This code computes a minimal generating set
- of the toric ideal of a matrix A or
- of the lattice ideal of a lattice L.
You must specify either a matrix or a lattice basis. If both exist,
'markov' will choose the matrix as input.
See
- A.M. Bigatti and R. LaScala and L. Robbiano. Computing toric
ideals. Journal of Symbolic Computation 27 (1999), 351--365.
- R. Gebauer and H. M. Möller. On an installation of
Buchberger's algorithm. Journal of Symbolic Computation 6 (1988),
275--286.
- R. Hemmecke and P. Malkin. Computing generating sets of lattice
ideals. e-print arXiv:math.CO/0508359, 2005.
- S. Hosten and B. Sturmfels. GRIN: An implementation of
Gröbner bases for integer program- ming. In: "Integer
programming and combinatorial optimisation", E. Balas and
J. Clausen, eds., LNCS 920, Springer-Verlag, 1995, 267--276.
for more details on the algorithms implemented.
Usage
./markov [--options] foo
Examples
./markov foo
./markov --quiet foo
Default behavior
- 'markov' always uses matrix file 'foo' as input if present. If you wish to
use a given lattice basis as input, specify only the lattice generators in 'foo.lat'.
Option
(not on SUN)
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Short-hand
(also on SUN)
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Effect
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--quiet
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-q
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no output is written to the screen
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Output file
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Content
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foo.mar
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list of Markov basis elements
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