1 | initial version |
To complement @rburing answer, you can specify an algorithm to solve the simplified system of equations:
sage: %time solve(list(map(SR, G)), list(map(SR, R.gens())), algorithm='giac', solution_dict=True)
CPU times: user 128 ms, sys: 0 ns, total: 128 ms
Wall time: 127 ms
[{a15: a15,
x13_14: x13_14,
a4: a4,
a11: a11,
a0: 1,
x14_15: x14_15,
x11_13: x11_13,
x5_5: x5_5,
x9_12: x9_12,
a5: 1/x5_5,
a12: a12,
x3_4: 0,
a1: 1,
x7_7: x7_7,
x11_14: x11_14,
x12_15: x12_15,
x5_6: x5_6,
x4_4: 1/a4,
x9_9: x9_9,
a6: a6,
a13: a13,
x3_5: x3_5,
a2: 1,
x10_10: x10_10,
x7_8: x7_8,
x6_6: 1/a6,
x5_7: x5_7,
x12_12: 1/a12,
x8_8: x8_8,
a7: 1/x7_7,
x3_6: x3_6,
x6_7: x6_7,
x14_14: x14_14,
a9: 1/x9_9,
x15_15: 1/a15,
x4_6: x4_6,
x11_11: 1/a11,
x8_9: 0,
a8: 1/x8_8,
x10_12: x10_12,
a14: 1/x14_14,
x13_13: 1/a13,
a3: 1,
a10: 1/x10_10,
x4_7: x4_7,
x12_14: x12_14,
x11_12: 0,
x13_15: x13_15,
x10_13: x10_13},
{a15: a15,
x13_14: x13_14,
a4: a4,
a11: a11,
a0: 1,
x14_15: x14_15,
x11_13: x11_13,
x5_5: x5_5,
x9_12: x9_12,
a5: 1/x5_5,
a12: a12,
x3_4: 0,
a1: 1,
x7_7: x7_7,
x11_14: x11_14,
x12_15: x12_15,
x5_6: x5_6,
x4_4: 1/a4,
x9_9: x9_9,
a6: a6,
a13: a13,
x3_5: x3_5,
a2: 1,
x10_10: x10_10,
x7_8: 0,
x6_6: 1/a6,
x5_7: x5_7,
x12_12: 1/a12,
x8_8: x8_8,
a7: 1/x7_7,
x3_6: x3_6,
x6_7: x6_7,
x14_14: x14_14,
a9: 1/x9_9,
x15_15: 1/a15,
x4_6: x4_6,
x11_11: 1/a11,
x8_9: x8_9,
a8: 1/x8_8,
x10_12: x10_12,
a14: 1/x14_14,
x13_13: 1/a13,
a3: 1,
a10: 1/x10_10,
x4_7: x4_7,
x12_14: x12_14,
x11_12: 0,
x13_15: x13_15,
x10_13: x10_13}]
Note that, in contrast with maxima, giac does not seem to introduce free parameter like r19
to describe the solutions, instead the values of the dict are unchanged if they are free.
2 | No.2 Revision |
To complement @rburing answer, you You can specify an algorithm to solve the simplified system of equations:
sage: %time solve(polys, vs, algorithm='giac', solution_dict=True)
// Giac share root-directory:/opt/sagemath/sage-source/local/share/giac/
// Giac share root-directory:/opt/sagemath/sage-source/local/share/giac/
Help file /opt/sagemath/sage-source/local/share/giac/doc/fr/aide_cas not found
Added 0 synonyms
CPU times: user 531 ms, sys: 32.8 ms, total: 564 ms
Wall time: 563 ms
[{a15: 1/x15_15,
x13_14: x13_14,
a4: 1/x4_4,
a11: 1/x11_11,
a0: 1,
x14_15: x14_15,
x11_13: x11_13,
x5_5: 1/a5,
x9_12: x9_12,
a5: a5,
a12: 1/x12_12,
x3_4: 0,
a1: 1,
x7_7: x7_7,
x11_14: x11_14,
x12_15: x12_15,
x5_6: x5_6,
x4_4: x4_4,
x9_9: x9_9,
a6: a6,
a13: a13,
x3_5: x3_5,
a2: 1,
x10_10: x10_10,
x7_8: x7_8,
x6_6: 1/a6,
x5_7: x5_7,
x12_12: x12_12,
x8_8: x8_8,
a7: 1/x7_7,
x3_6: x3_6,
x6_7: x6_7,
x14_14: x14_14,
a9: 1/x9_9,
x15_15: x15_15,
x4_6: x4_6,
x11_11: x11_11,
x8_9: 0,
a8: 1/x8_8,
