GradedLieAlgebras : Table of Contents
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- DerLie -- Unary negation of Lie derivations
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- MapLie -- Unary negation of Lie homomorphisms
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annLie -- computes a basis for the annihilator in a given degree
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basisLie -- a basis of Lie monomials in a given (multi-)degree
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coeffsLie -- computes the coefficients of a LieElement
compdeg -- the maximal computed degree of the Lie algebra
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cyclesTableLie -- a table of dimensions of the cycles of a Lie algebra
decompidealLie -- computes in the specified degree an ideal associated to an arrangement or matroid
defLie -- returns a LieElement corresponding to input
degLie -- the first degree of a graded element in the LieAlgebra
DerLie -- a Type for derivations in Lie algebras
derLie -- constructing a graded derivation
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DerLie List -- Application of a derivation to every element in a list
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diffl -- optional argument for lieAlgebra
diffLie -- the derivation defined by the differential
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dimsLie -- the dimensions of the Lie algebra up to a specified degree
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dimtotLie -- the sum of the dimensions up to a specified degree
divisorLie -- computes a basis for the divisor subspace
eulerLie -- computes the Euler characteristics
extBasisLie -- a basis up to a given degree of the Ext-algebra
extMultLie -- the (skew commutative) product in the Ext-algebra
extRepRing -- the ring representation of the Ext-algebra
extTableLie -- a table of dimensions of the Ext-algebra of a Lie algebra
field -- optional argument for lieAlgebra and holonomyLie
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genDiffs -- the value of the differential on the generators of a Lie algebra
genSigns -- optional argument for lieAlgebra
gensLie -- the list of generators of the Lie algebra
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holonomyLie -- gives the holonomy Lie algebra associated to an arrangement or matroid
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idealBasisLie -- computes a basis of a Lie ideal in a given degree or multi-degree
idealTableLie -- a table of dimensions of an ideal of a Lie algebra
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imageBasisLie -- a basis of the image of a Lie homomorphism or derivation in a specified degree
imageTableLie -- a table of dimensions of the image of a map or derivation
imapLie -- construction of a Lie map without checking correctness
indexFormLie -- returns an element in the ring representation corresponding to the input
innerDerLie -- the derivation defined by left Lie multiplication by a LieElement
intersectionLie -- computes a basis for the intersection of subspaces of a given degree
invImageBasisLie -- computes a basis for the inverse image of a map or derivation
invImageLie -- computes the dimension for the inverse image of a map or derivation
kernelBasisLie -- a basis of the kernel of a Lie homomorphism or derivation in a specified degree
kernelTableLie -- a table of dimensions of the kernel of a map or derivation
koszulDualLie -- gives the Lie algebra whose enveloping algebra is the Koszul dual of a quadratic algebra
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lieRing -- the internal ring for representation of Lie elements
List List -- Lie multiplication of lists or multiplication in the Ext-algebra of lists
localLie -- gives the Lie algebra for a local subalgebra of the holonomy Lie algebra
MapLie -- a Type for homomorphisms of Lie algebras
mapLie -- constructing a Lie algebra homomorphism
maplie -- the Lie homomorphism f in the definition of a derivation
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MapLie List -- Application of a Lie map to every element in a list
mbRing -- the ring representation of the Lie algebra used as an outputform
minmodel -- the minimal model of L obtained, if computed, as L.minmodel
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minPresLie -- gives a minimal presentation up to a specified degree
modelmap -- the Lie homomorphism from a minimal model of L to the Lie algebra L
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multLie -- The Lie multiplication as a prefix operator
multListLie -- Lie multiplication of lists of LieElement
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multOnly -- optional argument for multListLie
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peekLie -- gives information of a Lie algebra or map
permopLie -- the result of a permutation operating on a LieElement
randomLie -- gives a random element of a lie algebra
relsLie -- the list of relations of the Lie algebra
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sign -- the sign of a derivation
signExtLie -- returns the sign of a basis element in the Ext-algebra
signLie -- returns the sign of a homogeneous LieElement.
sourceLie -- the source of a derivation or map
subalgBasisLie -- computes a basis of a Lie subalgebra in a given degree or multi-degree
subalgTableLie -- a table of dimensions of a Lie subalgebra of a Lie algebra
symmetryLie -- checking if a permutation of the generators defines a map
targetLie -- the target of a derivation or map
useLie -- changes the current Lie Algebra
weight -- the weight of a derivation
weightExtLie -- returns the weight of a homogeneous element in the Ext-algebra
weightLie -- returns the weight of a homogeneous LieElement
whichLie -- prints the current Lie Algebra
zz -- the zero element of a Lie algebra