in the directory <i>test</i>.
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</BODY>

‎genmodel.html

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<pre>
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<!--- Autogenerated, do not edit. -->
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usage: genmodel [--options] FILENAME
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Computes the problem matrix corresponding to graphical statistical models
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given by a simplicial complex and levels on the nodes.
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Options:
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-q, --quiet No output is written to the screen
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Input file:
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FILENAME.mod Simplicial complex and levels on the nodes
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Output file:
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FILENAME.mat Matrix file
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Example: Consider the problem of 3x3x3 tables with 2-marginals. These
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are given by K_3 as the simplicial complex on 3 nodes and with levels
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of 3 on each node. In '333.mod' write:
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3
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3 3 3
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3
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2 1 2
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2 2 3
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2 3 1
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Calling 'genmodel 333' produces the following file '333.mat':
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27 27
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1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
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0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
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[...]
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1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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[...]
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1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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[...]
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</pre>

‎gensymm.html

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<pre>
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<!--- Autogenerated, do not edit. -->
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usage: gensymm [--options] A B C D FILENAME
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Computes the generators for the symmetry group acting on 4-way tables
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with 3-marginals. By putting one side length to 1, this includes
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3-way tables with 2-marginals.
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Options:
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-q, --quiet No output is written to the screen
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Output file:
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FILENAME.sym generators for the symmetry group
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Example: Consider the problem of 3x3x3 tables with 2-marginals. Calling
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gensymm 3 3 3 1 333
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produces the file '333.sym' containing the following lines.
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9 27
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10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 1 2 3 4 5 6 7 8 9
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10 11 12 13 14 15 16 17 18 1 2 3 4 5 6 7 8 9 19 20 21 22 23 24 25 26 27
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4 5 6 7 8 9 1 2 3 13 14 15 16 17 18 10 11 12 22 23 24 25 26 27 19 20 21
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4 5 6 1 2 3 7 8 9 13 14 15 10 11 12 16 17 18 22 23 24 19 20 21 25 26 27
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2 3 1 5 6 4 8 9 7 11 12 10 14 15 13 17 18 16 20 21 19 23 24 22 26 27 25
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2 1 3 5 4 6 8 7 9 11 10 12 14 13 15 17 16 18 20 19 21 23 22 24 26 25 27
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1 2 3 10 11 12 19 20 21 4 5 6 13 14 15 22 23 24 7 8 9 16 17 18 25 26 27
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1 10 19 4 13 22 7 16 25 2 11 20 5 14 23 8 17 26 3 12 21 6 15 24 9 18 27
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1 4 7 2 5 8 3 6 9 10 13 16 11 14 17 12 15 18 19 22 25 20 23 26 21 24 27
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</pre>

‎graver.html

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<pre>
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<!--- Autogenerated, do not edit. -->
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Usage: graver [options] PROJECT
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Computes the Graver basis of a matrix or a given lattice.
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Basic options:
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-p PREC, --precision=PREC Use precision (32, 64, gmp). Default is 32 bit
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-m, --maxnorm Write vectors with maximum norm to PROJECT.maxnorm
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-b [FREQ], --backup[=FREQ] Frequently backup status to PROJECT.backup
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-r, --resume Resume from backup file PROJECT.backup
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-h, --help Display this help
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--version Display version information
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Output options:
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-q, --quiet Quit mode
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-u, --update[=1] Updated output on console (default)
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-uu, --update=2 More verbose updated output on console
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-v, --verbose[=1] Output once every variable computation
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-vv, --verbose=2 Output once every norm sum computation
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-vvv, --verbose=3 Output once every norm computation
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Logging options:
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-n, --log=0 Disable logging (default)
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-l, --log[=1] Log once every variable computation to PROJECT.log
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-ll, --log=2 Log once every norm sum computation to PROJECT.log
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-lll, --log=3 Log once every norm computation to PROJECT.log
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Input files:
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PROJECT.mat Matrix
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PROJECT.lat Lattice basis (can be provided instead of matrix)
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PROJECT.sign Sign of columns (optional)
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PROJECT.lb Lower bounds of columns (optional)
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PROJECT.ub Upper bounds of columns (optional)
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Backup files:
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PROJECT.backup Backup file
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PROJECT.backup~ Temporary backup file
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(if it exists, it may be newer than PROJECT.backup)
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Output files:
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PROJECT.gra Graver basis
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PROJECT.zfree Free part of the solution
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PROJECT.maxnorm Vectors with maximum norm (if -m, --maxnorm is in use)
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</pre>