x10_12: x10_12,
a14: 1/x14_14,
x13_13: 1/a13,
a3: 1,
a10: 1/x10_10,
x4_7: x4_7,
x12_14: x12_14,
x11_12: 0,
x13_15: x13_15,
x10_13: x10_13},
{a15: 1/x15_15,
x13_14: x13_14,
a4: 1/x4_4,
a11: 1/x11_11,
a0: 1,
x14_15: x14_15,
x11_13: x11_13,
x5_5: 1/a5,
x9_12: x9_12,
a5: a5,
a12: 1/x12_12,
x3_4: 0,
a1: 1,
x7_7: x7_7,
x11_14: x11_14,
x12_15: x12_15,
x5_6: x5_6,
x4_4: x4_4,
x9_9: x9_9,
a6: a6,
a13: a13,
x3_5: x3_5,
a2: 1,
x10_10: x10_10,
x7_8: x7_8,
x6_6: 1/a6,
x5_7: x5_7,
x12_12: x12_12,
x8_8: x8_8,
a7: 1/x7_7,
x3_6: x3_6,
x6_7: x6_7,
x14_14: x14_14,
a9: 1/x9_9,
x15_15: x15_15,
x4_6: x4_6,
x11_11: x11_11,
x8_9: 0,
a8: 1/x8_8,
x10_12: x10_12,
a14: 1/x14_14,
x13_13: 1/a13,
a3: 1,
a10: 1/x10_10,
x4_7: x4_7,
x12_14: x12_14,
x11_12: 0,
x13_15: x13_15,
x10_13: 0},
{a15: 1/x15_15,
x13_14: x13_14,
a4: 1/x4_4,
a11: 1/x11_11,
a0: 1,
x14_15: x14_15,
x11_13: x11_13,
x5_5: 1/a5,
x9_12: x9_12,
a5: a5,
a12: 1/x12_12,
x3_4: 0,
a1: 1,
x7_7: x7_7,
x11_14: x11_14,
x12_15: x12_15,
x5_6: x5_6,
x4_4: x4_4,
x9_9: x9_9,
a6: a6,
a13: a13,
x3_5: x3_5,
a2: 1,
x10_10: x10_10,
x7_8: x7_8,
x6_6: 1/a6,
x5_7: x5_7,
x12_12: x12_12,
x8_8: x8_8,
a7: 1/x7_7,
x3_6: x3_6,
x6_7: x6_7,
x14_14: x14_14,
a9: 1/x9_9,
x15_15: x15_15,
x4_6: x4_6,
x11_11: x11_11,
x8_9: 0,
a8: 1/x8_8,
x10_12: 0,
a14: 1/x14_14,
x13_13: 1/a13,
a3: 1,
a10: 1/x10_10,
x4_7: x4_7,
x12_14: x12_14,
x11_12: 0,
x13_15: x13_15,
x10_13: 0},
{a15: 1/x15_15,
x13_14: x13_14,
a4: 1/x4_4,
a11: 1/x11_11,
a0: 1,
x14_15: x14_15,
x11_13: x11_13,
x5_5: 1/a5,
x9_12: x9_12,
a5: a5,
a12: 1/x12_12,
x3_4: 0,
a1: 1,
x7_7: x7_7,
x11_14: x11_14,
x12_15: x12_15,
x5_6: x5_6,
x4_4: x4_4,
x9_9: x9_9,
a6: a6,
a13: a13,
x3_5: x3_5,
a2: 1,
x10_10: x10_10,
x7_8: x7_8,
x6_6: 1/a6,
x5_7: x5_7,
x12_12: x12_12,
x8_8: x8_8,
a7: 1/x7_7,
x3_6: 0,
x6_7: x6_7,
x14_14: x14_14,
a9: 1/x9_9,
x15_15: x15_15,
x4_6: x12_14,
x11_11: x11_11,
x8_9: 0,
a8: 1/x8_8,
x10_12: 0,
a14: 1/x14_14,
x13_13: 1/a13,
a3: 1,
a10: 1/x10_10,
x4_7: x4_7,
x12_14: x12_14,
x11_12: 0,
x13_15: x13_15,
x10_13: 0},
{a15: 1/x15_15,
x13_14: x13_14,
a4: 1/x4_4,
a11: 1/x11_11,
a0: 1,
x14_15: x14_15,
x11_13: x11_13,
x5_5: 1/a5,
x9_12: x9_12,
a5: a5,
a12: 1/x12_12,
x3_4: 0,
a1: 1,
x7_7: x7_7,
x11_14: x11_14,
x12_15: x12_15,
x5_6: x5_6,
x4_4: x4_4,
x9_9: x9_9,
a6: a6,
a13: a13,
x3_5: x3_5,
a2: 1,
x10_10: x10_10,
x7_8: x7_8,
x6_6: 1/a6,
x5_7: x13_15,
x12_12: x12_12,
x8_8: x8_8,
a7: 1/x7_7,
x3_6: 0,
x6_7: x6_7,
x14_14: x14_14,
a9: 1/x9_9,
x15_15: x15_15,
x4_6: x12_14,
x11_11: x11_11,
x8_9: 0,
a8: 1/x8_8,
x10_12: 0,
a14: 1/x14_14,
x13_13: 1/a13,
a3: 1,
a10: 1/x10_10,
x4_7: x4_7,
x12_14: x12_14,
x11_12: 0,
x13_15: x13_15,
x10_13: 0},
{a15: 1/x15_15,
x13_14: x13_14,
a4: 1/x4_4,
a11: 1/x11_11,
a0: 1,
