msolve library for polynomial system solving implemented by J.
Berthomieu, C. Eder, M. Safey El Din
Basic call:
- ./msolve -f [FILE1] -o [FILE2]
FILE1 and FILE2 are respectively the input and output files
Standard options
-f FILE File name (mandatory).
-h Prints this help. -o FILE Name of output file.
-t THR Number of threads to be used.
- Default: 1.
-v n Level of verbosity, 0 - 2
- 0 - no output (default). 1 - global information at the start and
- end of the computation.
- 2 - detailed output for each step of the
- algorithm, e.g. matrix sizes, #pairs, ...
Input file format:
- - first line: variables separated by a comma - second line: characteristic
of the field - next lines provide the polynomials (one per line),
- separated by a comma (no comma after the final polynomial)
Output file format: When there is no solution in an algebraic
closure of the base field [-1]: Where there are infinitely many solutions in
an algebraic closure of the base field: [1, nvars, -1,[]]: Else: Over
prime fields: a rational parametrization of the solutions When input
coefficients are rational numbers: real solutions to the input system (see
the -P flag to recover a parametrization of the solutions) See the
msolve tutorial for more details (https://msolve.lip6.fr)
Advanced options:
-F FILE File name encoding parametrizations in binary
format.
-g GB Prints reduced Groebner bases of input system for
- first prime characteristic w.r.t. grevlex ordering. One element per line
is printed, commata separated. 0 - Nothing is printed. (default) 1 -
Leading ideal is printed. 2 - Full reduced Groebner basis is printed.
-c GEN Handling genericity: If the staircase is not
generic
- enough, msolve can automatically try to fix this situation via first
trying a change of the order of variables and finally adding a random
linear form with a new variable (smallest w.r.t. DRL) 0 - Nothing is done,
msolve quits. 1 - Change order of variables. 2 - Change order of
variables, then try adding a
- random linear form. (default)
-C Use sparse-FGLM-col algorithm:
- Given an input file with k polynomials compute the quotient of the ideal
generated by the first k-1 polynomials with respect to the kth
polynomial.
-e ELIM Define an elimination order: msolve supports
two
- blocks, each block using degree reverse lexicographical monomial order.
ELIM has to be a number between 1 and #variables-1. The basis the first
block eliminated is then computed.
-I Isolates the real roots (provided some univariate
data)
- without re-computing a Gr??bner basis Default: 0 (no).
-l LIN Linear algebra variant to be applied:
- 1 - exact sparse / dense 2 - exact sparse (default)
- 42 - sparse / dense linearization (probabilistic) 44 - sparse
linearization (probabilistic)
-m MPR Maximal number of pairs used per matrix.
- Default: 0 (unlimited).
-n NF Given n input generators compute normal form of the
last NF
- elements of the input w.r.t. a degree reverse lexicographical Gr??bner
basis of the irst (n - NF) input elements. At the moment this only works
for prime field computations. Combining this option with the
"-i" option assumes that the first (n - NF) elements generate
already a degree reverse lexicographical Gr??bner basis.
-p PRE Precision of the real root isolation.
- Default is 32.
-P PAR Get also rational parametrization of solution
set.
- Default is 0. For a detailed description of the output format please see
the general output data format section above.
-q Q Uses signature-based algorithms.
- Default: 0 (no).
-r RED Reduce Groebner basis.
- Default: 1 (yes).
-s HTS Initial hash table size given
- as power of two. Default: 17.
-S Use f4sat saturation algorithm:
- Given an input file with k polynomials compute the saturation of the ideal
generated by the first k-1 polynomials with respect to the kth
polynomial.
-u UHT Number of steps after which the
- hash table is newly generated. Default: 0, i.e. no update.
msolve library for polynomial system solving implemented by J.
Berthomieu, C. Eder, M. Safey El Din
Basic call:
- ./msolve -f [FILE1] -o [FILE2]
FILE1 and FILE2 are respectively the input and output files
Standard options
-f FILE File name (mandatory).
-h Prints this help. -o FILE Name of output file.
-t THR Number of threads to be used.
- Default: 1.
-v n Level of verbosity, 0 - 2
- 0 - no output (default). 1 - global information at the start and
- end of the computation.
- 2 - detailed output for each step of the
- algorithm, e.g. matrix sizes, #pairs, ...
Input file format:
- - first line: variables separated by a comma - second line: characteristic
of the field - next lines provide the polynomials (one per line),
- separated by a comma (no comma after the final polynomial)
Output file format: When there is no solution in an algebraic
closure of the base field [-1]: Where there are infinitely many solutions in
an algebraic closure of the base field: [1, nvars, -1,[]]: Else: Over
prime fields: a rational parametrization of the solutions When input
coefficients are rational numbers: real solutions to the input system (see
the -P flag to recover a parametrization of the solutions) See the
msolve tutorial for more details (https://msolve.lip6.fr)
Advanced options:
-F FILE File name encoding parametrizations in binary
format.
-g GB Prints reduced Groebner bases of input system for
- first prime characteristic w.r.t. grevlex ordering. One element per line
is printed, commata separated. 0 - Nothing is printed. (default) 1 -
Leading ideal is printed. 2 - Full reduced Groebner basis is printed.
-c GEN Handling genericity: If the staircase is not
generic
- enough, msolve can automatically try to fix this situation via first
trying a change of the order of variables and finally adding a random
linear form with a new variable (smallest w.r.t. DRL) 0 - Nothing is done,
msolve quits. 1 - Change order of variables. 2 - Change order of
variables, then try adding a
- random linear form. (default)
-C Use sparse-FGLM-col algorithm:
- Given an input file with k polynomials compute the quotient of the ideal
generated by the first k-1 polynomials with respect to the kth
polynomial.
-e ELIM Define an elimination order: msolve supports
two
- blocks, each block using degree reverse lexicographical monomial order.
ELIM has to be a number between 1 and #variables-1. The basis the first
block eliminated is then computed.
-I Isolates the real roots (provided some univariate
data)
- without re-computing a Gr??bner basis Default: 0 (no).
-l LIN Linear algebra variant to be applied:
- 1 - exact sparse / dense 2 - exact sparse (default)
- 42 - sparse / dense linearization (probabilistic) 44 - sparse
linearization (probabilistic)
-m MPR Maximal number of pairs used per matrix.
- Default: 0 (unlimited).
-n NF Given n input generators compute normal form of the
last NF
- elements of the input w.r.t. a degree reverse lexicographical Gr??bner
basis of the irst (n - NF) input elements. At the moment this only works
for prime field computations. Combining this option with the
"-i" option assumes that the first (n - NF) elements generate
already a degree reverse lexicographical Gr??bner basis.
-p PRE Precision of the real root isolation.
- Default is 32.
-P PAR Get also rational parametrization of solution
set.
- Default is 0. For a detailed description of the output format please see
the general output data format section above.
-q Q Uses signature-based algorithms.
- Default: 0 (no).
-r RED Reduce Groebner basis.
- Default: 1 (yes).
-s HTS Initial hash table size given
- as power of two. Default: 17.
-S Use f4sat saturation algorithm:
- Given an input file with k polynomials compute the saturation of the ideal
generated by the first k-1 polynomials with respect to the kth
polynomial.
-u UHT Number of steps after which the
- hash table is newly generated. Default: 0, i.e. no update.