‎groebner.html

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<pre>
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<!--- Autogenerated, do not edit. -->
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Usage: groebner [options] PROJECT
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Computes a Groebner basis of the toric ideal of a matrix,
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or, more general, of the lattice ideal of a lattice.
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Input Files:
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PROJECT.mat A matrix (optional if lattice basis is given).
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PROJECT.lat A lattice basis (optional if matrix is given).
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PROJECT.cost The cost matrix, which determines the term ordering
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(optional, default is degrevlex).
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Ties are broken with degrevlex.
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PROJECT.sign The sign constraints of the variables ('1' means
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non-negative and '0' means a free variable).
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It is optional, and the default is all non-negative.
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PROJECT.mar The Markov basis/generating set of the lattice (optional).
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PROJECT.weights The weight vectors used for truncation (optional).
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PROJECT.weights.max The maximum weights used for truncation.
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This file is needed when PROJECT.weights exists.
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PROJECT.zsol An integer solution to specify a fiber (optional).
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The integer solution is used for truncation.
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Output Files:
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PROJECT.gro The Groebner basis of the lattice.
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Options:
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-p, --precision=PREC Select PREC as the integer arithmetic precision.
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PREC is one of the following: `64' (default),
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`32', and `arbitrary' (only `arb` is needed).
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-a, --algorithm=ALG Select ALG as the completion procedure for
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computing Groebner bases. ALG is one of
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`fifo', `weighted', or 'unbounded.'
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-g, --generation=ALG Select ALG as the procedure for computing
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a generating set or Markov basis. ALG is
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one of `hybrid' (default), `project-and-lift',
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`max-min', or 'saturation'.
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-t, --truncation=TRUNC Set TRUNC as the truncation method. TRUNC is
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of the following: `ip', `lp', `weight' (default),
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or `none'. Only relevant if `zsol' is given.
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-m, --minimal=STATE If STATE is `yes' (default), then 4ti2 will
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compute a minimal Markov basis. If STATE is
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'no', then the Markov basis will not
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necessarily be minimal.
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-r, --auto-reduce-freq=n Set the frequency of auto reduction.
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(default is 2500).
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-f, --output-freq=n Set the frequency of output (default is 1000).
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-q, --quiet Do not output anything to the screen.
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-h, --help Display this help and exit.
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</pre>

‎hilbert.html

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<pre>
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<!--- Autogenerated, do not edit. -->
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Usage: hilbert [options] PROJECT
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Computes the Hilbert basis of a matrix or a given lattice.
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Basic options:
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-p PREC, --precision=PREC Use precision (32, 64, gmp). Default is 32 bit
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-m, --maxnorm Write vectors with maximum norm to PROJECT.maxnorm
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-b [FREQ], --backup[=FREQ] Frequently backup status to PROJECT.backup
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-r, --resume Resume from backup file PROJECT.backup
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-h, --help Display this help
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--version Display version information
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Output options:
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-q, --quiet Quit mode
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-u, --update[=1] Updated output on console (default)
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-uu, --update=2 More verbose updated output on console
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-v, --verbose[=1] Output once every variable computation
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-vv, --verbose=2 Output once every norm sum computation
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-vvv, --verbose=3 Output once every norm computation
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Logging options:
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-n, --log=0 Disable logging (default)
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-l, --log[=1] Log once every variable computation to PROJECT.log
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-ll, --log=2 Log once every norm sum computation to PROJECT.log
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-lll, --log=3 Log once every norm computation to PROJECT.log
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Input files:
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PROJECT.mat Matrix
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PROJECT.lat Lattice basis (can be provided instead of matrix)
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PROJECT.rel Relations (<, >, =)
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PROJECT.sign Sign of columns (optional)
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PROJECT.ub Upper bounds of columns (optional)
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Backup files:
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PROJECT.backup Backup file
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PROJECT.backup~ Temporary backup file
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(if it exists, it may be newer than PROJECT.backup)
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Output files:
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PROJECT.hil Hilbert basis
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PROJECT.zfree Free part of the solution
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PROJECT.maxnorm Vectors with maximum norm (if -m, --maxnorm is in use)
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</pre>