x14_15: x14_15,
x11_13: x11_13,
x5_5: 1/a5,
x9_12: x9_12,
a5: a5,
a12: 1/x12_12,
x3_4: 0,
a1: 1,
x7_7: x7_7,
x11_14: x11_14,
x12_15: x12_15,
x5_6: x5_6,
x4_4: x4_4,
x9_9: x9_9,
a6: 1/x14_14,
a13: a13,
x3_5: 0,
a2: 1,
x10_10: x10_10,
x7_8: 0,
x6_6: x14_14,
x5_7: x13_15,
x12_12: x12_12,
x8_8: x8_8,
a7: 1/x7_7,
x3_6: 0,
x6_7: x6_7,
x14_14: x14_14,
a9: 1/x9_9,
x15_15: x15_15,
x4_6: x12_14,
x11_11: x11_11,
x8_9: 0,
a8: 1/x8_8,
x10_12: 0,
a14: 1/x14_14,
x13_13: 1/a13,
a3: 1,
a10: 1/x10_10,
x4_7: x4_7,
x12_14: x12_14,
x11_12: 0,
x13_15: x13_15,
x10_13: 0},
{a15: 1/x15_15,
x13_14: x13_14,
a4: 1/x12_12,
a11: 1/x11_11,
a0: 1,
x14_15: x14_15,
x11_13: x11_13,
x5_5: 1/a5,
x9_12: x9_12,
a5: a5,
a12: 1/x12_12,
x3_4: 0,
a1: 1,
x7_7: x7_7,
x11_14: x11_14,
x12_15: x12_15,
x5_6: x5_6,
x4_4: x12_12,
x9_9: x9_9,
a6: 1/x14_14,
a13: a13,
x3_5: 0,
a2: 1,
x10_10: x10_10,
x7_8: 0,
x6_6: x14_14,
x5_7: x13_15,
x12_12: x12_12,
x8_8: x8_8,
a7: 1/x7_7,
x3_6: 0,
x6_7: x6_7,
x14_14: x14_14,
a9: 1/x9_9,
x15_15: x15_15,
x4_6: x12_14,
x11_11: x11_11,
x8_9: 0,
a8: 1/x8_8,
x10_12: 0,
a14: 1/x14_14,
x13_13: 1/a13,
a3: 1,
a10: 1/x10_10,
x4_7: x4_7,
x12_14: x12_14,
x11_12: 0,
x13_15: x13_15,
x10_13: 0},
{a15: 1/x15_15,
x13_14: x13_14,
a4: 1/x12_12,
a11: 1/x11_11,
a0: 1,
x14_15: x14_15,
x11_13: x11_13,
x5_5: 1/a5,
x9_12: x9_12,
a5: a5,
a12: 1/x12_12,
x3_4: 0,
a1: 1,
x7_7: x7_7,
x11_14: x11_14,
x12_15: x4_7,
x5_6: x5_6,
x4_4: x12_12,
x9_9: x9_9,
a6: 1/x14_14,
a13: a13,
x3_5: 0,
a2: 1,
x10_10: x10_10,
x7_8: 0,
x6_6: x14_14,
x5_7: x13_15,
x12_12: x12_12,
x8_8: x8_8,
a7: 1/x7_7,
x3_6: 0,
x6_7: x6_7,
x14_14: x14_14,
a9: 1/x9_9,
x15_15: x15_15,
x4_6: x12_14,
x11_11: x11_11,
x8_9: 0,
a8: 1/x8_8,
x10_12: 0,
a14: 1/x14_14,
x13_13: 1/a13,
a3: 1,
a10: 1/x10_10,
x4_7: x4_7,
x12_14: x12_14,
x11_12: 0,
x13_15: x13_15,
x10_13: 0},
{a15: 1/x15_15,
x13_14: x13_14,
a4: 1/x12_12,
a11: 1/x11_11,
a0: 1,
x14_15: x14_15,
x11_13: x11_13,
x5_5: 1/a5,
x9_12: x9_12,
a5: a5,
a12: 1/x12_12,
x3_4: 0,
a1: 1,
x7_7: x7_7,
x11_14: 0,
x12_15: x4_7,
x5_6: x5_6,
x4_4: x12_12,
x9_9: x9_9,
a6: 1/x14_14,
a13: a13,
x3_5: 0,
a2: 1,
x10_10: x10_10,
x7_8: 0,
x6_6: x14_14,
x5_7: x13_15,
x12_12: x12_12,
x8_8: x8_8,
a7: 1/x7_7,
x3_6: 0,
x6_7: x6_7,
x14_14: x14_14,
a9: 1/x9_9,
x15_15: x15_15,
x4_6: x12_14,
x11_11: x11_11,
x8_9: 0,
a8: 1/x8_8,
x10_12: 0,
a14: 1/x14_14,
x13_13: 1/a13,
a3: 1,
a10: 1/x10_10,
x4_7: x4_7,
x12_14: x12_14,
x11_12: 0,
x13_15: x13_15,
x10_13: 0},
{a15: 1/x15_15,
x13_14: x13_14,
a4: 1/x4_4,
a11: 1/x11_11,
a0: 1,
x14_15: x14_15,
x11_13: x11_13,
x5_5: 1/a5,
x9_12: x9_12,
a5: a5,
a12: 1/x12_12,
x3_4: 0,
a1: 1,
x7_7: x7_7,
x11_14: x11_14,
x12_15: x12_15,
x5_6: x5_6,
x4_4: x4_4,
x9_9: x9_9,
a6: 1/x14_14,
a13: a13,
