GradedLieAlgebras : Index
- - DerLie -- Unary negation of Lie derivations
- - LieElement -- Unary negation of LieElements
- - MapLie -- Unary negation of Lie homomorphisms
- ambient(LieAlgebra) -- the free underlying Lie algebra
- 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
- baseName(LieElement)
- 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 Lie algebra
- boundariesBasisLie(List) -- computes a basis for the boundaries of a Lie algebra
- boundariesBasisLie(ZZ,ZZ) -- computes a basis for the boundaries of a Lie algebra
- boundariesTableLie -- a table of dimensions of the boundaries of a Lie algebra
- centerAllLie -- computes all central elements
- centerLie -- computes the central elements
- centerLie(ZZ) -- computes the central elements
- characterLie -- computes the trace of a Lie representation
- characterLie(List,List) -- computes the trace of a Lie representation
- coeffsLie -- computes the coefficients of a LieElement
- coeffsLie(LieElement) -- computes the coefficients of a LieElement
- compdeg -- the maximal computed degree of the Lie algebra
- Constructing Lie algebras -- An overview of ways to construct Lie algebras and maps
- cyclesBasisLie -- a basis for the cycles of a Lie algebra
- cyclesBasisLie(List) -- a basis for the cycles of a Lie algebra
- cyclesBasisLie(ZZ,ZZ) -- a basis for the cycles of a Lie algebra
- 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
- decompidealLie(ZZ) -- computes in the specified degree an ideal associated to an arrangement or matroid
- defLie -- returns a LieElement corresponding to input
- defLie(List) -- returns a LieElement corresponding to input
- defLie(RingElement) -- returns a LieElement corresponding to input
- degLie -- the first degree of a graded element in the LieAlgebra
- degLie(DerLie) -- the first degree of a graded element in the LieAlgebra
- degLie(LieElement) -- the first degree of a graded element in the LieAlgebra
- degLie(List) -- 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 derivations in Lie algebras
- derLie -- constructing a graded derivation
- DerLie * MapLie -- operation of maps to the right of a derivation
- DerLie + DerLie -- Addition of Lie derivations
- DerLie - DerLie -- Subtraction of Lie derivations
- DerLie DerLie -- Lie multiplication of ordinary derivations
- DerLie LieElement -- Application of a derivation to a LieElement
- DerLie List -- Application of a derivation to every element in a list
- derLie(List) -- constructing a graded derivation
- derLie(MapLie,List) -- constructing a graded derivation
- Differential LieAlgebra Tutorial -- A tutorial for differential Lie algebras
- diffl -- optional argument for lieAlgebra
- diffLie -- the derivation defined by the differential
- diffLieAlgebra -- A differential Lie algebra
- dimsLie -- the dimensions of the Lie algebra up to a specified degree
- dimsLie(ZZ) -- the dimensions of the Lie algebra up to a specified degree
- dimTableLie -- a table of dimensions of a Lie algebra
- dimTableLie(ZZ) -- a table of dimensions of a Lie algebra
- dimTableLie(ZZ,ZZ) -- a table of dimensions of a Lie algebra
- dimtotLie -- the sum of the dimensions up to a specified degree
- dimtotLie(ZZ) -- the sum of the dimensions up to a specified degree
- 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
- extBasisLie -- a basis up to a given degree of the Ext-algebra
- extBasisLie(List) -- a basis up to a given degree of the Ext-algebra
- extBasisLie(ZZ) -- a basis up to a given degree of the Ext-algebra
- extBasisLie(ZZ,ZZ) -- a basis up to a given degree of the Ext-algebra
- extMultLie -- the (skew commutative) product in the Ext-algebra
- extMultLie(RingElement,RingElement) -- 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
- extTableLie(ZZ) -- a table of dimensions of the Ext-algebra of a Lie algebra
- field -- optional argument for lieAlgebra and holonomyLie
- First LieAlgebra Tutorial -- A tutorial of the package GradedLieAlgebras
- 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
- genWeights -- optional argument for lieAlgebra
- GradedLieAlgebras -- A package for doing computations in graded Lie algebras
- Holonomy Lie algebras and Symmetries -- Hyperplane arrangements and automorphisms
- holonomyLie -- gives the holonomy Lie algebra associated to an arrangement or matroid
- holonomyLie(..., field => ...) -- optional argument for holonomyLie