‎markov.html

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<pre>
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<!--- Autogenerated, do not edit. -->
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Usage: markov [options] PROJECT
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Computes a Markov basis (generating set) of the toric ideal
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of a matrix or, more general, of the lattice ideal of a lattice.
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Input Files:
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PROJECT A matrix (optional only if lattice basis is given).
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PROJECT.lat A lattice basis (optional only if matrix is given).
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PROJECT.sign The sign constraints of the variables ('1' means
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non-negative and '0' means a free variable).
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It is optional, and the default is all non-negative.
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PROJECT.weights The weight vectors used for truncation (optional).
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PROJECT.weights.max The maximum weights used for truncation.
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This file is needed when PROJECT.weights exists.
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PROJECT.zsol An integer solution to specify a fiber (optional).
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The integer solution is used for truncation.
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Output Files:
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PROJECT.mar The Markov basis/generating set of the lattice.
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Options:
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-p, --precision=PREC Select PREC as the integer arithmetic precision.
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PREC is one of the following: `64' (default),
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`32', and `arbitrary' (only `arb` is needed).
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-a, --algorithm=ALG Select ALG as the completion procedure for
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computing Groebner bases. ALG is one of
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`fifo', `weighted', or 'unbounded.'
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-g, --generation=ALG Select ALG as the procedure for computing
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a generating set or Markov basis. ALG is
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one of `hybrid' (default), `project-and-lift',
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`max-min', or 'saturation'.
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-t, --truncation=TRUNC Set TRUNC as the truncation method. TRUNC is
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of the following: `ip', `lp', `weight' (default),
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or `none'. Only relevant if `zsol' is given.
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-m, --minimal=STATE If STATE is `yes' (default), then 4ti2 will
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compute a minimal Markov basis. If STATE is
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'no', then the Markov basis will not
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necessarily be minimal.
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-r, --auto-reduce-freq=n Set the frequency of auto reduction.
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(default is 2500).
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-f, --output-freq=n Set the frequency of output (default is 1000).
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-q, --quiet Do not output anything to the screen.
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-h, --help Display this help and exit.
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</pre>

‎minimize.html

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<pre>
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<!--- Autogenerated, do not edit. -->
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Usage: minimize [options] PROJECT
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Computes the minimal solution of an integer linear program
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or, more general, a lattice program, using a Groebner basis.
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Input Files:
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PROJECT.mat A matrix (optional only if lattice basis is given).
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PROJECT.lat A lattice basis (optional only if matrix is given).
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PROJECT.cost The cost vector. Exactly one vector allowed.
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PROJECT.zsol An integer solution to specify a fiber (needed).
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PROJECT.sign The sign constraints of the variables ('1' means
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non-negative and '0' means a free variable).
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It is optional, and the default is all non-negative.
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Output Files:
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PROJECT.min The minimal solution for the given fiber.
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Options:
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-p, --precision=PREC Select PREC as the integer arithmetic precision.
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PREC is one of the following: `64' (default),
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`32', and `arbitrary' (only `arb` is needed).
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-a, --algorithm=ALG Select ALG as the completion procedure for
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computing Groebner bases. ALG is one of
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`fifo', `weighted', or 'unbounded.'
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-t, --truncation=TRUNC Set TRUNC as the truncation method. TRUNC is
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of the following: `ip', `lp', `weight' (default),
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or `none'. Only relevant if `zsol' is given.
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-r, --auto-reduce-freq=n Set the frequency of auto reduction.
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(default is 2500).
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-f, --output-freq=n Set the frequency of output (default is 1000).
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-q, --quiet Do not output anything to the screen.
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-h, --help Display this help and exit.
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</pre>

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