--- name: "msolve" section: "1" platform: "linux" package: "msolve" version: "0.7.5-1" release: "Debian 13 (Trixie)" platforms: ["linux"] url: "https://new.carta.tech/msolve" --- # msolve(1) computer algebra algorithms for solving polynomial systems ## NAME msolve - computer algebra algorithms for solving polynomial systems ## DESCRIPTION msolve library for polynomial system solving, version 0.7.5 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 (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** 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 0.7.5 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 (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** 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