.\" DO NOT MODIFY THIS FILE! It was generated by help2man 1.49.3. .TH MSOLVE "1" "February 2024" "msolve " "User Commands" .SH NAME msolve \- computer algebra algorithms for solving polynomial systems .SH DESCRIPTION msolve library for polynomial system solving implemented by J. Berthomieu, C. Eder, M. Safey El Din .SS "Basic call:" .IP \&./msolve \fB\-f\fR [FILE1] \fB\-o\fR [FILE2] .PP FILE1 and FILE2 are respectively the input and output files .PP Standard options .PP \fB\-f\fR FILE File name (mandatory). .PP \fB\-h\fR Prints this help. \fB\-o\fR FILE Name of output file. \fB\-t\fR THR Number of threads to be used. .IP Default: 1. .PP \fB\-v\fR n Level of verbosity, 0 \- 2 .IP 0 \- no output (default). 1 \- global information at the start and .IP end of the computation. .IP 2 \- detailed output for each step of the .IP algorithm, e.g. matrix sizes, #pairs, ... .SS "Input file format:" .IP \- first line: variables separated by a comma \- second line: characteristic of the field \- next lines provide the polynomials (one per line), .IP separated by a comma (no comma after the final polynomial) .PP 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, \fB\-1\fR,[]]: Else: Over prime fields: a rational parametrization of the solutions When input coefficients are rational numbers: real solutions to the input system (see the \fB\-P\fR flag to recover a parametrization of the solutions) See the msolve tutorial for more details (https://msolve.lip6.fr) .PP Advanced options: .PP \fB\-F\fR FILE File name encoding parametrizations in binary format. .PP \fB\-g\fR GB Prints reduced Groebner bases of input system for .IP 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. .PP \fB\-c\fR GEN Handling genericity: If the staircase is not generic .IP 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 .IP random linear form. (default) .SS "-C Use sparse-FGLM-col algorithm:" .IP 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. .PP \fB\-e\fR ELIM Define an elimination order: msolve supports two .IP 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. .PP \fB\-I\fR Isolates the real roots (provided some univariate data) .IP without re\-computing a Gr??bner basis Default: 0 (no). .SS "-l LIN Linear algebra variant to be applied:" .IP 1 \- exact sparse / dense 2 \- exact sparse (default) .IP 42 \- sparse / dense linearization (probabilistic) 44 \- sparse linearization (probabilistic) .PP \fB\-m\fR MPR Maximal number of pairs used per matrix. .IP Default: 0 (unlimited). .PP \fB\-n\fR NF Given n input generators compute normal form of the last NF .IP 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. .PP \fB\-p\fR PRE Precision of the real root isolation. .IP Default is 32. .PP \fB\-P\fR PAR Get also rational parametrization of solution set. .IP Default is 0. For a detailed description of the output format please see the general output data format section above. .PP \fB\-q\fR Q Uses signature\-based algorithms. .IP Default: 0 (no). .PP \fB\-r\fR RED Reduce Groebner basis. .IP Default: 1 (yes). .PP \fB\-s\fR HTS Initial hash table size given .IP as power of two. Default: 17. .SS "-S Use f4sat saturation algorithm:" .IP 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. .PP \fB\-u\fR UHT Number of steps after which the .IP hash table is newly generated. Default: 0, i.e. no update. .PP msolve library for polynomial system solving implemented by J. Berthomieu, C. Eder, M. Safey El Din .SS "Basic call:" .IP \&./msolve \fB\-f\fR [FILE1] \fB\-o\fR [FILE2] .PP FILE1 and FILE2 are respectively the input and output files .PP Standard options .PP \fB\-f\fR FILE File name (mandatory). .PP \fB\-h\fR Prints this help. \fB\-o\fR FILE Name of output file. \fB\-t\fR THR Number of threads to be used. .IP Default: 1. .PP \fB\-v\fR n Level of verbosity, 0 \- 2 .IP 0 \- no output (default). 1 \- global information at the start and .IP end of the computation. .IP 2 \- detailed output for each step of the .IP algorithm, e.g. matrix sizes, #pairs, ... .SS "Input file format:" .IP \- first line: variables separated by a comma \- second line: characteristic of the field \- next lines provide the polynomials (one per line), .IP separated by a comma (no comma after the final polynomial) .PP 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, \fB\-1\fR,[]]: Else: Over prime fields: a rational parametrization of the solutions When input coefficients are rational numbers: real solutions to the input system (see the \fB\-P\fR flag to recover a parametrization of the solutions) See the msolve tutorial for more details (https://msolve.lip6.fr) .PP Advanced options: .PP \fB\-F\fR FILE File name encoding parametrizations in binary format. .PP \fB\-g\fR GB Prints reduced Groebner bases of input system for .IP 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. .PP \fB\-c\fR GEN Handling genericity: If the staircase is not generic .IP 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 .IP random linear form. (default) .SS "-C Use sparse-FGLM-col algorithm:" .IP 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. .PP \fB\-e\fR ELIM Define an elimination order: msolve supports two .IP 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. .PP \fB\-I\fR Isolates the real roots (provided some univariate data) .IP without re\-computing a Gr??bner basis Default: 0 (no). .SS "-l LIN Linear algebra variant to be applied:" .IP 1 \- exact sparse / dense 2 \- exact sparse (default) .IP 42 \- sparse / dense linearization (probabilistic) 44 \- sparse linearization (probabilistic) .PP \fB\-m\fR MPR Maximal number of pairs used per matrix. .IP Default: 0 (unlimited). .PP \fB\-n\fR NF Given n input generators compute normal form of the last NF .IP 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. .PP \fB\-p\fR PRE Precision of the real root isolation. .IP Default is 32. .PP \fB\-P\fR PAR Get also rational parametrization of solution set. .IP Default is 0. For a detailed description of the output format please see the general output data format section above. .PP \fB\-q\fR Q Uses signature\-based algorithms. .IP Default: 0 (no). .PP \fB\-r\fR RED Reduce Groebner basis. .IP Default: 1 (yes). .PP \fB\-s\fR HTS Initial hash table size given .IP as power of two. Default: 17. .SS "-S Use f4sat saturation algorithm:" .IP 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. .PP \fB\-u\fR UHT Number of steps after which the .IP hash table is newly generated. Default: 0, i.e. no update.