primes: 2000000089 2000000137
cross-validation modp vs exact (30 random f, D=6): 30 / 30 agree
Thm A (1,sqrt2,sqrt3): 250 random integer-coeff f, deg<=4, 2-6 terms, D=9: {'certified': 247, 'mismatch_dependent': 3, 'COUNTEREXAMPLE': 0} [9s]
Thm A: 150 random f with coefficients in Z[sqrt2,sqrt3], deg<=3, D=8: {'certified': 149, 'mismatch_dependent': 1, 'COUNTEREXAMPLE': 0} [3s]
Thm A: ALL trinomials m1 +- m2 +- m3, deg<=2 (336 f), D=8: {'certified': 336, 'mismatch_dependent': 0, 'COUNTEREXAMPLE': 0} [3s]
4.10c (1,sqrt2,-1-sqrt2): 150 random f, D=8: {'certified': 149, 'mismatch_dependent': 1, 'COUNTEREXAMPLE': 0} [2s]
4.10d (sqrt2,-2,1): same 150 f, D=8: {'certified': 149, 'mismatch_dependent': 1, 'COUNTEREXAMPLE': 0} [2s]
Thm D (theta=2^(1/6)): 120 random f, deg<=3, D=6: {'certified': 120, 'mismatch_dependent': 0, 'COUNTEREXAMPLE': 0} [3s]
   NON-DEPENDENT centralizer element for f = [((0, 1, 0), (Fraction(1, 1), Fraction(0, 1), Fraction(0, 1), Fraction(0, 1))), ((1, 0, 1), (Fraction(1, 1), Fraction(0, 1), Fraction(0, 1), Fraction(0, 1)))]
   NON-DEPENDENT centralizer element for f = [((1, 0, 1), (Fraction(1, 1), Fraction(0, 1), Fraction(0, 1), Fraction(0, 1)))]
   NON-DEPENDENT centralizer element for f = [((0, 2, 0), (Fraction(3, 1), Fraction(0, 1), Fraction(0, 1), Fraction(0, 1))), ((1, 1, 1), (Fraction(-1, 1), Fraction(0, 1), Fraction(0, 1), Fraction(0, 1))), ((2, 0, 2), (Fraction(1, 1), Fraction(0, 1), Fraction(0, 1), Fraction(0, 1)))]
CONTROL 4.10b (1,1,sqrt2) with f in C[xz,y] (non-dependent elements expected): {'certified': 0, 'mismatch_dependent': 0, 'COUNTEREXAMPLE': 3} [0s]
   NON-DEPENDENT centralizer element for f = [((0, 0, 1, 0), (Fraction(1, 1), Fraction(0, 1), Fraction(0, 1), Fraction(0, 1), Fraction(0, 1), Fraction(0, 1))), ((0, 1, 0, 1), (Fraction(1, 1), Fraction(0, 1), Fraction(0, 1), Fraction(0, 1), Fraction(0, 1), Fraction(0, 1)))]
CONTROL n=4 all lam_ij=1, f = x3 + x2 x4 (non-dependent elements expected): {'certified': 0, 'mismatch_dependent': 0, 'COUNTEREXAMPLE': 1} [0s]
