def unify_with_symbols(K0, K1, symbols):
if (K0.is_Composite and (set(K0.symbols) & set(symbols))) or (
K1.is_Composite and (set(K1.symbols) & set(symbols))):
raise UnificationFailed(
"can't unify %s with %s, given %s generators" %
(K0, K1, tuple(symbols)))
return K0.unify(K1)
def unify(f, g):
"""Unify representations of two algebraic numbers. """
if not isinstance(g, ANP) or f.mod != g.mod:
raise UnificationFailed("can't unify %s with %s" % (f, g))
if f.dom == g.dom:
return f.dom, f.per, f.rep, g.rep, f.mod
else:
dom = f.dom.unify(g.dom)
F = dup_convert(f.rep, f.dom, dom)
G = dup_convert(g.rep, g.dom, dom)
if dom != f.dom and dom != g.dom:
mod = dup_convert(f.mod, f.dom, dom)
else:
if dom == f.dom:
H = f.mod
else:
H = g.mod
per = lambda rep: ANP(rep, mod, dom)
return dom, per, F, G, mod
def frac_unify(f, g):
"""Unify representations of two multivariate fractions. """
if not isinstance(g, DMF) or f.lev != g.lev:
raise UnificationFailed("can't unify %s with %s" % (f, g))
if f.dom == g.dom and f.ring == g.ring:
return (f.lev, f.dom, f.per, (f.num, f.den),
(g.num, g.den))
else:
lev, dom = f.lev, f.dom.unify(g.dom)
ring = f.ring
if g.ring is not None:
if ring is not None:
ring = ring.unify(g.ring)
else:
ring = g.ring
F = (dmp_convert(f.num, lev, f.dom, dom),
dmp_convert(f.den, lev, f.dom, dom))
G = (dmp_convert(g.num, lev, g.dom, dom),
dmp_convert(g.den, lev, g.dom, dom))
def per(num, den, cancel=True, kill=False, lev=lev):
if kill:
if not lev:
return num/den
else:
lev = lev - 1
if cancel:
num, den = dmp_cancel(num, den, lev, dom)
return f.__class__.new((num, den), dom, lev, ring=ring)
return lev, dom, per, F, G
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 unify(K0, K1, gens=None):
"""Returns a maximal domain containg `K0` and `K1`. """
if gens is not None:
if (K0.is_Composite and
(set(K0.gens) & set(gens))) or (K1.is_Composite and
(set(K1.gens) & set(gens))):
raise UnificationFailed(
"can't unify %s with %s, given %s generators" %
(K0, K1, tuple(gens)))
if K0 == K1:
return K0
if not K0.has_CharacteristicZero:
if not K1.has_CharacteristicZero:
if K0.mod == K1.mod and K0.dom == K1.dom:
return K0
elif K1.is_ZZ:
return K0
raise UnificationFailed("can't unify %s with %s" % (K0, K1))
if not K1.has_CharacteristicZero:
if K0.is_ZZ:
return K1
else:
raise UnificationFailed("can't unify %s with %s" % (K0, K1))
if K0.is_EX:
return K0
if K1.is_EX:
return K1
if not K0.is_Exact:
return K0
if not K1.is_Exact:
return K1
if K0.is_Composite:
if K1.is_Composite:
if K0.gens == K1.gens:
if K0.has_Field and K1.has_Field:
if K0.dom.has_Field:
return K0
else:
return K1
elif K0.has_Field:
if K0.dom == K1.dom:
return K0
elif K1.has_Field:
if K0.dom == K1.dom:
return K1
else:
if K0.dom.has_Field:
return K0
else:
return K1
else:
gens = set(K0.gens + K1.gens)
try:
gens = sorted(gens)
except TypeError:
gens = list(gens)
if K0.has_Field and K1.has_Field:
if K0.dom.has_Field:
return K0.__class__(K0.dom, *gens)
else:
return K1.__class__(K1.dom, *gens)
elif K0.has_Field:
if K0.dom == K1.dom:
return K0.__class__(K0.dom, *gens)
elif K1.has_Field:
if K0.dom == K1.dom:
return K1.__class__(K1.dom, *gens)
else:
if K0.dom.has_Field:
return K0.__class__(K0.dom, *gens)
else:
return K1.__class__(K1.dom, *gens)
elif K1.is_Algebraic:
return K0.__class__(K1.unify(K0.dom), *K0.gens)
else:
if K0.has_Field:
if K0.dom == K1:
return K0
else:
if K0.dom.has_Field:
return K0
else:
return K0.__class__(K1, *K0.gens)
elif K0.is_Algebraic:
if K1.is_Composite:
return K1.__class__(K0.unify(K1.dom), *K1.gens)
elif K1.is_Algebraic:
raise NotImplementedError(
"unification of different algebraic extensions")
elif K1.is_ZZ or K1.is_QQ:
return K0
else:
raise UnificationFailed("can't unify %s with %s" % (K0, K1))
else:
if K1.is_Composite:
if K1.has_Field:
if K0 == K1.dom:
return K1
else:
if K1.dom.has_Field:
return K1
else:
return K1.__class__(K0, *K1.gens)
elif K1.is_Algebraic:
if K0.is_ZZ or K0.is_QQ:
return K1
else:
raise UnificationFailed("can't unify %s with %s" %
(K0, K1))
else:
if K0.has_Field:
return K0
else:
return K1
from sympy.polys.domains import EX
return EX