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domain.characteristic()
isinstance(domain, FractionField_generic)
RingDerivationModule(domain.ring()
self._base_derivation.gens()
self._base_derivation.basis()
self._base_derivation.dual_basis()
constants.fraction_field()
isinstance(domain, PolynomialQuotientRing_generic)
RingDerivationModule(domain.base()
domain.modulus()
self._base_derivation.gens()
der(modulus)
self._base_derivation.gens()
self._base_derivation.basis()
self._base_derivation.dual_basis()
isinstance(domain, QuotientRing_generic)
RingDerivationModule(domain.cover_ring()
any(der(modulus)
domain.defining_ideal()
gens()
self._base_derivation.gens()
self._base_derivation.gens()
self._base_derivation.basis()
self._base_derivation.dual_basis()
NotImplementedError("derivations over this ring is not implemented")
Modules(codomain)
ModulesWithBasis(codomain)
LieAlgebras(self._constants[0])
Module.__init__(self, codomain, category=category)
self.element_class(self, x)
self.element_class(self, x)
domain(x)
__hash__(self)
R.derivation_module()
hash(M)
hash((M.domain()
M.codomain()
M.twisting_morphism()
hash((self._domain, self._codomain, self._twist)
_coerce_map_from_(self, R)
A.derivation_module()
A.derivation_module(B)
M1._coerce_map_from_(M2)
M1.has_coerce_map_from(M2)
M2.has_coerce_map_from(M1)
M1.has_coerce_map_from(ZZ)
M1.has_coerce_map_from(QQ)
M1.has_coerce_map_from(A)
isinstance(R, RingDerivationModule)
R.domain()
has_coerce_map_from(self._domain)
self._codomain.has_coerce_map_from(R.codomain()
R.defining_morphism()
self._domain.gens()
morR(g)
morS(g)
except (AttributeError, NotImplementedError)
super(RingDerivationModule, self)
_coerce_map_from_(R)
_repr_(self)
R.derivation_module()
R.hom([y,x])
R.derivation_module(twist=theta)
Ring (twisting morphism: x |--> y, y |--> x)
self._twist._repr_short()
domain(self)
R.derivation_module()
M.domain()
codomain(self)
R.derivation_module()
M.codomain()
defining_morphism(self)
R.derivation_module()
M.defining_morphism()
R.derivation_module(S)
M.defining_morphism()
R.hom([QQ(0)
R.derivation_module(ev)
M.defining_morphism()
twisting_morphism(self)
R.hom([y,x])
R.derivation_module(twist=theta)
Ring (twisting morphism: x |--> y, y |--> x)
M.twisting_morphism()
R.derivation_module()
M.twisting_morphism()
ngens(self)
R.derivation_module()
M.ngens()
M.gens()
R.fraction_field()
K.hom([K(y)
K(x)
K.derivation_module(twist=theta)
Ring (twisting morphism: x |--> y, y |--> x)
M.ngens()
M.gen()
NotImplementedError("generators are not implemented for this derivation module")
len(self._gens)
gens(self)