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MollerSig_strong_test_Katsura.m
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MollerSig_strong_test_Katsura.m
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// Created: Tue Oct 9 14:20:56 2018
// Last modified: Wed Mar 6 11:47:50 2019
// Hash: 94d7e2c5368bf84a4b0420a7f4016147
load "MollerSig_strong.m";
load "MollerSig_euclidean.m";
if assigned n and Type(n) eq MonStgElt then
n := eval n;
elif not assigned n then
n := 3;
end if;
if assigned sig and Type(sig) eq MonStgElt then
sig := eval n;
elif not assigned sig then
sig := true;
end if;
if assigned F5 and Type(F5) eq MonStgElt then
F5 := eval n;
elif not assigned F5 then
F5 := true;
end if;
if assigned sing and Type(sing) eq MonStgElt then
sing := eval n;
elif not assigned sing then
sing := true;
end if;
load "def_Katsura.m";
time G,SG := MollerSig(K:
Signature := true,
F5_Criterion := true,
Sing_Criterion := true,
GebauerMoller := true,
InterReduce := false);
/* time G,SG := MollerSig_Euclid(K: */
/* Signature := true, */
/* F5_Criterion := true, */
/* Sing_Criterion := true, */
/* GebauerMoller := true, */
/* LC_red := true, */
/* InterReduce := true); */
printf "Is the weak GB Gröbner? %o\n", IsGroebner(G);
printf "Generates the correct ideal? %o\n", Ideal(G) eq Ideal(K);
/* printf "Is the strong GB Gröbner? %o\n", IsGroebner(SG); */
SSG := ReduceGroebnerBasis_Euclid(SG,divmod_Z : NoCheck := true); // Error if not a GB due to partial LC reduction
printf "Is the reduced strong GB Gröbner? %o\n", IsGroebner(SSG);
/* Katsura 3:
Magma 2.24:
Total # of S-polynomials: 178
Total # of considered pairs: 472
Total # of reductions to 0: 0
Total # of skipped pairs with coprime criterion: 157
Total # of skipped pairs with chain criterion: 153
Total # of skipped pairs with F5 criterion: 115
Total # of skipped pairs with sing criterion: 1
Total # of skipped 1-singular-reducible pols: 6
Time: 1.460
Magma 2.20:
Total # of S-polynomials: 62
Total # of considered pairs: 214
Total # of reductions to 0: 0
Total # of skipped pairs with coprime criterion: 83
Total # of skipped pairs with Gebauer-Moller criteria: 52
Total # of skipped pairs with F5 criterion: 30
Total # of skipped pairs with sing criterion: 0
Total # of skipped 1-singular-reducible pols: 4
Time: 0.060
Magma 2.24, no signatures:
###############
Katsura 4:
Magma 2.24:
Total # of S-polynomials: 603
Total # of considered pairs: 1660
Total # of reductions to 0: 0
Total # of skipped pairs with coprime criterion: 509
Total # of skipped pairs with Gebauer-Moller criteria: 517
Total # of skipped pairs with F5 criterion: 388
Total # of skipped pairs with sing criterion: 9
Total # of skipped 1-singular-reducible pols: 84
Time: 16.910
Without signatures
Total # of S-polynomials: 837
Total # of considered pairs: 2712
Total # of reductions to 0: 739
Total # of skipped pairs with coprime criterion: 759
Total # of skipped pairs with Gebauer-Moller "B" criterion: 6
Total # of skipped pairs with Gebauer-Moller "M" criterion: 1040
Total # of skipped pairs with Gebauer-Moller "F" criterion: 70
Total # of skipped pairs with F5 criterion: 0
Total # of skipped pairs with sing criterion: 0
Total # of skipped 1-singular-reducible pols: 0
Time: 7123.540
*/