msolve - Man Page

./msolve -f [FILE1] -o [FILE2]

FILE1 and FILE2 are respectively the input and output files

Standard options

-f, --file            FILE  File name (mandatory).

-h, --help                  Prints this help. -o, --output-file     FILE  Name of output file. -t, --threads         THR   Number of threads to be used.

1

- one thread (default).

THR > 1 - THR threads.

-v, --verbose         VERB  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, ...

- first line: variables separated by a comma

(no comma at end of line)

- second line: characteristic of the field - next lines provide the polynomials (one per line),

separated by a comma (no comma after the last 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, --groebner-basis  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)

-d                    GEN   Handling genericity further: If the staircase is not generic

enough, msolve can still try to perform the full computation

by computing some normal forms and build the multiplication matrix, before fixing the situation via option -c 0 - No normal forms are computed. 1 - Few normal forms are computed. 2 - Some normal forms are computed. (default) 3 - Lots of normal forms are computed. 4 - All the normal forms are computed.

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, --elimination     ELIM  Define an elimination order: msolve supports two

blocks of variables, each block using the degree reverse

lexicographical monomial order. ELIM has to be a number between 1 and #variables-1, and gives the number of eliminated variables. The basis with the first block of ELIM variables eliminated is then computed.

-I, --isolate         ISOL  Isolates the real roots (provided some univariate data)

without re-computing a Gröbner basis

0 - no (default). 1 - yes.

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.

0 - unlimited (default).

-n, --normal-form     NF    Given n input generators compute normal form of the last NF

elements of the input w.r.t. a degree reverse lexicographical

Gröbner basis of the first (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 Gröbner basis.

-p, --precision       PRE   Precision (in bits) on the output of real root isolation.

128 (default).

-P, --parametrization PAR   Get also rational parametrization of solution set.

0 (default). For a detailed description of the output

format please see the general output data format section above.

-L, --lifting-mulmat  LIF   Controls lifting of multplication matrices over the rationals.

0 - no lifting (default).

1 - matrices are lifted. Warning: when activated, this option may cause higher memory consumption.

-q                    Q     Uses signature-based algorithms.

0 - no (default).

1 - yes.

--random-seed

SEED  Random seed to initialize the pseudo random generator -1       - time(0) will be used (default) SEED ≥ 0 - use at your own risks;

this is intended for developers and

debug purposes only

-r, --reduce-gb       RED   Reduce Groebner basis.

0 - no.

1 - yes (default).

-s                    HTS   Initial hash table size given

as power of two.

17 (default).

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. Note: At the moment restricted to 32 bit prime fields.

-u                    UHT   Number of steps after which the

hash table is newly generated.

0 - no update (default).

-V, --version               Prints msolve's version

msolve library for polynomial system solving, version 0.9.5 implemented by J. Berthomieu, C. Eder, M. Safey El Din

./msolve -f [FILE1] -o [FILE2]

FILE1 and FILE2 are respectively the input and output files

Standard options

-f, --file            FILE  File name (mandatory).

-h, --help                  Prints this help. -o, --output-file     FILE  Name of output file. -t, --threads         THR   Number of threads to be used.

1

- one thread (default).

THR > 1 - THR threads.

-v, --verbose         VERB  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, ...

- first line: variables separated by a comma

(no comma at end of line)

- second line: characteristic of the field - next lines provide the polynomials (one per line),

separated by a comma (no comma after the last 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, --groebner-basis  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)

-d                    GEN   Handling genericity further: If the staircase is not generic

enough, msolve can still try to perform the full computation

by computing some normal forms and build the multiplication matrix, before fixing the situation via option -c 0 - No normal forms are computed. 1 - Few normal forms are computed. 2 - Some normal forms are computed. (default) 3 - Lots of normal forms are computed. 4 - All the normal forms are computed.

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, --elimination     ELIM  Define an elimination order: msolve supports two

blocks of variables, each block using the degree reverse

lexicographical monomial order. ELIM has to be a number between 1 and #variables-1, and gives the number of eliminated variables. The basis with the first block of ELIM variables eliminated is then computed.

-I, --isolate         ISOL  Isolates the real roots (provided some univariate data)

without re-computing a Gröbner basis

0 - no (default). 1 - yes.

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.

0 - unlimited (default).

-n, --normal-form     NF    Given n input generators compute normal form of the last NF

elements of the input w.r.t. a degree reverse lexicographical

Gröbner basis of the first (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 Gröbner basis.

-p, --precision       PRE   Precision (in bits) on the output of real root isolation.

128 (default).

-P, --parametrization PAR   Get also rational parametrization of solution set.

0 (default). For a detailed description of the output

format please see the general output data format section above.

-L, --lifting-mulmat  LIF   Controls lifting of multplication matrices over the rationals.

0 - no lifting (default).

1 - matrices are lifted. Warning: when activated, this option may cause higher memory consumption.

-q                    Q     Uses signature-based algorithms.

0 - no (default).

1 - yes.

--random-seed

SEED  Random seed to initialize the pseudo random generator -1       - time(0) will be used (default) SEED ≥ 0 - use at your own risks;

this is intended for developers and

debug purposes only

-r, --reduce-gb       RED   Reduce Groebner basis.

0 - no.

1 - yes (default).

-s                    HTS   Initial hash table size given

as power of two.

17 (default).

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. Note: At the moment restricted to 32 bit prime fields.

-u                    UHT   Number of steps after which the

hash table is newly generated.

0 - no update (default).

-V, --version               Prints msolve's version