- holonomyLie(List) -- gives the holonomy Lie algebra associated to an arrangement or matroid
- holonomyLie(List,List) -- gives the holonomy Lie algebra associated to an arrangement or matroid
- homologyBasisLie -- computes a basis for the homology of a given degree
- homologyBasisLie(List) -- computes a basis for the homology of a given degree
- homologyBasisLie(ZZ,ZZ) -- computes a basis for the homology of a given degree
- homologyTableLie -- a table of dimensions of the homology of a Lie algebra
- homologyTableLie(ZZ) -- a table of dimensions of the homology of a Lie algebra
- idealBasisLie -- computes a basis of a Lie ideal in a given degree or multi-degree
- idealBasisLie(List,List) -- computes a basis of a Lie ideal in a given degree or multi-degree
- idealBasisLie(ZZ,List) -- computes a basis of a Lie ideal in a given degree or multi-degree
- idealBasisLie(ZZ,ZZ,List) -- 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
- idealTableLie(ZZ,List) -- a table of dimensions of an ideal of a Lie algebra
- idealTableLie(ZZ,ZZ,List) -- a table of dimensions of an ideal of a Lie algebra
- idMapLie -- the identity map
- imageBasisLie -- a basis of the image of a Lie homomorphism or derivation in a specified degree
- imageBasisLie(List,DerLie) -- a basis of the image of a Lie homomorphism or derivation in a specified degree
- imageBasisLie(List,MapLie) -- a basis of the image of a Lie homomorphism or derivation in a specified degree
- imageBasisLie(ZZ,DerLie) -- a basis of the image of a Lie homomorphism or derivation in a specified degree
- imageBasisLie(ZZ,MapLie) -- a basis of the image of a Lie homomorphism or derivation in a specified degree
- imageBasisLie(ZZ,ZZ,DerLie) -- a basis of the image of a Lie homomorphism or derivation in a specified degree
- imageBasisLie(ZZ,ZZ,MapLie) -- 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
- imapLie(LieAlgebra,LieAlgebra) -- construction of a Lie map without checking correctness
- imapLie(LieAlgebra,LieAlgebra,List) -- construction of a Lie map without checking correctness
- indexFormLie -- returns an element in the ring representation corresponding to the input
- indexFormLie(LieElement) -- returns an element in the ring representation corresponding to the input
- indexFormLie(List) -- returns an element in the ring representation corresponding to the input
- innerDerLie -- the derivation defined by left Lie multiplication by a LieElement
- innerDerLie(LieElement) -- the derivation defined by left Lie multiplication by a LieElement
- 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(DerLie,List) -- computes a basis for the inverse image of a map or derivation
- invImageBasisLie(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(DerLie,List) -- computes the dimension for the inverse image of a map or derivation
- invImageLie(MapLie,List) -- 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
- kernelBasisLie(List,DerLie) -- a basis of the kernel of a Lie homomorphism or derivation in a specified degree
- kernelBasisLie(List,MapLie) -- a basis of the kernel of a Lie homomorphism or derivation in a specified degree
- kernelBasisLie(ZZ,DerLie) -- a basis of the kernel of a Lie homomorphism or derivation in a specified degree
- kernelBasisLie(ZZ,MapLie) -- a basis of the kernel of a Lie homomorphism or derivation in a specified degree
- kernelBasisLie(ZZ,ZZ,DerLie) -- a basis of the kernel of a Lie homomorphism or derivation in a specified degree
- kernelBasisLie(ZZ,ZZ,MapLie) -- 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
- 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 free Lie algebra
- LieAlgebra * LieAlgebra -- Free product of Lie algebras
- LieAlgebra ** LieAlgebra -- Direct sum of Lie algebras
- LieAlgebra / List -- A quotient Lie algebra
- LieAlgebra / MapLie -- A quotient Lie algebra by the image of a map
- lieAlgebra(..., diffl => ...) -- optional argument for lieAlgebra
- lieAlgebra(..., field => ...) -- optional argument for lieAlgebra
- lieAlgebra(..., genSigns => ...) -- optional argument for lieAlgebra
- lieAlgebra(..., genWeights => ...) -- optional argument for lieAlgebra
- lieAlgebra(List) -- constructing a free Lie algebra
- LieElement -- a Type for elements in Lie algebras
- LieElement + LieElement -- Addition of LieElements
- LieElement ++ LieElement -- Formal addition of LieElements
- LieElement - LieElement -- Subtraction of LieElements
