GradedLieAlgebras : Index
- annLie -- computes a basis for the annihilator in a given degree
- annLie(ZZ,ZZ,List) -- computes a basis for the annihilator in a given degree
- axiomsLie -- the axioms for Lie algebras
- basicExpressionLie -- checks if a general Lie expression is of normal form
- basicMonomialLie -- checks if an array is a basis element for the Lie algebra
- basisExtLie -- a basis in a given degree of the Ext-algebra
- basisExtLie(List) -- a basis in a given degree of the Ext-algebra
- basisExtLie(ZZ) -- a basis in a given degree of the Ext-algebra
- basisExtLie(ZZ,ZZ) -- a basis in a given degree of the Ext-algebra
- basisLie -- a basis of Lie monomials in a given (multi-)degree
- basisLie(List) -- a basis of Lie monomials in a given (multi-)degree
- basisLie(ZZ) -- a basis of Lie monomials in a given (multi-)degree
- basisLie(ZZ,ZZ) -- a basis of Lie monomials in a given (multi-)degree
- boundariesBasisLie -- computes a basis for the boundaries of a given degree and homological degree
- boundariesBasisLie(ZZ,ZZ) -- computes a basis for the boundaries of a given degree and homological degree
- centreLie -- computes the central elements
- centreLie(LieAlgebra) -- computes the central elements
- centreLie(ZZ) -- computes the central elements
- characterLie -- computes the trace of a Lie representation
- characterLie(ZZ,List,List) -- computes the trace of a Lie representation
- compdeg -- the maximal computed degree of the Lie algebra
- computeLie -- computes everything that is needed for a Lie algebra up to a given degree
- computeLie(ZZ) -- computes everything that is needed for a Lie algebra up to a given degree
- Constructing Lie algebras -- An overview of ways to construct Lie algebras and maps
- decompidealLie -- computes in the specified degree an ideal associated to an arrangement or matroid
- decompidealLie(ZZ) -- computes in the specified degree an ideal associated to an arrangement or matroid
- defLie -- returns a general Lie expression corresponding to input
- defLie(List) -- returns a general Lie expression corresponding to input
- defLie(RingElement) -- 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
- degLie(Array) -- the first degree of a graded element in the LieAlgebra
- degLie(IndexedVariable) -- the first degree of a graded element in the LieAlgebra
- degLie(List) -- the first degree of a graded element in the LieAlgebra
- degLie(Symbol) -- the first degree of a graded element in the LieAlgebra
- degLie(ZZ) -- the first degree of a graded element in the LieAlgebra
- DerLie -- a Type for Lie algebra derivations
- derLie -- constructing a graded derivation
- derLie(List) -- constructing a graded derivation
- derLie(MapLie,List) -- constructing a graded derivation
- Differential Lie algebras Tutorial -- A tutorial for differential Lie algebras
- diffLie -- the derivation obtained from the differential defined in the current Lie algebra
- dimLie -- the dimension of a Lie algebra
- dimLie(List) -- the dimension of a Lie algebra
- dimLie(ZZ) -- the dimension of a Lie algebra
- dimLie(ZZ,ZZ) -- the dimension of a Lie algebra
- dimsLie -- the dimensions of a Lie algebra
- dimsLie(ZZ) -- the dimensions of a Lie algebra
- dimTableLie -- a table of dimensions of the Lie algebra in first and last degree
- dimTableLie(ZZ) -- a table of dimensions of the Lie algebra in first and last degree
- dimTableLie(ZZ,ZZ) -- a table of dimensions of the Lie algebra in first and last degree
- dimtotLie -- the total dimension up to degree d
- dimtotLie(ZZ) -- the total dimension up to degree d
- divisorLie -- computes a basis for the divisor subspace
- divisorLie(ZZ,ZZ,List,List) -- computes a basis for the divisor subspace
- eulerLie -- computes the Euler characteristics
- eulerLie(ZZ) -- computes the Euler characteristics
- evalDerLie -- the value of a Lie derivation applied to an argument
- evalDerLie(DerLie,Array) -- the value of a Lie derivation applied to an argument
- evalDerLie(DerLie,List) -- 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
- evalDiffLie(Array) -- the value of the differential of the current Lie algebra applied to an argument
- evalDiffLie(List) -- 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
