Provided by: msolve_0.7.1-1_amd64 
NAME
msolve - computer algebra algorithms for solving polynomial systems
DESCRIPTION
msolve library for polynomial system solving, version 0.7.1 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)
-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.
-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 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 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.
-L LIF Controls lifting of multplication matrices over the rationals.
Default is 0 (no lifting). Matrices are lifted when LIF is 1. Warning: when activated, this
option may cause higher memory consumption.
-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. Note: At the moment restricted to 32 bit
prime fields.
-u UHT Number of steps after which the
hash table is newly generated. Default: 0, i.e. no update.
-V Prints msolve's version
msolve library for polynomial system solving, version 0.7.1 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)
-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.
-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 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 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.
-L LIF Controls lifting of multplication matrices over the rationals.
Default is 0 (no lifting). Matrices are lifted when LIF is 1. Warning: when activated, this
option may cause higher memory consumption.
-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. Note: At the moment restricted to 32 bit
prime fields.
-u UHT Number of steps after which the
hash table is newly generated. Default: 0, i.e. no update.
-V Prints msolve's version
msolve July 2024 MSOLVE(1)