def dmp_zz_modular_resultant(f, g, p, u, K):
"""
Compute resultant of `f` and `g` modulo a prime `p`.
Examples
========
>>> from sympy.polys import ring, ZZ
>>> R, x,y = ring("x,y", ZZ)
>>> f = x + y + 2
>>> g = 2*x*y + x + 3
>>> R.dmp_zz_modular_resultant(f, g, 5)
-2*y**2 + 1
"""
if not u:
return gf_int(dup_prs_resultant(f, g, K)[0] % p, p)
v = u - 1
n = dmp_degree(f, u)
m = dmp_degree(g, u)
N = dmp_degree_in(f, 1, u)
M = dmp_degree_in(g, 1, u)
B = n*M + m*N
D, a = [K.one], -K.one
r = dmp_zero(v)
while dup_degree(D) <= B:
while True:
a += K.one
if a == p:
raise HomomorphismFailed('no luck')
F = dmp_eval_in(f, gf_int(a, p), 1, u, K)
if dmp_degree(F, v) == n:
G = dmp_eval_in(g, gf_int(a, p), 1, u, K)
if dmp_degree(G, v) == m:
break
R = dmp_zz_modular_resultant(F, G, p, v, K)
e = dmp_eval(r, a, v, K)
if not v:
R = dup_strip([R])
e = dup_strip([e])
else:
R = [R]
e = [e]
d = K.invert(dup_eval(D, a, K), p)
d = dup_mul_ground(D, d, K)
d = dmp_raise(d, v, 0, K)
c = dmp_mul(d, dmp_sub(R, e, v, K), v, K)
r = dmp_add(r, c, v, K)
r = dmp_ground_trunc(r, p, v, K)
D = dup_mul(D, [K.one, -a], K)
D = dup_trunc(D, p, K)
return r
def test_pickling_polys_errors():
from sympy.polys.polyerrors import (
ExactQuotientFailed, OperationNotSupported, HeuristicGCDFailed,
HomomorphismFailed, IsomorphismFailed, ExtraneousFactors,
EvaluationFailed, RefinementFailed, CoercionFailed, NotInvertible,
NotReversible, NotAlgebraic, DomainError, PolynomialError,
UnificationFailed, GeneratorsError, GeneratorsNeeded,
ComputationFailed, UnivariatePolynomialError,
MultivariatePolynomialError, PolificationFailed, OptionError,
FlagError)
x = Symbol('x')
# TODO: TypeError: __init__() takes at least 3 arguments (1 given)
# for c in (ExactQuotientFailed, ExactQuotientFailed(x, 3*x, ZZ)):
# check(c)
# TODO: TypeError: can't pickle instancemethod objects
# for c in (OperationNotSupported, OperationNotSupported(Poly(x), Poly.gcd)):
# check(c)
for c in (HeuristicGCDFailed, HeuristicGCDFailed()):
check(c)
for c in (HomomorphismFailed, HomomorphismFailed()):
check(c)
for c in (IsomorphismFailed, IsomorphismFailed()):
check(c)
for c in (ExtraneousFactors, ExtraneousFactors()):
check(c)
for c in (EvaluationFailed, EvaluationFailed()):
check(c)
for c in (RefinementFailed, RefinementFailed()):
check(c)
for c in (CoercionFailed, CoercionFailed()):
check(c)
for c in (NotInvertible, NotInvertible()):
check(c)
for c in (NotReversible, NotReversible()):
check(c)
for c in (NotAlgebraic, NotAlgebraic()):
check(c)
for c in (DomainError, DomainError()):
check(c)
for c in (PolynomialError, PolynomialError()):
check(c)
for c in (UnificationFailed, UnificationFailed()):
check(c)
for c in (GeneratorsError, GeneratorsError()):
check(c)
for c in (GeneratorsNeeded, GeneratorsNeeded()):
check(c)
# TODO: PicklingError: Can't pickle <function <lambda> at 0x38578c0>: it's not found as __main__.<lambda>
# for c in (ComputationFailed, ComputationFailed(lambda t: t, 3, None)):
# check(c)
for c in (UnivariatePolynomialError, UnivariatePolynomialError()):
check(c)
for c in (MultivariatePolynomialError, MultivariatePolynomialError()):
check(c)
# TODO: TypeError: __init__() takes at least 3 arguments (1 given)
# for c in (PolificationFailed, PolificationFailed({}, x, x, False)):
# check(c)
for c in (OptionError, OptionError()):
check(c)
for c in (FlagError, FlagError()):
check(c)
def dmp_zz_modular_resultant(f, g, p, u, K):
"""
Compute resultant of `f` and `g` modulo a prime `p`.
Examples
========
>>> from sympy.polys.domains import ZZ
>>> from sympy.polys.euclidtools import dmp_zz_modular_resultant
>>> f = ZZ.map([[1], [1, 2]])
>>> g = ZZ.map([[2, 1], [3]])
>>> dmp_zz_modular_resultant(f, g, ZZ(5), 1, ZZ)
[-2, 0, 1]
"""
if not u:
return gf_int(dup_prs_resultant(f, g, K)[0] % p, p)
v = u - 1
n = dmp_degree(f, u)
m = dmp_degree(g, u)
N = dmp_degree_in(f, 1, u)
M = dmp_degree_in(g, 1, u)
B = n * M + m * N
D, a = [K.one], -K.one
r = dmp_zero(v)
while dup_degree(D) <= B:
while True:
a += K.one
if a == p:
raise HomomorphismFailed('no luck')
F = dmp_eval_in(f, gf_int(a, p), 1, u, K)
if dmp_degree(F, v) == n:
G = dmp_eval_in(g, gf_int(a, p), 1, u, K)
if dmp_degree(G, v) == m:
break
R = dmp_zz_modular_resultant(F, G, p, v, K)
e = dmp_eval(r, a, v, K)
if not v:
R = dup_strip([R])
e = dup_strip([e])
else:
R = [R]
e = [e]
d = K.invert(dup_eval(D, a, K), p)
d = dup_mul_ground(D, d, K)
d = dmp_raise(d, v, 0, K)
c = dmp_mul(d, dmp_sub(R, e, v, K), v, K)
r = dmp_add(r, c, v, K)
r = dmp_ground_trunc(r, p, v, K)
D = dup_mul(D, [K.one, -a], K)
D = dup_trunc(D, p, K)
return r
