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_sub_(self, other)
R.hom([y,x])
R.derivation(x, twist=theta)
R.derivation(y, twist=theta)
der2 (x - y)
type(self)
self.parent()
_rmul_(self, factor)
R.hom([y,x])
R.derivation(x, twist=theta)
type(self)
self.parent()
_lmul_(self, factor)
R.hom([y,x])
R.derivation(x, twist=theta)
self._rmul_(factor)
_call_(self, x)
R.hom([y,x])
R.derivation(1, twist=theta)
f(x)
self.parent()
parent.twisting_morphism()
parent.defining_morphism()
list(self)
R.fraction_field()
K.hom([y,x])
K.derivation_module(twist=theta)
M.basis()
Family (twisting_morphism - id,)
M.gen()
f (x + y)
f.list()
precompose(self, morphism)
R.hom([y,x])
R.derivation(x, twist=theta)
R.hom([x^2, y^3])
D.postcompose(f)
g.parent()
twisting_morphism()
self.parent()
Rings()
Commutative()
parent.domain()
has_coerce_map_from(morphism)
parent.domain()
coerce_map_from(morphism)
TypeError("the given ring does not coerce to the domain of the derivation")
not (isinstance(morphism, Map)
morphism.category_for()
is_subcategory(Rings()
TypeError("you must give an homomorphism of rings")
RingDerivationModule(morphism.domain()
parent.defining_morphism()
parent.twisting_morphism()
M(self._scalar)
postcompose(self, morphism)
R.hom([y,x])
R.derivation(x, twist=theta)
R.hom([x^2, y^3])
D.precompose(f)
g.parent()
twisting_morphism()
self.parent()
Rings()
Commutative()
morphism.has_coerce_map_from(parent.codomain()
morphism.coerce_map_from(parent.codomain()
TypeError("the codomain of the derivation does not coerce to the given ring")
not (isinstance(morphism, Map)
morphism.category_for()
is_subcategory(Rings()
TypeError("you must give an homomorphism of rings")
RingDerivationModule(parent.domain()
parent.defining_morphism()
parent.twisting_morphism()
M(morphism(self._scalar)
_richcmp_(self, other, op)
R.hom([y,x])
R.derivation(x, twist=theta)
R.derivation(y, twist=theta)
R.derivation(x+y, twist=theta)
D (x + y)
isinstance(other, RingDerivationWithTwist_generic)
isinstance(other, RingDerivationWithTwist_generic)
extend_to_fraction_field(self)
R.hom([y,x])
R.derivation(x, twist=theta)
d.extend_to_fraction_field()
D.domain()
D(1/x)
self.parent()
parent.domain()
fraction_field()
parent.codomain()
fraction_field()
parent.twisting_morphism()
extend_to_fraction_field()
RingDerivationModule(domain, codomain, twist)
M(codomain(self._scalar)
JPARC_EngeFunctionFactory(quad)