1MSOLVE(1) User Commands MSOLVE(1)
2
6 msolve - manual page for msolve
7
9 msolve library for polynomial system solving implemented by J.
10 Berthomieu, C. Eder, M. Safey El Din
11 Basic call:
13 ./msolve -f [FILE1] -o [FILE2]
14 FILE1 and FILE2 are respectively the input and output files
16 Standard options
18 -f FILE File name (mandatory).
20 -h Prints this help. -o FILE Name of output file. -t THR
22 Number of threads to be used.
23 Default: 1.
25 -v n Level of verbosity, 0 - 2
27 0 - no output (default). 1 - global information at the start
29 and
30 end of the computation.
32 2 - detailed output for each step of the
34 algorithm, e.g. matrix sizes, #pairs, ...
36 Input file format:
38 - first line: variables separated by a comma - second line:
39 characteristic of the field - next lines provide the polynomials
40 (one per line),
41 separated by a comma (no comma after the final polynomial)
43 Output file format: When there is no solution in an algebraic closure
45 of the base field [-1]: Where there are infinitely many solutions in an
46 algebraic closure of the base field: [1, nvars, -1,[]]: Else: Over
47 prime fields: a rational parametrization of the solutions When input
48 coefficients are rational numbers: real solutions to the input system
49 (see the -P flag to recover a parametrization of the solutions) See the
50 msolve tutorial for more details (https://msolve.lip6.fr)
51 Advanced options:
53 -F FILE File name encoding parametrizations in binary format.
55 -g GB Prints reduced Groebner bases of input system for
57 first prime characteristic w.r.t. grevlex ordering. One element
59 per line is printed, commata separated. 0 - Nothing is printed.
60 (default) 1 - Leading ideal is printed. 2 - Full reduced Groeb‐
61 ner basis is printed.
62 -c GEN Handling genericity: If the staircase is not generic
64 enough, msolve can automatically try to fix this situation via
66 first trying a change of the order of and finally adding a ran‐
67 dom linear form with a new variable (smallest w.r.t. DRL) 0 -
68 Nothing is done, msolve quits. 1 - Change order of variables.
69 2 - Change order of variables, then try adding a
70 random linear form. (default)
72 -C Use sparse-FGLM-col algorithm:
74 Given an input file with k polynomials compute the quotient of
75 the ideal generated by the first k-1 polynomials with respect to
76 the kth polynomial.
77 -e ELIM Define an elimination order: msolve supports two
79 blocks, each block using degree reverse lexicographical monomial
81 order. ELIM has to be a number between 1 and #variables-1. The
82 basis the first block eliminated is then computed.
83 -I Isolates the real roots (provided some univariate data)
85 without re-computing a Gröbner basis Default: 0 (no).
87 -l LIN Linear algebra variant to be applied:
89 1 - exact sparse / dense 2 - exact sparse (default)
90 42 - sparse / dense linearization (probabilistic) 44 - sparse
92 linearization (probabilistic)
93 -m MPR Maximal number of pairs used per matrix.
95 Default: 0 (unlimited).
97 -n NF Given n input generators compute normal form of the last NF
99 elements of the input w.r.t. a degree reverse lexicographical
101 Gröbner basis of the irst (n - NF) input elements. At the mo‐
102 ment this only works for prime field computations. Combining
103 this option with the "-i" option assumes that the first (n - NF)
104 elements generate already a degree reverse lexicographical
105 Gröbner basis.
106 -p PRE Precision of the real root isolation.
108 Default is 32.
110 -P PAR Get also rational parametrization of solution set.
112 Default is 0. For a detailed description of the output format
114 please see the general output data format section above.
115 -q Q Uses signature-based algorithms.
117 Default: 0 (no).
119 -r RED Reduce Groebner basis.
121 Default: 1 (yes).
123 -s HTS Initial hash table size given
125 as power of two. Default: 17.
127 -S Use f4sat saturation algorithm:
129 Given an input file with k polynomials compute the saturation of
130 the ideal generated by the first k-1 polynomials with respect to
131 the kth polynomial.
132 -u UHT Number of steps after which the
134 hash table is newly generated. Default: 0, i.e. no update.
