Bug in msolve call in last versions

[rprebet]

There's a problem when running msolve from the last versions of AlgebraicSolving.jl with the following polynomial system. in the following sense: the lifting of the parametrization does not terminate in a reasonable time.
Its seems that the main difference with the previous versions is the version of msolve_jll that is used: v0.6.5+0 vs v0.600.700+0.

Indeed, when executing directly the binary of msolve on this system this takes 0.02s.

Regarding the different version this code:

• does not work for downloaded releases >=v0.4.15 and the current repository , which use msolve_jll v0.600.700+0 from the output;
• works for downloaded releases v0.4.13 and v0.4.14, which use msolve_jll v0.6.5+0 from the output;

using Pkg
Pkg.activate("AlgebraicSolving.jl")
using AlgebraicSolving

R,(x1,x2,x3,x4) = polynomial_ring(QQ, ["x1","x2","x3","x4"])

F = [
x1^4 - 8*x1^3*x2 - 32*x1^3*x3 + 36*x1^3*x4 + 26*x1^2*x2^2 + 152*x1^2*x2*x3 - 204*x1^2*x2*x4 + 586*x1^2*x3^2 - 996*x1^2*x3*x4 + 524*x1^2*x4^2 - 20*x1^2 - 40*x1*x2^3 - 256*x1*x2^2*x3 + 420*x1*x2^2*x4 - 1704*x1*x2*x3^2 + 3072*x1*x2*x3*x4 - 1880*x1*x2*x4^2 + 80*x1*x2 - 5280*x1*x3^3 + 12660*x1*x3^2*x4 - 10760*x1*x3*x4^2 + 320*x1*x3 + 3600*x1*x4^3 - 360*x1*x4 + 25*x2^4 + 120*x2^3*x3 - 300*x2^3*x4 + 1794*x2^2*x3^2 - 2820*x2^2*x3*x4 + 1900*x2^2*x4^2 - 100*x2^2 + 3960*x2*x3^3 - 14940*x2*x3^2*x4 + 15000*x2*x3*x4^2 - 240*x2*x3 - 6000*x2*x4^3 + 600*x2*x4 + 27225*x3^4 - 69300*x3^3*x4 + 77100*x3^2*x4^2 - 3300*x3^2 - 42000*x3*x4^3 + 4200*x3*x4 + 10000*x4^4 - 1964*x4^2 + 64,
-32*x1^3 + 152*x1^2*x2 + 1172*x1^2*x3 - 996*x1^2*x4 - 256*x1*x2^2 - 3408*x1*x2*x3 + 3072*x1*x2*x4 - 15840*x1*x3^2 + 25320*x1*x3*x4 - 10760*x1*x4^2 + 320*x1 + 120*x2^3 + 3588*x2^2*x3 - 2820*x2^2*x4 + 11880*x2*x3^2 - 29880*x2*x3*x4 + 15000*x2*x4^2 - 240*x2 + 108900*x3^3 - 207900*x3^2*x4 + 154200*x3*x4^2 - 6600*x3 - 42000*x4^3 + 4200*x4,
36*x1^3 - 204*x1^2*x2 - 996*x1^2*x3 + 1048*x1^2*x4 + 420*x1*x2^2 + 3072*x1*x2*x3 - 3760*x1*x2*x4 + 12660*x1*x3^2 - 21520*x1*x3*x4 + 10800*x1*x4^2 - 360*x1 - 300*x2^3 - 2820*x2^2*x3 + 3800*x2^2*x4 - 14940*x2*x3^2 + 30000*x2*x3*x4 - 18000*x2*x4^2 + 600*x2 - 69300*x3^3 + 154200*x3^2*x4 - 126000*x3*x4^2 + 4200*x3 + 40000*x4^3 - 3928*x4,