- LieElement / LieElement -- Formal subtraction of LieElements
- LieElement @ LieElement -- Formal multiplication of LieElements
- LieElement LieElement -- The Lie multiplication
- 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
- localLie(ZZ) -- 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
- MapLie * DerLie -- operation of maps to the left of a derivation
- MapLie * MapLie -- composition of homomorphisms
- MapLie + MapLie -- Addition of Lie homomorphisms
- MapLie - MapLie -- Subtraction of Lie homomorphisms
- MapLie LieElement -- Application of a Lie map to a LieElement
- MapLie List -- Application of a Lie map to every element in a list
- mapLie(LieAlgebra,LieAlgebra) -- constructing a Lie algebra homomorphism
- mapLie(LieAlgebra,LieAlgebra,List) -- constructing a Lie algebra homomorphism
- mbRing -- the ring representation of the Lie algebra used as an outputform
- minmodel -- the minimal model of L obtained, if computed, as L.minmodel
- minmodelLie -- gives the minimal model
- minmodelLie(ZZ) -- gives the 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 a minimal model of L to the Lie algebra L
- monomialsLie -- computes the monomials of a LieElement
- monomialsLie(LieElement) -- computes the monomials of a LieElement
- multLie -- The Lie multiplication as a prefix operator
- multLie(LieElement,LieElement) -- The Lie multiplication as a prefix operator
- multListLie -- Lie multiplication of lists of LieElement
- multListLie(..., multOnly => ...) -- optional argument for multListLie
- multListLie(List,List) -- Lie multiplication of lists of LieElement
- multOnly -- optional argument for multListLie
- normalFormLie -- computes the normal form of a LieElement
- normalFormLie(LieElement) -- computes the normal form of a LieElement
- Number @ LieElement -- Formal multiplication of a number and a LieElement
- Number DerLie -- Multiplication of a Number and a Derivation
- Number LieElement -- Multiplication of a Number and a LieElement
- Number MapLie -- Multiplication of a Number and a homomorphism
- peekLie -- gives information of a Lie algebra or map
- peekLie(DerLie) -- gives information of a Lie algebra or map
- peekLie(LieAlgebra) -- gives information of a Lie algebra or map
- peekLie(MapLie) -- 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
- randomLie(List) -- gives a random element of a lie algebra
- randomLie(ZZ) -- gives a random element of a lie algebra
- relsLie -- the list of relations of the Lie algebra
- RingElement @ LieElement -- Formal multiplication of a RingElement and a LieElement
- RingElement DerLie -- Multiplication of a field element and a derivation
- RingElement LieElement -- Multiplication of a field element and a LieElement
- RingElement MapLie -- Multiplication of a field element and a homomorphism
- RingElement RingElement -- Multiplication in the Ext-algebra
- Second LieAlgebra Tutorial -- Second tutorial of the package GradedLieAlgebras
- sign -- the sign of a derivation
- signExtLie -- returns the sign of a basis element in the Ext-algebra
- signExtLie(List) -- returns the sign of a basis element in the Ext-algebra
- signExtLie(RingElement) -- returns the sign of a basis element in the Ext-algebra
- signLie -- returns the sign of a homogeneous LieElement.
- signLie(LieElement) -- returns the sign of a homogeneous LieElement.
- signLie(List) -- 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
- subalgBasisLie(List,List) -- computes a basis of a Lie subalgebra in a given degree or multi-degree
- subalgBasisLie(ZZ,List) -- computes a basis of a Lie subalgebra in a given degree or multi-degree
- subalgBasisLie(ZZ,ZZ,List) -- 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
- subalgTableLie(ZZ,List) -- 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
- useLie(LieAlgebra) -- changes the current Lie Algebra
- weight -- the weight of a derivation
- weightExtLie -- returns the weight of a homogeneous element in the Ext-algebra
- weightExtLie(List) -- returns the weight of a homogeneous element in the Ext-algebra
- weightExtLie(RingElement) -- returns the weight of a homogeneous element in the Ext-algebra
- weightLie -- returns the weight of a homogeneous LieElement
- weightLie(LieElement) -- returns the weight of a homogeneous LieElement
- weightLie(List) -- returns the weight of a homogeneous LieElement
- whichLie -- prints the current Lie Algebra
- zz -- the zero element of a Lie algebra