136 msolve library for polynomial system solving implemented by J.
138 Berthomieu, C. Eder, M. Safey El Din
139 Basic call:
141 ./msolve -f [FILE1] -o [FILE2]
142 FILE1 and FILE2 are respectively the input and output files
144 Standard options
146 -f FILE File name (mandatory).
148 -h Prints this help. -o FILE Name of output file. -t THR
150 Number of threads to be used.
151 Default: 1.
153 -v n Level of verbosity, 0 - 2
155 0 - no output (default). 1 - global information at the start
157 and
158 end of the computation.
160 2 - detailed output for each step of the
162 algorithm, e.g. matrix sizes, #pairs, ...
164 Input file format:
166 - first line: variables separated by a comma - second line:
167 characteristic of the field - next lines provide the polynomials
168 (one per line),
169 separated by a comma (no comma after the final polynomial)
171 Output file format: When there is no solution in an algebraic closure
173 of the base field [-1]: Where there are infinitely many solutions in an
174 algebraic closure of the base field: [1, nvars, -1,[]]: Else: Over
175 prime fields: a rational parametrization of the solutions When input
176 coefficients are rational numbers: real solutions to the input system
177 (see the -P flag to recover a parametrization of the solutions) See the
178 msolve tutorial for more details (https://msolve.lip6.fr)
179 Advanced options:
181 -F FILE File name encoding parametrizations in binary format.
183 -g GB Prints reduced Groebner bases of input system for
185 first prime characteristic w.r.t. grevlex ordering. One element
187 per line is printed, commata separated. 0 - Nothing is printed.
188 (default) 1 - Leading ideal is printed. 2 - Full reduced Groeb‐
189 ner basis is printed.
190 -c GEN Handling genericity: If the staircase is not generic
192 enough, msolve can automatically try to fix this situation via
194 first trying a change of the order of and finally adding a ran‐
195 dom linear form with a new variable (smallest w.r.t. DRL) 0 -
196 Nothing is done, msolve quits. 1 - Change order of variables.
197 2 - Change order of variables, then try adding a
198 random linear form. (default)
200 -C Use sparse-FGLM-col algorithm:
202 Given an input file with k polynomials compute the quotient of
203 the ideal generated by the first k-1 polynomials with respect to
204 the kth polynomial.
205 -e ELIM Define an elimination order: msolve supports two
207 blocks, each block using degree reverse lexicographical monomial
209 order. ELIM has to be a number between 1 and #variables-1. The
210 basis the first block eliminated is then computed.
211 -I Isolates the real roots (provided some univariate data)
213 without re-computing a Gröbner basis Default: 0 (no).
215 -l LIN Linear algebra variant to be applied:
217 1 - exact sparse / dense 2 - exact sparse (default)
218 42 - sparse / dense linearization (probabilistic) 44 - sparse
220 linearization (probabilistic)
221 -m MPR Maximal number of pairs used per matrix.
223 Default: 0 (unlimited).
225 -n NF Given n input generators compute normal form of the last NF
227 elements of the input w.r.t. a degree reverse lexicographical
229 Gröbner basis of the irst (n - NF) input elements. At the mo‐
230 ment this only works for prime field computations. Combining
231 this option with the "-i" option assumes that the first (n - NF)
232 elements generate already a degree reverse lexicographical
233 Gröbner basis.
234 -p PRE Precision of the real root isolation.
236 Default is 32.
238 -P PAR Get also rational parametrization of solution set.
240 Default is 0. For a detailed description of the output format
242 please see the general output data format section above.
243 -q Q Uses signature-based algorithms.
245 Default: 0 (no).
247 -r RED Reduce Groebner basis.
249 Default: 1 (yes).
251 -s HTS Initial hash table size given
253 as power of two. Default: 17.
255 -S Use f4sat saturation algorithm:
257 Given an input file with k polynomials compute the saturation of
258 the ideal generated by the first k-1 polynomials with respect to
259 the kth polynomial.
260 -u UHT Number of steps after which the
262 hash table is newly generated. Default: 0, i.e. no update.
264msolve November 2023 MSOLVE(1)