-10320*x1^5 + 112080*x1^4*x2 + 330240*x1^4*x3 - 459120*x1^4*x4 - 504480*x1^3*x2^2 - 2513280*x1^3*x2*x3 + 3868800*x1^3*x2*x4 - 6047520*x1^3*x3^2 + 13081920*x1^3*x3*x4 - 8561280*x1^3*x4^2 + 206400*x1^3 + 1180320*x1^2*x2^3 + 7128960*x1^2*x2^2*x3 - 12634080*x1^2*x2^2*x4 + 34884000*x1^2*x2*x3^2 - 74420160*x1^2*x2*x3*x4 + 52740480*x1^2*x2*x4^2 - 1416000*x1^2*x2 + 54489600*x1^2*x3^3 - 181984800*x1^2*x3^2*x4 + 198292800*x1^2*x3*x4^2 - 3302400*x1^2*x3 - 83054400*x1^2*x4^3 + 5382816*x1^2*x4 - 1438800*x1*x2^4 - 8795520*x1*x2^3*x3 + 18998400*x1*x2^3*x4 - 68816160*x1*x2^2*x3^2 + 142213440*x1*x2^2*x3*x4 - 111897600*x1*x2^2*x4^2 + 3393600*x1*x2^2 - 196732800*x1*x2*x3^3 + 677174400*x1*x2*x3^2*x4 - 741542400*x1*x2*x3*x4^2 + 11923200*x1*x2*x3 + 332880000*x1*x2*x4^3 - 23581824*x1*x2*x4 - 280962000*x1*x3^4 + 1177704000*x1*x3^3*x4 - 1904688000*x1*x3^2*x4^2 + 34056000*x1*x3^2 + 1376016000*x1*x3*x4^3 - 69095040*x1*x3*x4 - 418560000*x1*x4^4 + 50352960*x1*x4^2 - 1032000*x1 + 738000*x2^5 + 3542400*x2^4*x3 - 11046000*x2^4*x4 + 52958880*x2^3*x3^2 - 93758400*x2^3*x3*x4 + 82368000*x2^3*x4^2 - 2952000*x2^3 + 116899200*x2^2*x3^3 - 598183200*x2^2*x3^2*x4 + 689832000*x2^2*x3*x4^2 - 7084800*x2^2*x3 - 343560000*x2^2*x4^3 + 26213664*x2^2*x4 + 803682000*x2*x3^4 - 2392632000*x2*x3^3*x4 + 3584736000*x2*x3^2*x4^2 - 97416000*x2*x3^2 - 2553840000*x2*x3*x4^3 + 143297280*x2*x3*x4 + 820800000*x2*x4^4 - 109448640*x2*x4^2 + 2952000*x2 - 2384910000*x3^4*x4 + 6070680000*x3^3*x4^2 - 6753960000*x3^2*x4^3 + 265557600*x3^2*x4 + 3679200000*x3*x4^4 - 337982400*x3*x4^2 - 876000000*x4^5 + 164097600*x4^3 - 8284800*x4,
2320*x1^5 - 34160*x1^4*x2 + 13360*x1^4*x3 + 83520*x1^4*x4 + 185120*x1^3*x2^2 + 151040*x1^3*x2*x3 - 1034880*x1^3*x2*x4 - 1443680*x1^3*x3^2 + 842880*x1^3*x3*x4 + 1215680*x1^3*x4^2 - 48704*x1^3 - 498400*x1^2*x2^3 - 687520*x1^2*x2^2*x3 + 4156800*x1^2*x2^2*x4 + 220320*x1^2*x2*x3^2 + 4794240*x1^2*x2*x3*x4 - 12536000*x1^2*x2*x4^2 + 508544*x1^2*x2 + 39084000*x1^2*x3^3 - 57878400*x1^2*x3^2*x4 + 20939200*x1^2*x3*x4^2 - 925216*x1^2*x3 + 8352000*x1^2*x4^3 - 835200*x1^2*x4 + 682000*x1*x2^4 + 768000*x1*x2^3*x3 - 7248000*x1*x2^3*x4 + 8318880*x1*x2^2*x3^2 - 17673600*x1*x2^2*x3*x4 + 33736000*x1*x2^2*x4^2 - 1498432*x1*x2^2 - 57715200*x1*x2*x3^3 + 36950400*x1*x2*x3^2*x4 + 37968000*x1*x2*x3*x4^2 + 1213824*x1*x2*x3 - 70080000*x1*x2*x4^3 + 7008000*x1*x2*x4 - 399366000*x1*x3^4 + 948240000*x1*x3^3*x4 - 763704000*x1*x3^2*x4^2 + 19235520*x1*x3^2 + 217920000*x1*x3*x4^3 - 21792000*x1*x3*x4 + 23200000*x1*x4^4 - 3865280*x1*x4^2 + 255040*x1 - 390000*x2^5 + 318000*x2^4*x3 + 4680000*x2^4*x4 - 17474400*x2^3*x3^2 + 17712000*x2^3*x3*x4 - 29640000*x2^3*x4^2 + 1568640*x2^3 + 95378400*x2^2*x3^3 - 13968000*x2^2*x3^2*x4 - 67560000*x2^2*x3*x4^2 - 4757664*x2^2*x3 + 93600000*x2^2*x4^3 - 9360000*x2^2*x4 - 77814000*x2*x3^4 - 227664000*x2*x3^3*x4 + 111240000*x2*x3^2*x4^2 + 31311360*x2*x3^2 + 129600000*x2*x3*x4^3 - 12960000*x2*x3*x4 - 156000000*x2*x4^4 + 30120000*x2*x4^2 - 1577280*x2 + 2384910000*x3^5 - 6070680000*x3^4*x4 + 6753960000*x3^3*x4^2 - 281239200*x3^3 - 3679200000*x3^2*x4^3 + 367920000*x3^2*x4 + 876000000*x3*x4^4 - 186302400*x3*x4^2 + 8284800*x3 + 6048000*x4^3,
236240*x1^4 - 1858880*x1^3*x2 - 7984640*x1^3*x3 + 8982720*x1^3*x4 + 5973280*x1^2*x2^2 + 37430400*x1^2*x2*x3 - 50343360*x1^2*x2*x4 + 149618400*x1^2*x3^2 - 256171200*x1^2*x3*x4 + 135051200*x1^2*x4^2 - 3154016*x1^2 - 9115200*x1*x2^3 - 62787840*x1*x2^2*x3 + 103060800*x1*x2^2*x4 - 425160000*x1*x2*x3^2 + 778492800*x1*x2*x3*x4 - 480336000*x1*x2*x4^2 + 12397824*x1*x2 - 1387584000*x1*x3^3 + 3327048000*x1*x3^2*x4 - 2827728000*x1*x3*x4^2 + 53783040*x1*x3 + 946080000*x1*x4^3 - 61248960*x1*x4 + 5682000*x2^4 + 29404800*x2^3*x3 - 73512000*x2^3*x4 + 442159200*x2^2*x3^2 - 703800000*x2^2*x3*x4 + 481560000*x2^2*x4^2 - 15485664*x2^2 + 1040688000*x2*x3^3 - 3926232000*x2*x3^2*x4 + 3942000000*x2*x3*x4^2 - 40337280*x2*x3 - 1576800000*x2*x4^3 + 102968640*x2*x4 + 7154730000*x3^4 - 18212040000*x3^3*x4 + 20261880000*x3^2*x4^2 - 554637600*x3^2 - 11037600000*x3*x4^3 + 705902400*x3*x4 + 2628000000*x4^4 - 339297600*x4^2 + 8284800
]

real_solutions(AlgebraicSolving.Ideal(F), info_level=2)

Here is the output after ~1min of execution: output.txt

[rprebet]

I ended up noticing that this problem seems to have been very recently raised in for msolve in issue #156 and also solved in PR #156 of the github repo.

I imagine that a new release of msolve with this (important) bug-fix is planned and the corresponding new version of msolve_jll would follow. Since I can generate many polynomial systems triggering this bug, I think this will be very appreciated.