x3_5: x3_5,
a2: 1,
x10_10: x10_10,
x7_8: 0,
x6_6: x14_14,
x5_7: x13_15,
x12_12: x12_12,
x8_8: x8_8,
a7: 1/x7_7,
x3_6: 0,
x6_7: x6_7,
x14_14: x14_14,
a9: 1/x9_9,
x15_15: x15_15,
x4_6: x12_14,
x11_11: x11_11,
x8_9: 0,
a8: 1/x8_8,
x10_12: 0,
a14: 1/x14_14,
x13_13: 1/a13,
a3: 1,
a10: 1/x10_10,
x4_7: x4_7,
x12_14: x12_14,
x11_12: 0,
x13_15: x13_15,
x10_13: 0},
{a15: 1/x15_15,
x13_14: x13_14,
a4: 1/x4_4,
a11: 1/x11_11,
a0: 1,
x14_15: x14_15,
x11_13: x11_13,
x5_5: 1/a5,
x9_12: x9_12,
a5: a5,
a12: 1/x12_12,
x3_4: 0,
a1: 1,
x7_7: x7_7,
x11_14: x11_14,
x12_15: x12_15,
x5_6: x5_6,
x4_4: x4_4,
x9_9: x9_9,
a6: 1/x14_14,
a13: a13,
x3_5: x3_5,
a2: 1,
x10_10: x10_10,
x7_8: x7_8,
x6_6: x14_14,
x5_7: x13_15,
x12_12: x12_12,
x8_8: x8_8,
a7: 1/x7_7,
x3_6: 0,
x6_7: x6_7,
x14_14: x14_14,
a9: 1/x9_9,
x15_15: x15_15,
x4_6: x12_14,
x11_11: x11_11,
x8_9: 0,
a8: 1/x8_8,
x10_12: 0,
a14: 1/x14_14,
x13_13: 1/a13,
a3: 1,
a10: 1/x10_10,
x4_7: x4_7,
x12_14: x12_14,
x11_12: 0,
x13_15: x13_15,
x10_13: 0},
{a15: 1,
x13_14: x13_14,
a4: 1/x4_4,
a11: 1/x11_11,
a0: 1,
x14_15: x14_15,
x11_13: x11_13,
x5_5: 1/a5,
x9_12: x9_12,
a5: a5,
a12: 1/x12_12,
x3_4: 0,
a1: 1,
x7_7: x7_7,
x11_14: x11_14,
x12_15: x12_15,
x5_6: x5_6,
x4_4: x4_4,
x9_9: x9_9,
a6: 1/x14_14,
a13: a13,
x3_5: 0,
a2: 1,
x10_10: x10_10,
x7_8: x7_8,
x6_6: x14_14,
x5_7: x13_15,
x12_12: x12_12,
x8_8: x8_8,
a7: 1/x7_7,
x3_6: 0,
x6_7: x6_7,
x14_14: x14_14,
a9: 1/x9_9,
x15_15: 1,
x4_6: x12_14,
x11_11: x11_11,
x8_9: 0,
a8: 1/x8_8,
x10_12: 0,
a14: 1/x14_14,
x13_13: 1/a13,
a3: 1,
a10: 1/x10_10,
x4_7: x4_7,
x12_14: x12_14,
x11_12: 0,
x13_15: x13_15,
x10_13: 0},
{a15: 1,
x13_14: x13_14,
a4: 1/x12_12,
a11: 1/x11_11,
a0: 1,
x14_15: x14_15,
x11_13: x11_13,
x5_5: 1/a5,
x9_12: x9_12,
a5: a5,
a12: 1/x12_12,
x3_4: 0,
a1: 1,
x7_7: x7_7,
x11_14: x11_14,
x12_15: x12_15,
x5_6: x5_6,
x4_4: x12_12,
x9_9: x9_9,
a6: 1/x14_14,
a13: a13,
x3_5: 0,
a2: 1,
x10_10: x10_10,
x7_8: x7_8,
x6_6: x14_14,
x5_7: x13_15,
x12_12: x12_12,
x8_8: x8_8,
a7: 1/x7_7,
x3_6: 0,
x6_7: x6_7,
x14_14: x14_14,
a9: 1/x9_9,
x15_15: 1,
x4_6: x12_14,
x11_11: x11_11,
x8_9: 0,
a8: 1/x8_8,
x10_12: 0,
a14: 1/x14_14,
x13_13: 1/a13,
a3: 1,
a10: 1/x10_10,
x4_7: x4_7,
x12_14: x12_14,
x11_12: 0,
x13_15: x13_15,
x10_13: 0},
{a15: 1,
x13_14: x13_14,
a4: 1/x12_12,
a11: 1/x11_11,
a0: 1,
x14_15: x14_15,
x11_13: x11_13,
x5_5: 1/a5,
x9_12: x9_12,
a5: a5,
a12: 1/x12_12,
x3_4: 0,
a1: 1,
x7_7: x7_7,
x11_14: x11_14,
x12_15: x4_7,
x5_6: x5_6,
x4_4: x12_12,
x9_9: x9_9,
a6: 1/x14_14,
a13: a13,
x3_5: 0,
a2: 1,
x10_10: x10_10,
x7_8: x7_8,
x6_6: x14_14,
x5_7: x13_15,
x12_12: x12_12,
x8_8: x8_8,
a7: 1/x7_7,
x3_6: 0,
x6_7: x6_7,
x14_14: x14_14,
a9: 1/x9_9,
x15_15: 1,
x4_6: x12_14,
x11_11: x11_11,
x8_9: 0,