- evalMapLie(MapLie,Array) -- the value of a Lie homomorphism applied to an argument
- evalMapLie(MapLie,List) -- the value of a Lie homomorphism applied to an argument
- extAlgLie -- the matrix of dimensions of the Ext-algebra
- extAlgLie(ZZ) -- the matrix of dimensions of the Ext-algebra
- extAlgMultLie -- the (skew commutative) product in the Ext-algebra
- extAlgMultLie(RingElement,RingElement) -- the (skew commutative) product in the Ext-algebra
- extAlgRing -- the ring representation of the Ext-algebra
- field -- optional argument for lieAlgebra, holonomyLie and randomLie
- First LieAlgebra Tutorial -- A tutorial of the package GradedLieAlgebras
- genDiffs -- optional argument for lieAlgebra
- generalExpressionLie -- checks if an expression is of right input form for e.g. relations
- genSigns -- optional argument for lieAlgebra and randomLie
- gensLie -- the list of generators of the Lie algebra
- genWeights -- optional argument for lieAlgebra and randomLie
- GradedLieAlgebras -- A package for doing computations in graded Lie algebras
- holonomyLie -- gives the holonomy Lie algebra associated to an arrangement or matroid
- holonomyLie(..., field => ...) -- optional argument for lieAlgebra, holonomyLie and randomLie
- holonomyLie(List) -- gives the holonomy Lie algebra associated to an arrangement or matroid
- homologyBasisLie -- computes a basis for the homology of a given degree
- homologyBasisLie(ZZ,ZZ) -- computes a basis for the homology of a given degree
- homologyLie -- computes the dimensions of the homology
- homologyLie(ZZ) -- computes the dimensions of the homology
- homologyLie(ZZ,ZZ) -- computes the dimensions of the homology
- How to write Lie elements -- An overview of the different representations of elements of a graded Lie Algebra
- idealBasisLie -- computes a basis of a Lie ideal in a given degree or multidegree
- idealBasisLie(List,List) -- computes a basis of a Lie ideal in a given degree or multidegree
- idealBasisLie(ZZ,List) -- computes a basis of a Lie ideal in a given degree or multidegree
- idealLie -- computes the dimensions of a Lie ideal
- idealLie(List,List) -- computes the dimensions of a Lie ideal
- idealLie(ZZ,List) -- computes the dimensions of a Lie ideal
- imageBasisLie -- a basis of the image of a Lie homomorphism in a specified degree
- imageBasisLie(ZZ,MapLie) -- a basis of the image of a Lie homomorphism in a specified degree
- imageBasisLie(ZZ,ZZ,MapLie) -- 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
- indexFormLie(Array) -- returns an element in the ring representation corresponding to the input
- indexFormLie(IndexedVariable) -- returns an element in the ring representation corresponding to the input
- indexFormLie(List) -- returns an element in the ring representation corresponding to the input
- indexFormLie(Symbol) -- returns an element in the ring representation corresponding to the input
- indexFormLie(ZZ) -- returns an element in the ring representation corresponding to the input
- intersectionLie -- computes a basis for the intersection of subspaces of a given degree
- intersectionLie(ZZ,List) -- 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
- invImageBasisLie(ZZ,DerLie,List) -- computes a basis for the inverse image of a map or derivation
- invImageBasisLie(ZZ,MapLie,List) -- computes a basis for the inverse image of a map or derivation
- invImageBasisLie(ZZ,ZZ,DerLie,List) -- computes a basis for the inverse image of a map or derivation
- invImageBasisLie(ZZ,ZZ,MapLie,List) -- 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
- invImageLie(ZZ,DerLie,List) -- computes the dimension for the inverse image of a map or derivation
- invImageLie(ZZ,MapLie,List) -- computes the dimension for the inverse image of a map or derivation
- invImageLie(ZZ,ZZ,DerLie,List) -- computes the dimension for the inverse image of a map or derivation
- invImageLie(ZZ,ZZ,MapLie,List) -- 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
- kernelBasisLie(ZZ,MapLie) -- a basis of the kernel of a Lie homomorphism in a specified degree
- kernelBasisLie(ZZ,ZZ,MapLie) -- 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
- koszulDualLie(PolynomialRing) -- gives the Lie algebra whose enveloping algebra is the Koszul dual of a quadratic algebra
