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ica_mono64_t12r8c4d4_1.magma
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// [{x0: 9784331746762330056*x4 + 3734870611573924684*x5 + 16104840467185498941*x6 + 3265764628588623755*x7 + 2359527063649446767, y0: 9784331746762330056*y4 + 3734870611573924684*y5 + 16104840467185498941*y6 + 3265764628588623755*y7 + 3110310341617426683, x1: 17689384804779105057*x4 + 17636301759336031532*x5 + 6263567895514755713*x6 + 6228076324433630972*x7 + 15567986575791273050, y1: 17689384804779105057*y4 + 17636301759336031532*y5 + 6263567895514755713*y6 + 6228076324433630972*y7 + 8608728260773771411, x2: 3568291694260558778*x4 + 9711728337224637922*x5 + 1173690824534933838*x6 + 16435066389418572622*x7 + 4095417597240858460, y2: 3568291694260558778*y4 + 9711728337224637922*y5 + 1173690824534933838*y6 + 16435066389418572622*y7 + 1218855293469636999, x3: 17513007127623776452*x4 + 5946535579053143621*x5 + 404449599146208466*x6 + 15514985986935067099*x7 + 10925433440561934115, y3: 17513007127623776452*y4 + 5946535579053143621*y5 + 404449599146208466*y6 + 15514985986935067099*y7 + 5968236371293273717}];
// [2, 2, 2, 2, 4, 4, 4, 4];
p := 18446744069414584321;
R<x4,y4,x5,y5,x6,y6,x7,y7> := PolynomialRing(GF(p),8, "grevlex");
I := ideal<R |
16935428837899377181*x4^2 + 1511315231515207140*y4^2 + 15576270455143091828*x4*x5 + 7924605026907324653*x5^2 + 2870473614271492493*y4*y5 + 10522139042507259668*y5^2 + 8193151796135725230*x4*x6 + 216348111075034303*x5*x6 + 5798561677559092433*x6^2 + 10253592273278859091*y4*y6 + 18230395958339550018*y5*y6 + 12648182391855491888*y6^2 + 4564201446384195747*x4*x7 + 10986263128929795370*x5*x7 + 8841136949977856543*x6*x7 + 10638987825501196219*x7^2 + 13882542623030388574*y4*y7 + 7460480940484788951*y5*y7 + 9605607119436727778*y6*y7 + 7807756243913388102*y7^2 + 14344737607261757268*x4 + 14149641436855713377*y4 + 16499684246588005790*x5 + 933765287703688837*y5 + 15353031623476375931*x6 + 8989295147729647798*y6 + 3798289278312027514*x7 + 6109521351680657778*y7 + 13275898971550910009,
11778154545857486936*x4^2 + 6668589523557097385*y4^2 + 6395733088726094246*x4*x5 + 8135945413813193415*x5^2 + 12051010980688490075*y4*y5 + 10310798655601390906*y5^2 + 15000354011325960678*x4*x6 + 1569979262137812972*x5*x6 + 4198961822360819567*x6^2 + 3446390058088623643*y4*y6 + 16876764807276771349*y5*y6 + 14247782247053764754*y6^2 + 12480453243915519881*x4*x7 + 3469936168383828307*x5*x7 + 439139382355012307*x6*x7 + 17698984911850802343*x7^2 + 5966290825499064440*y4*y7 + 14976807901030756014*y5*y7 + 18007604687059572014*y6*y7 + 747759157563781978*y7^2 + 8296686620133615354*x4 + 4440389772121419216*y4 + 12035691518441395795*x5 + 124313041207261688*y5 + 769268636006131428*x6 + 283384244836059017*y6 + 13655340361415796993*x7 + 9839549122374501635*y7 + 14571858664006559769,
3262900833267625586*x4^2 + 15183843236146958735*y4^2 + 4451790372708657702*x4*x5 + 12623098204726130845*x5^2 + 13994953696705926619*y4*y5 + 5823645864688453476*y5^2 + 15118530733065066291*x4*x6 + 9704851822616835051*x5*x6 + 12320947172713064039*x6^2 + 3328213336349518030*y4*y6 + 8741892246797749270*y5*y6 + 6125796896701520282*y6^2 + 12726918779574011605*x4*x7 + 3759089061260492011*x5*x7 + 6010199384481180417*x6*x7 + 5866608278670013148*x7^2 + 5719825289840572716*y4*y7 + 14687655008154092310*y5*y7 + 12436544684933403904*y6*y7 + 12580135790744571173*y7^2 + 8529960327838291145*x4 + 10220006083943767342*y4 + 16669167754487066908*x5 + 11729934468428644413*y5 + 10265856733450805004*x6 + 13043964370765503658*y6 + 1979046481191045825*x7 + 3269697703705066923*y7 + 18179049163655182802,
11157971247585112805*x4^2 + 7288772821829471516*y4^2 + 15850094711214309166*x4*x5 + 5756762207119117994*x5^2 + 2596649358200275155*y4*y5 + 12689981862295466327*y5^2 + 14185280392828083712*x4*x6 + 2907505070987301200*x5*x6 + 6280475976955225621*x6^2 + 4261463676586500609*y4*y6 + 15539238998427283121*y5*y6 + 12166268092459358700*y6^2 + 10048003858871750759*x4*x7 + 7043356323362406946*x5*x7 + 16700454829282157245*x6*x7 + 7503571243603141587*x7^2 + 8398740210542833562*y4*y7 + 11403387746052177375*y5*y7 + 1746289240132427076*y6*y7 + 10943172825811442734*y7^2 + 9659066876551095396*x4 + 13892009510556404545*y4 + 15378507671279796326*x5 + 7141348478367629063*y5 + 3887059054292297845*x6 + 8206642578888865450*y6 + 974797861955450411*x7 + 15749022203637098288*y7 + 16999097541164980017,
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>;
SetNthreads(8);
printf "---------------\nDREG computation\n---------------\n";
function SolvingDegree( system_of_polynomials )
gb := GroebnerBasis(system_of_polynomials);
maxdeg, idx := Maximum([Degree(p) : p in gb]);
step := -1;
have_groebner := false;
while have_groebner eq false do
step := step + 1;
time gb_ := GroebnerBasis(system_of_polynomials, maxdeg + step);
have_groebner := gb eq gb_;
end while;
return maxdeg + step;
end function;
SetVerbose("Faugere",0);
time dreg := SolvingDegree(Basis(I));
dreg;
SetVerbose("Faugere",2);
SetVerbose("FGLM",3);
printf "---------------\nGB computation\n---------------\n";
time GB, dregs := GroebnerBasis(I : Al := "Direct", Faugere := true);
dregs;
#GB;
[Degree(f) : f in GB];
printf "---------------\nFGLM computation\n---------------\n";
I := ChangeOrder(I,"lex");
time GB_lex := GroebnerBasis(I: Al := "FGLM");
#GB_lex;
[Degree(f) : f in GB_lex];
printf "---------------\nVARIETY computation\n---------------\n";
time V := Variety(I);
V;
#V;
// exit;