a8: 1/x8_8,
x10_12: 0,
a14: 1/x14_14,
x13_13: 1/a13,
a3: 1,
a10: 1/x10_10,
x4_7: x4_7,
x12_14: x12_14,
x11_12: 0,
x13_15: x13_15,
x10_13: 0},
{a15: 1,
x13_14: x13_14,
a4: 1/x12_12,
a11: 1/x11_11,
a0: 1,
x14_15: x14_15,
x11_13: x11_13,
x5_5: 1/a5,
x9_12: x9_12,
a5: a5,
a12: 1/x12_12,
x3_4: 0,
a1: 1,
x7_7: x7_7,
x11_14: 0,
x12_15: x4_7,
x5_6: x5_6,
x4_4: x12_12,
x9_9: x9_9,
a6: 1/x14_14,
a13: a13,
x3_5: 0,
a2: 1,
x10_10: x10_10,
x7_8: x7_8,
x6_6: x14_14,
x5_7: x13_15,
x12_12: x12_12,
x8_8: x8_8,
a7: 1/x7_7,
x3_6: 0,
x6_7: x6_7,
x14_14: x14_14,
a9: 1/x9_9,
x15_15: 1,
x4_6: x12_14,
x11_11: x11_11,
x8_9: 0,
a8: 1/x8_8,
x10_12: 0,
a14: 1/x14_14,
x13_13: 1/a13,
a3: 1,
a10: 1/x10_10,
x4_7: x4_7,
x12_14: x12_14,
x11_12: 0,
x13_15: x13_15,
x10_13: 0},
{a15: 1,
x13_14: x13_14,
a4: 1/x4_4,
a11: 1/x11_11,
a0: 1,
x14_15: x14_15,
x11_13: x11_13,
x5_5: 1/a5,
x9_12: x9_12,
a5: a5,
a12: 1/x12_12,
x3_4: 0,
a1: 1,
x7_7: x7_7,
x11_14: x11_14,
x12_15: x12_15,
x5_6: x5_6,
x4_4: x4_4,
x9_9: x9_9,
a6: 1/x14_14,
a13: a13,
x3_5: x3_5,
a2: 1,
x10_10: x10_10,
x7_8: x7_8,
x6_6: x14_14,
x5_7: x13_15,
x12_12: x12_12,
x8_8: x8_8,
a7: 1/x7_7,
x3_6: 0,
x6_7: x6_7,
x14_14: x14_14,
a9: 1/x9_9,
x15_15: 1,
x4_6: x12_14,
x11_11: x11_11,
x8_9: 0,
a8: 1/x8_8,
x10_12: 0,
a14: 1/x14_14,
x13_13: 1/a13,
a3: 1,
a10: 1/x10_10,
x4_7: x4_7,
x12_14: x12_14,
x11_12: 0,
x13_15: x13_15,
x10_13: 0},
{a15: 1/x15_15,
x13_14: x13_14,
a4: 1/x4_4,
a11: 1/x11_11,
a0: 1,
x14_15: x14_15,
x11_13: x11_13,
x5_5: 1/a5,
x9_12: x9_12,
a5: a5,
a12: 1/x12_12,
x3_4: 0,
a1: 1,
x7_7: x7_7,
x11_14: x11_14,
x12_15: x12_15,
x5_6: x5_6,
x4_4: x4_4,
x9_9: x9_9,
a6: a6,
a13: a13,
x3_5: x3_5,
a2: 1,
x10_10: x10_10,
x7_8: x7_8,
x6_6: 1/a6,
x5_7: x5_7,
x12_12: x12_12,
x8_8: x8_8,
a7: 1/x7_7,
x3_6: x3_6,
x6_7: x6_7,
x14_14: x14_14,
a9: 1/x9_9,
x15_15: x15_15,
x4_6: x12_14,
x11_11: x11_11,
x8_9: 0,
a8: 1/x8_8,
x10_12: 0,
a14: 1/x14_14,
x13_13: 1/a13,
a3: 1,
a10: 1/x10_10,
x4_7: x4_7,
x12_14: x12_14,
x11_12: 0,
x13_15: x13_15,
x10_13: 0},
{a15: 1/x15_15,
x13_14: x13_14,
a4: 1/x4_4,
a11: 1/x11_11,
a0: 1,
x14_15: x14_15,
x11_13: x11_13,
x5_5: 1/a5,
x9_12: x9_12,
a5: a5,
a12: 1/x12_12,
x3_4: 0,
a1: 1,
x7_7: x7_7,
x11_14: x11_14,
x12_15: x12_15,
x5_6: x5_6,
x4_4: x4_4,
x9_9: x9_9,
a6: a6,
a13: a13,
x3_5: x3_5,
a2: 1,
x10_10: x10_10,
x7_8: 0,
x6_6: 1/a6,
x5_7: x5_7,
x12_12: x12_12,
x8_8: x8_8,
a7: 1/x7_7,
x3_6: x3_6,
x6_7: x6_7,
x14_14: x14_14,
a9: 1/x9_9,
x15_15: x15_15,
x4_6: x4_6,
x11_11: x11_11,
x8_9: x8_9,
a8: 1/x8_8,
x10_12: x10_12,
a14: 1/x14_14,
x13_13: 1/a13,
a3: 1,
a10: 1/x10_10,
x4_7: x4_7,
x12_14: x12_14,
x11_12: 0,
x13_15: x13_15,
x10_13: x10_13},
{a15: 1/x15_15,
x13_14: x13_14,
a4: 1/x4_4,
a11: 1/x11_11,
a0: 1,
x14_15: x14_15,
