GradedLieAlgebras : Table of Contents
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annLie -- computes a basis for the annihilator in a given degree
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basisExtLie -- a basis in a given degree of the Ext-algebra
basisLie -- a basis of Lie monomials in a given (multi-)degree
boundariesBasisLie -- computes a basis for the boundaries of a given degree and homological degree
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compdeg -- the maximal computed degree of the Lie algebra
computeLie -- computes everything that is needed for a Lie algebra up to a given degree
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decompidealLie -- computes in the specified degree an ideal associated to an arrangement or matroid
defLie -- returns a general Lie expression corresponding to input
deglength -- the length of each weight of the generators of the Lie algebra
degLie -- the first degree of a graded element in the LieAlgebra
DerLie -- a Type for Lie algebra derivations
derLie -- constructing a graded derivation
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diffLie -- the derivation obtained from the differential defined in the current Lie algebra
dimLie -- the dimension of a Lie algebra
dimsLie -- the dimensions of a Lie algebra
dimTableLie -- a table of dimensions of the Lie algebra in first and last degree
dimtotLie -- the total dimension up to degree d
divisorLie -- computes a basis for the divisor subspace
eulerLie -- computes the Euler characteristics
evalDerLie -- the value of a Lie derivation applied to an argument
evalDiffLie -- the value of the differential of the current Lie algebra applied to an argument
evalMapLie -- the value of a Lie homomorphism applied to an argument
extAlgLie -- the matrix of dimensions of the Ext-algebra
extAlgMultLie -- the (skew commutative) product in the Ext-algebra
extAlgRing -- the ring representation of the Ext-algebra
field -- optional argument for lieAlgebra, holonomyLie and randomLie
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genDiffs -- optional argument for lieAlgebra
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genSigns -- optional argument for lieAlgebra and randomLie
gensLie -- the list of generators of the Lie algebra
genWeights -- optional argument for lieAlgebra and randomLie
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 multidegree
idealLie -- computes the dimensions of a Lie ideal
imageBasisLie -- a basis of the image of a Lie homomorphism in a specified degree
imageLie -- gives the dimensions of the image of a Lie homomorphism up to a specified degree
indexFormLie -- returns an element in the ring representation corresponding to the input
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 in a specified degree
kernelLie -- gives the dimensions of the kernel of a Lie homomorphism up to a specified degree
koszulDualLie -- gives the Lie algebra whose enveloping algebra is the Koszul dual of a quadratic algebra
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lieAlgebra -- constructing a Lie algebra from its presentation
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lieRing -- the internal ring for representation of Lie elements
localLie -- gives the Lie algebra and a basis for a local subalgebra of the holonomy Lie algebra of an arrangement or matroid
MapLie -- a Type for Lie algebra homomorphisms
mapLie -- constructing a Lie algebra homomorphism
maplie -- the Lie homomorphism f in the definition of a derivation
maxDeg -- determines the number of variables in the internal ring of representation, lieRing
mbRing -- the ring representation of the Lie algebra used as output
minmodel -- the minimal model of the Lie algebra, if it is constructed
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minPresLie -- gives a minimal presentation up to a specified degree
modelmap -- the Lie homomorphism from the minimal model M to the Lie algebra L
monomialLie -- checks if an array is a correct iterated Lie product
multDerLie -- defines the Lie multiplication of two derivations on a Lie algebra
multLie -- Lie multiplication of two general Lie expression elements
multListLie -- Lie multiplication of lists of general Lie expressions
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multOnly -- optional argument for multListLie
normalFormLie -- returns a basic Lie expression for the Lie algebra equal to the input
numGen -- the number of the generators of the Lie algebra
permopLie -- the result of a permutation operating on a general Lie expression
randomLie -- gives a random element of a lie algebra
relsLie -- the list of relations of the Lie algebra
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signDer -- gives the sign of a derivation
signExtLie -- returns the sign of a generator in the Ext-algebra
signLie -- returns the sign of a graded Lie element.
sourceLie -- the source Lie algebra of a derivation or a Lie homomorphism
subalgBasisLie -- computes a basis of a Lie subalgebra in a given degree or multidegree
subalgLie -- computes the dimensions of a Lie subalgebra up to a specified degree
symmCyclePermLie -- checks if a permutation of the generators in the form of cycles is an automorphism
Symmetries -- Operating by permutations of the generators
symmPermLie -- checks if a permutation of the generators is an automorphism
targetLie -- the target Lie algebra of a derivation or a Lie homomorphism
toMonomialLie -- expresses an arbitrary Lie product as a general Lie expression
useLie -- changes the current Lie algebra and its mbRing
weightDer -- gives the weight of a derivation
weightLie -- gives the multi-degree of a graded element in a Lie algebra
whichLie -- prints the current Lie algebra