def dup_invert(f, g, K):
"""
Compute multiplicative inverse of `f` modulo `g` in `F[x]`.
Examples
========
>>> from sympy.polys.domains import QQ
>>> from sympy.polys.euclidtools import dup_invert
>>> f = QQ.map([1, 0, -1])
>>> g = QQ.map([2, -1])
>>> h = QQ.map([1, -1])
>>> dup_invert(f, g, QQ)
[-4/3]
>>> dup_invert(f, h, QQ)
Traceback (most recent call last):
...
NotInvertible: zero divisor
"""
s, h = dup_half_gcdex(f, g, K)
if h == [K.one]:
return dup_rem(s, g, K)
else:
raise NotInvertible("zero divisor")
def dup_invert(f, g, K):
"""
Compute multiplicative inverse of `f` modulo `g` in `F[x]`.
Examples
========
>>> from sympy.polys import ring, QQ
>>> R, x = ring("x", QQ)
>>> f = x**2 - 1
>>> g = 2*x - 1
>>> h = x - 1
>>> R.dup_invert(f, g)
-4/3
>>> R.dup_invert(f, h)
Traceback (most recent call last):
...
NotInvertible: zero divisor
"""
s, h = dup_half_gcdex(f, g, K)
if h == [K.one]:
return dup_rem(s, g, K)
else:
raise NotInvertible("zero divisor")
def invert(self, a, b):
"""Returns inversion of ``a mod b``. """
s, t, h = self.gcdex(a, b)
if self.is_one(h):
return s % b
else:
raise NotInvertible("zero divisor")
def _divcheck(f):
"""Raise if division is not implemented for this divisor"""
if not f:
raise NotInvertible('Zero divisor')
elif f.ext.is_Field:
return True
elif f.rep.is_ground and f.ext.domain.is_unit(f.rep.rep[0]):
return True
else:
# Some cases like (2*x + 2)/2 over ZZ will fail here. It is
# unclear how to implement division in general if the ground
# domain is not a field so for now it was decided to restrict the
# implementation to division by invertible constants.
msg = (f"Can not invert {f} in {f.ext}. "
"Only division by invertible constants is implemented.")
raise NotImplementedError(msg)
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)