x11_13: x11_13,
x5_5: 1/a5,
x9_12: x9_12,
a5: a5,
a12: 1/x12_12,
x3_4: 0,
a1: 1,
x7_7: x7_7,
x11_14: x11_14,
x12_15: x12_15,
x5_6: x5_6,
x4_4: x4_4,
x9_9: x9_9,
a6: a6,
a13: a13,
x3_5: x3_5,
a2: 1,
x10_10: x10_10,
x7_8: 0,
x6_6: 1/a6,
x5_7: x5_7,
x12_12: x12_12,
x8_8: x8_8,
a7: 1/x7_7,
x3_6: x3_6,
x6_7: x6_7,
x14_14: x14_14,
a9: 1/x9_9,
x15_15: x15_15,
x4_6: x4_6,
x11_11: x11_11,
x8_9: x8_9,
a8: 1/x8_8,
x10_12: x10_12,
a14: 1/x14_14,
x13_13: 1/a13,
a3: 1,
a10: 1/x10_10,
x4_7: x4_7,
x12_14: x12_14,
x11_12: 0,
x13_15: x13_15,
x10_13: 0},
{a15: 1/x15_15,
x13_14: x13_14,
a4: 1/x4_4,
a11: 1/x11_11,
a0: 1,
x14_15: x14_15,
x11_13: x11_13,
x5_5: 1/a5,
x9_12: x9_12,
a5: a5,
a12: 1/x12_12,
x3_4: 0,
a1: 1,
x7_7: x7_7,
x11_14: x11_14,
x12_15: x12_15,
x5_6: x5_6,
x4_4: x4_4,
x9_9: x9_9,
a6: a6,
a13: a13,
x3_5: x3_5,
a2: 1,
x10_10: x10_10,
x7_8: 0,
x6_6: 1/a6,
x5_7: x5_7,
x12_12: x12_12,
x8_8: x8_8,
a7: 1/x7_7,
x3_6: x3_6,
x6_7: x6_7,
x14_14: x14_14,
a9: 1/x9_9,
x15_15: x15_15,
x4_6: x4_6,
x11_11: x11_11,
x8_9: x8_9,
a8: 1/x8_8,
x10_12: 0,
a14: 1/x14_14,
x13_13: 1/a13,
a3: 1,
a10: 1/x10_10,
x4_7: x4_7,
x12_14: x12_14,
x11_12: 0,
x13_15: x13_15,
x10_13: 0},
{a15: 1/x15_15,
x13_14: x13_14,
a4: 1/x4_4,
a11: 1/x11_11,
a0: 1,
x14_15: x14_15,
x11_13: x11_13,
x5_5: 1/a5,
x9_12: x9_12,
a5: a5,
a12: 1/x12_12,
x3_4: 0,
a1: 1,
x7_7: x7_7,
x11_14: x11_14,
x12_15: x12_15,
x5_6: x5_6,
x4_4: x4_4,
x9_9: x9_9,
a6: a6,
a13: a13,
x3_5: x3_5,
a2: 1,
x10_10: x10_10,
x7_8: 0,
x6_6: 1/a6,
x5_7: x5_7,
x12_12: x12_12,
x8_8: x8_8,
a7: 1/x7_7,
x3_6: 0,
x6_7: x6_7,
x14_14: x14_14,
a9: 1/x9_9,
x15_15: x15_15,
x4_6: x12_14,
x11_11: x11_11,
x8_9: x8_9,
a8: 1/x8_8,
x10_12: 0,
a14: 1/x14_14,
x13_13: 1/a13,
a3: 1,
a10: 1/x10_10,
x4_7: x4_7,
x12_14: x12_14,
x11_12: 0,
x13_15: x13_15,
x10_13: 0},
{a15: 1/x15_15,
x13_14: x13_14,
a4: 1/x4_4,
a11: 1/x11_11,
a0: 1,
x14_15: x14_15,
x11_13: x11_13,
x5_5: 1/a5,
x9_12: x9_12,
a5: a5,
a12: 1/x12_12,
x3_4: 0,
a1: 1,
x7_7: x7_7,
x11_14: x11_14,
x12_15: x12_15,
x5_6: x5_6,
x4_4: x4_4,
x9_9: x9_9,
a6: a6,
a13: a13,
x3_5: x3_5,
a2: 1,
x10_10: x10_10,
x7_8: 0,
x6_6: 1/a6,
x5_7: x13_15,
x12_12: x12_12,
x8_8: x8_8,
a7: 1/x7_7,
x3_6: 0,
x6_7: x6_7,
x14_14: x14_14,
a9: 1/x9_9,
x15_15: x15_15,
x4_6: x12_14,
x11_11: x11_11,
x8_9: x8_9,
a8: 1/x8_8,
x10_12: 0,
a14: 1/x14_14,
x13_13: 1/a13,
a3: 1,
a10: 1/x10_10,
x4_7: x4_7,
x12_14: x12_14,
x11_12: 0,
x13_15: x13_15,
x10_13: 0},
{a15: 1/x15_15,
x13_14: x13_14,
a4: 1/x4_4,
a11: 1/x11_11,
a0: 1,
x14_15: x14_15,
x11_13: x11_13,
x5_5: 1/a5,
x9_12: x9_12,
a5: a5,
a12: 1/x12_12,
x3_4: 0,
a1: 1,
x7_7: x7_7,
x11_14: x11_14,
x12_15: x12_15,
x5_6: x5_6,
x4_4: x4_4,
x9_9: x9_9,
a6: 1/x14_14,
a13: a13,
x3_5: 0,
a2: 1,
