def zzX_fateman_poly_F_3(n): """Fateman's GCD benchmark: sparse inputs (deg f ~ vars f) """ u = zzx_from_dict({n+1:1}) for i in xrange(1, n): u = zzX_add_term([u], zzX_const(i, 1), n+1) v = zzX_add_term(u, zzX_const(n-1, 2)) f = zzX_sqr(zzX_add_term([zzX_neg(v)], zzX_const(n, 1), n+1)) g = zzX_sqr(zzX_add_term([v], zzX_const(n, 1), n+1)) v = zzX_add_term(u, zzX_const(n-1, 1)) h = zzX_sqr(zzX_add_term([v], zzX_const(n, 1), n+1)) return zzX_mul(f,h), zzX_mul(g,h), h
def zzX_fateman_poly_F_2(n): """Fateman's GCD benchmark: linearly dense quartic inputs """ u = [1, 0] for i in xrange(1, n): u = [zzX_const(i, 1), u] v = zzX_add_term(u, zzX_const(n - 1, 2)) f = zzX_sqr([zzX_const(n, 1), zzX_neg(v)]) g = zzX_sqr([zzX_const(n, 1), v]) v = zzX_add_term(u, zzX_const(n - 1, 1)) h = zzX_sqr([zzX_const(n, 1), v]) return zzX_mul(f, h), zzX_mul(g, h), h
def zzX_fateman_poly_F_2(n): """Fateman's GCD benchmark: linearly dense quartic inputs """ u = [1, 0] for i in xrange(1, n): u = [zzX_const(i, 1), u] v = zzX_add_term(u, zzX_const(n-1, 2)) f = zzX_sqr([zzX_const(n, 1), zzX_neg(v)]) g = zzX_sqr([zzX_const(n, 1), v]) v = zzX_add_term(u, zzX_const(n-1, 1)) h = zzX_sqr([zzX_const(n, 1), v]) return zzX_mul(f,h), zzX_mul(g,h), h
def zzX_fateman_poly_F_3(n): """Fateman's GCD benchmark: sparse inputs (deg f ~ vars f) """ u = zzx_from_dict({n + 1: 1}) for i in xrange(1, n): u = zzX_add_term([u], zzX_const(i, 1), n + 1) v = zzX_add_term(u, zzX_const(n - 1, 2)) f = zzX_sqr(zzX_add_term([zzX_neg(v)], zzX_const(n, 1), n + 1)) g = zzX_sqr(zzX_add_term([v], zzX_const(n, 1), n + 1)) v = zzX_add_term(u, zzX_const(n - 1, 1)) h = zzX_sqr(zzX_add_term([v], zzX_const(n, 1), n + 1)) return zzX_mul(f, h), zzX_mul(g, h), h
def test_zzX_sqf(): assert zzX_sqf_p(f_0) == True assert zzX_sqf_p(zzX_sqr(f_0)) == False assert zzX_sqf_p(f_1) == True assert zzX_sqf_p(zzX_sqr(f_1)) == False assert zzX_sqf_p(f_2) == True assert zzX_sqf_p(zzX_sqr(f_2)) == False assert zzX_sqf_p(f_3) == True assert zzX_sqf_p(zzX_sqr(f_3)) == False assert zzX_sqf_p(f_5) == False assert zzX_sqf_p(zzX_sqr(f_5)) == False assert zzX_sqf_p(f_4) == True assert zzX_sqf_part(f_4) == f_4 assert zzX_sqf_p(f_6) == True assert zzX_sqf_part(f_6) == f_6 assert zzX_sqf_part(f_5) == [[[-1]], [[-1], [1, 0]]]
def test_zzX_sqr(): assert zzX_sqr([[[]]]) == [[[]]] assert zzX_sqr([[[2]]]) == [[[4]]]