markov.html

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Usage: markov [options] PROJECT

Computes a Markov basis (generating set) of the toric ideal
of a matrix or, more general, of the lattice ideal of a lattice.

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

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