x10_10: x10_10,
x7_8: 0,
x6_6: x14_14,
x5_7: x13_15,
x12_12: x12_12,
x8_8: x8_8,
a7: 1/x7_7,
x3_6: 0,
x6_7: x6_7,
x14_14: x14_14,
a9: 1/x9_9,
x15_15: x15_15,
x4_6: x12_14,
x11_11: x11_11,
x8_9: x8_9,
a8: 1/x8_8,
x10_12: 0,
a14: 1/x14_14,
x13_13: 1/a13,
a3: 1,
a10: 1/x10_10,
x4_7: x4_7,
x12_14: x12_14,
x11_12: 0,
x13_15: x13_15,
x10_13: 0},
{a15: 1/x15_15,
x13_14: x13_14,
a4: 1/x12_12,
a11: 1/x11_11,
a0: 1,
x14_15: x14_15,
x11_13: x11_13,
x5_5: 1/a5,
x9_12: x9_12,
a5: a5,
a12: 1/x12_12,
x3_4: 0,
a1: 1,
x7_7: x7_7,
x11_14: x11_14,
x12_15: x12_15,
x5_6: x5_6,
x4_4: x12_12,
x9_9: x9_9,
a6: 1/x14_14,
a13: a13,
x3_5: 0,
a2: 1,
x10_10: x10_10,
x7_8: 0,
x6_6: x14_14,
x5_7: x13_15,
x12_12: x12_12,
x8_8: x8_8,
a7: 1/x7_7,
x3_6: 0,
x6_7: x6_7,
x14_14: x14_14,
a9: 1/x9_9,
x15_15: x15_15,
x4_6: x12_14,
x11_11: x11_11,
x8_9: x8_9,
a8: 1/x8_8,
x10_12: 0,
a14: 1/x14_14,
x13_13: 1/a13,
a3: 1,
a10: 1/x10_10,
x4_7: x4_7,
x12_14: x12_14,
x11_12: 0,
x13_15: x13_15,
x10_13: 0},
{a15: 1/x15_15,
x13_14: x13_14,
a4: 1/x12_12,
a11: 1/x11_11,
a0: 1,
x14_15: x14_15,
x11_13: x11_13,
x5_5: 1/a5,
x9_12: x9_12,
a5: a5,
a12: 1/x12_12,
x3_4: 0,
a1: 1,
x7_7: x7_7,
x11_14: x11_14,
x12_15: x4_7,
x5_6: x5_6,
x4_4: x12_12,
x9_9: x9_9,
a6: 1/x14_14,
a13: a13,
x3_5: 0,
a2: 1,
x10_10: x10_10,
x7_8: 0,
x6_6: x14_14,
x5_7: x13_15,
x12_12: x12_12,
x8_8: x8_8,
a7: 1/x7_7,
x3_6: 0,
x6_7: x6_7,
x14_14: x14_14,
a9: 1/x9_9,
x15_15: x15_15,
x4_6: x12_14,
x11_11: x11_11,
x8_9: x8_9,
a8: 1/x8_8,
x10_12: 0,
a14: 1/x14_14,
x13_13: 1/a13,
a3: 1,
a10: 1/x10_10,
x4_7: x4_7,
x12_14: x12_14,
x11_12: 0,
x13_15: x13_15,
x10_13: 0},
{a15: 1/x15_15,
x13_14: x13_14,
a4: 1/x12_12,
a11: 1/x11_11,
a0: 1,
x14_15: x14_15,
x11_13: x11_13,
x5_5: 1/a5,
x9_12: x9_12,
a5: a5,
a12: 1/x12_12,
x3_4: 0,
a1: 1,
x7_7: x7_7,
x11_14: 0,
x12_15: x4_7,
x5_6: x5_6,
x4_4: x12_12,
x9_9: x9_9,
a6: 1/x14_14,
a13: a13,
x3_5: 0,
a2: 1,
x10_10: x10_10,
x7_8: 0,
x6_6: x14_14,
x5_7: x13_15,
x12_12: x12_12,
x8_8: x8_8,
a7: 1/x7_7,
x3_6: 0,
x6_7: x6_7,
x14_14: x14_14,
a9: 1/x9_9,
x15_15: x15_15,
x4_6: x12_14,
x11_11: x11_11,
x8_9: x8_9,
a8: 1/x8_8,
x10_12: 0,
a14: 1/x14_14,
x13_13: 1/a13,
a3: 1,
a10: 1/x10_10,
x4_7: x4_7,
x12_14: x12_14,
x11_12: 0,
x13_15: x13_15,
x10_13: 0},
{a15: 1/x15_15,
x13_14: x13_14,
a4: 1/x4_4,
a11: 1/x11_11,
a0: 1,
x14_15: x14_15,
x11_13: x11_13,
x5_5: 1/a5,
x9_12: x9_12,
a5: a5,
a12: 1/x12_12,
x3_4: 0,
a1: 1,
x7_7: x7_7,
x11_14: x11_14,
x12_15: x12_15,
x5_6: x5_6,
x4_4: x4_4,
x9_9: x9_9,
a6: 1/x14_14,
a13: a13,
x3_5: x3_5,
a2: 1,
x10_10: x10_10,
x7_8: 0,
x6_6: x14_14,
x5_7: x13_15,
x12_12: x12_12,
x8_8: x8_8,
a7: 1/x7_7,
x3_6: 0,
x6_7: x6_7,
x14_14: x14_14,
a9: 1/x9_9,
x15_15: x15_15,
x4_6: x12_14,
x11_11: x11_11,
