def test_pickling_polys_errors():
# 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(), HomomorphismFailed,
HomomorphismFailed(), IsomorphismFailed, IsomorphismFailed(),
ExtraneousFactors, ExtraneousFactors(), EvaluationFailed,
EvaluationFailed(),
RefinementFailed, RefinementFailed(), CoercionFailed,
CoercionFailed(), NotInvertible, NotInvertible(), NotReversible,
NotReversible(), NotAlgebraic, NotAlgebraic(), DomainError,
DomainError(), PolynomialError, PolynomialError(),
UnificationFailed, UnificationFailed(), GeneratorsError,
GeneratorsError(), 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(),
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(), FlagError, FlagError()):
check(c)
def dmp_revert(f, g, u, K):
"""
Compute ``f**(-1)`` mod ``x**n`` using Newton iteration.
Examples
========
>>> from diofant.polys import ring, QQ
>>> R, x,y = ring("x,y", QQ)
"""
if not u:
return dup_revert(f, g, K)
else:
raise MultivariatePolynomialError(f, g)
def dmp_half_gcdex(f, g, u, K):
"""
Half extended Euclidean algorithm in `F[X]`.
Examples
========
>>> from diofant.polys import ring, ZZ
>>> R, x,y = ring("x,y", ZZ)
"""
if not u:
return dup_half_gcdex(f, g, K)
else:
raise MultivariatePolynomialError(f, g)
def dmp_gff_list(f, u, K):
"""
Compute greatest factorial factorization of ``f`` in ``K[X]``.
Examples
========
>>> from diofant.polys import ring, ZZ
>>> R, x,y = ring("x,y", ZZ)
"""
if not u:
return dup_gff_list(f, K)
else:
raise MultivariatePolynomialError(f)
def dmp_primitive_prs(f, g, u, K):
"""
Primitive polynomial remainder sequence (PRS) in `K[X]`.
Examples
========
>>> from diofant.polys import ring, ZZ
>>> R, x,y = ring("x,y", ZZ)
"""
if not u:
return dup_primitive_prs(f, g, K)
else:
raise MultivariatePolynomialError(f, g)
def dmp_invert(f, g, u, K):
"""
Compute multiplicative inverse of `f` modulo `g` in `F[X]`.
Examples
========
>>> from diofant.polys import ring, QQ
>>> R, x = ring("x", QQ)
"""
if not u:
return dup_invert(f, g, K)
else:
raise MultivariatePolynomialError(f, g)
def __new__(cls, expr, func=None, x=None, auto=True, quadratic=False):
"""Construct a new ``RootSum`` instance carrying all roots of a polynomial. """
coeff, poly = cls._transform(expr, x)
if not poly.is_univariate:
raise MultivariatePolynomialError(
"only univariate polynomials are allowed")
if func is None:
func = Lambda(poly.gen, poly.gen)
else:
try:
is_func = func.is_Function
except AttributeError:
is_func = False
if is_func and 1 in func.nargs:
if not isinstance(func, Lambda):
func = Lambda(poly.gen, func(poly.gen))
else:
raise ValueError("expected a univariate function, got %s" %
func)
var, expr = func.variables[0], func.expr
if coeff is not S.One:
expr = expr.subs(var, coeff * var)
deg = poly.degree()
if not expr.has(var):
return deg * expr
if expr.is_Add:
add_const, expr = expr.as_independent(var)
else:
add_const = S.Zero
if expr.is_Mul:
mul_const, expr = expr.as_independent(var)
else:
mul_const = S.One
func = Lambda(var, expr)
rational = cls._is_func_rational(poly, func)
(_, factors), terms = poly.factor_list(), []
for poly, k in factors:
if poly.is_linear:
term = func(roots_linear(poly)[0])
elif quadratic and poly.is_quadratic:
term = sum(map(func, roots_quadratic(poly)))
else:
if not rational or not auto:
term = cls._new(poly, func, auto)
else:
term = cls._rational_case(poly, func)
terms.append(k * term)
return mul_const * Add(*terms) + deg * add_const