code stringlengths 3 6.57k |
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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) |
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