x8_9: x8_9,
a8: 1/x8_8,
x10_12: 0,
a14: 1/x14_14,
x13_13: 1/a13,
a3: 1,
a10: 1/x10_10,
x4_7: x4_7,
x12_14: x12_14,
x11_12: 0,
x13_15: x13_15,
x10_13: 0},
{a15: 1/x15_15,
x13_14: x13_14,
a4: 1/x4_4,
a11: 1/x11_11,
a0: 1,
x14_15: x14_15,
x11_13: x11_13,
x5_5: 1/a5,
x9_12: x9_12,
a5: a5,
a12: 1/x12_12,
x3_4: 0,
a1: 1,
x7_7: x7_7,
x11_14: x11_14,
x12_15: x12_15,
x5_6: x5_6,
x4_4: x4_4,
x9_9: x9_9,
a6: a6,
a13: a13,
x3_5: x3_5,
a2: 1,
x10_10: x10_10,
x7_8: 0,
x6_6: 1/a6,
x5_7: x5_7,
x12_12: x12_12,
x8_8: x8_8,
a7: 1/x7_7,
x3_6: x3_6,
x6_7: x6_7,
x14_14: x14_14,
a9: 1/x9_9,
x15_15: x15_15,
x4_6: x12_14,
x11_11: x11_11,
x8_9: x8_9,
a8: 1/x8_8,
x10_12: 0,
a14: 1/x14_14,
x13_13: 1/a13,
a3: 1,
a10: 1/x10_10,
x4_7: x4_7,
x12_14: x12_14,
x11_12: 0,
x13_15: x13_15,
x10_13: 0}]
Note that, in contrast with maxima, giac does not seem to introduce free parameter like r19
to describe the solutions, instead the values of the dict are unchanged if they are free.
You can also use this to work with @rburing answer (giac knows about Groebner basis, but the solution is shorted here, perhaps because of a different monomial ordering):
sage: %time solve(list(map(SR, G)), list(map(SR, R.gens())), algorithm='giac', solution_dict=True)
CPU times: user 128 ms, sys: 0 ns, total: 128 ms
Wall time: 127 ms
[{a15: a15,
x13_14: x13_14,
a4: a4,
a11: a11,
a0: 1,
x14_15: x14_15,
x11_13: x11_13,
x5_5: x5_5,
x9_12: x9_12,
a5: 1/x5_5,
a12: a12,
x3_4: 0,
a1: 1,
x7_7: x7_7,
x11_14: x11_14,
x12_15: x12_15,
x5_6: x5_6,
x4_4: 1/a4,
x9_9: x9_9,
a6: a6,
a13: a13,
x3_5: x3_5,
a2: 1,
x10_10: x10_10,
x7_8: x7_8,
x6_6: 1/a6,
x5_7: x5_7,
x12_12: 1/a12,
x8_8: x8_8,
a7: 1/x7_7,
x3_6: x3_6,
x6_7: x6_7,
x14_14: x14_14,
a9: 1/x9_9,
x15_15: 1/a15,
x4_6: x4_6,
x11_11: 1/a11,
x8_9: 0,
a8: 1/x8_8,
x10_12: x10_12,
a14: 1/x14_14,
x13_13: 1/a13,
a3: 1,
a10: 1/x10_10,
x4_7: x4_7,
x12_14: x12_14,
x11_12: 0,
x13_15: x13_15,
x10_13: x10_13},
{a15: a15,
x13_14: x13_14,
a4: a4,
a11: a11,
a0: 1,
x14_15: x14_15,
x11_13: x11_13,
x5_5: x5_5,
x9_12: x9_12,
a5: 1/x5_5,
a12: a12,
x3_4: 0,
a1: 1,
x7_7: x7_7,
x11_14: x11_14,
x12_15: x12_15,
x5_6: x5_6,
x4_4: 1/a4,
x9_9: x9_9,
a6: a6,
a13: a13,
x3_5: x3_5,
a2: 1,
x10_10: x10_10,
x7_8: 0,
x6_6: 1/a6,
x5_7: x5_7,
x12_12: 1/a12,
x8_8: x8_8,
a7: 1/x7_7,
x3_6: x3_6,
x6_7: x6_7,
x14_14: x14_14,
a9: 1/x9_9,
x15_15: 1/a15,
x4_6: x4_6,
x11_11: 1/a11,
x8_9: x8_9,
a8: 1/x8_8,
x10_12: x10_12,
a14: 1/x14_14,
x13_13: 1/a13,
a3: 1,
a10: 1/x10_10,
x4_7: x4_7,
x12_14: x12_14,
x11_12: 0,
x13_15: x13_15,
x10_13: x10_13}]
Note that, in contrast with maxima, giac does not seem to introduce free parameter like r19
to describe the solutions, instead the values of the dict are unchanged if they are free.