- koszulDualLie(QuotientRing) -- gives the Lie algebra whose enveloping algebra is the Koszul dual of a quadratic algebra
- LieAlgebra -- a Type for Lie algebras
- lieAlgebra -- constructing a Lie algebra from its presentation
- lieAlgebra(..., field => ...) -- optional argument for lieAlgebra, holonomyLie and randomLie
- lieAlgebra(..., genDiffs => ...) -- optional argument for lieAlgebra
- lieAlgebra(..., genSigns => ...) -- optional argument for lieAlgebra and randomLie
- lieAlgebra(..., genWeights => ...) -- optional argument for lieAlgebra and randomLie
- lieAlgebra(List,List) -- constructing a Lie algebra from its presentation
- 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
- localLie(ZZ) -- gives the Lie algebra and a basis for a local subalgebra of the holonomy Lie algebra of an arrangement or matroid
- localLie(ZZ,ZZ) -- 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
- mapLie(LieAlgebra,LieAlgebra,List) -- constructing a Lie algebra homomorphism
- 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
- minmodelLie -- gives a minimal model
- minmodelLie(ZZ) -- gives a minimal model
- minPresLie -- gives a minimal presentation up to a specified degree
- minPresLie(ZZ) -- 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
- multDerLie(DerLie,DerLie) -- defines the Lie multiplication of two derivations on a Lie algebra
- multLie -- Lie multiplication of two general Lie expression elements
- multLie(Thing,Thing) -- Lie multiplication of two general Lie expression elements
- multListLie -- Lie multiplication of lists of general Lie expressions
- multListLie(..., multOnly => ...) -- optional argument for multListLie
- multListLie(List,List) -- Lie multiplication of lists of general Lie expressions
- 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
- randomLie(..., field => ...) -- optional argument for lieAlgebra, holonomyLie and randomLie
- randomLie(..., genSigns => ...) -- optional argument for lieAlgebra and randomLie
- randomLie(..., genWeights => ...) -- optional argument for lieAlgebra and randomLie
- randomLie(List) -- gives a random element of a lie algebra
- randomLie(ZZ,List) -- gives a random element of a lie algebra
- relsLie -- the list of relations of the Lie algebra
- Second LieAlgebra Tutorial -- Second tutorial of the package GradedLieAlgebras
- signDer -- gives the sign of a derivation
- signExtLie -- returns the sign of a generator in the Ext-algebra
- signExtLie(RingElement) -- returns the sign of a generator in the Ext-algebra
- signLie -- returns the sign of a graded Lie element.
- signLie(Array) -- returns the sign of a graded Lie element.
- signLie(IndexedVariable) -- returns the sign of a graded Lie element.
- signLie(List) -- returns the sign of a graded Lie element.
- signLie(RingElement) -- returns the sign of a graded Lie element.
- signLie(Symbol) -- returns the sign of a graded Lie element.
- signLie(ZZ) -- 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
- subalgBasisLie(List,List) -- computes a basis of a Lie subalgebra in a given degree or multidegree
- subalgBasisLie(ZZ,List) -- 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
- subalgLie(List,List) -- computes the dimensions of a Lie subalgebra up to a specified degree
- subalgLie(ZZ,List) -- 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
- toMonomialLie(Array) -- expresses an arbitrary Lie product as a general Lie expression
- toMonomialLie(Array,List,List) -- expresses an arbitrary Lie product as a general Lie expression
- toMonomialLie(List) -- expresses an arbitrary Lie product as a general Lie expression
- useLie -- changes the current Lie algebra and its mbRing
- useLie(LieAlgebra) -- 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
- weightLie(Array) -- gives the multi-degree of a graded element in a Lie algebra
- weightLie(IndexedVariable) -- gives the multi-degree of a graded element in a Lie algebra
- weightLie(List) -- gives the multi-degree of a graded element in a Lie algebra
- weightLie(Symbol) -- gives the multi-degree of a graded element in a Lie algebra
- weightLie(ZZ) -- gives the multi-degree of a graded element in a Lie algebra
- whichLie -- prints the current Lie algebra