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HighestWeights : Index
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decomposeWeightsList
-- decompose a list of weights into highest weights
Example 1
-- The coordinate ring of the Grassmannian
Example 2
-- The Buchsbaum-Rim complex
Example 3
-- A multigraded Eagon-Northcott complex
Example 4
-- The Eisenbud-Fløystad-Weyman complex
Example 5
-- The singular locus of a symplectic invariant
Example 6
-- The coordinate ring of the spinor variety
Example 7
-- With the exceptional group G2
Forward
-- propagate weights from domain to codomain
getWeights
-- retrieve the (Lie theoretic) weight of a monomial
getWeights(RingElement)
-- retrieve the (Lie theoretic) weight of a monomial
GroupActing
-- stores the Dynkin type of the group acting on a ring
HighestWeights
-- decompose free resolutions and graded modules with a semisimple Lie group action
highestWeightsDecomposition
-- irreducible decomposition of a complex, ring, ideal or module
highestWeightsDecomposition(...,Range=>...)
-- decompose only part of a complex
highestWeightsDecomposition(ChainComplex)
-- decompose an equivariant complex of graded free modules
highestWeightsDecomposition(ChainComplex,ZZ,List)
-- decompose an equivariant complex of graded free modules
highestWeightsDecomposition(Ideal,List)
-- decompose an ideal with a semisimple Lie group action
highestWeightsDecomposition(Ideal,ZZ)
-- decompose an ideal with a semisimple Lie group action
highestWeightsDecomposition(Ideal,ZZ,ZZ)
-- decompose an ideal with a semisimple Lie group action
highestWeightsDecomposition(Module,List,List)
-- decompose a module with a semisimple Lie group action
highestWeightsDecomposition(Module,ZZ,List)
-- decompose a module with a semisimple Lie group action
highestWeightsDecomposition(Module,ZZ,ZZ,List)
-- decompose a module with a semisimple Lie group action
highestWeightsDecomposition(Ring,List)
-- decompose a ring with a semisimple Lie group action
highestWeightsDecomposition(Ring,ZZ)
-- decompose a ring with a semisimple Lie group action
highestWeightsDecomposition(Ring,ZZ,ZZ)
-- decompose a ring with a semisimple Lie group action
LeadingTermTest
-- check the columns of the input matrix for repeated leading terms
LieWeights
-- stores the (Lie theoretic) weights of the variables of a ring
MinimalityTest
-- check that the input map is minimal
propagateWeights
-- propagate (Lie theoretic) weights along equivariant maps
propagateWeights(...,Forward=>...)
-- propagate weights from domain to codomain
propagateWeights(...,LeadingTermTest=>...)
-- check the columns of the input matrix for repeated leading terms
propagateWeights(...,MinimalityTest=>...)
-- check that the input map is minimal
propagateWeights(Matrix,List)
-- propagate (Lie theoretic) weights along an equivariant map of graded free modules
Range
-- decompose only part of a complex
setWeights
-- attach (Lie theoretic) weights to the variables of a ring
setWeights(PolynomialRing,DynkinType,List)
-- attach (Lie theoretic) weights to the variables of a ring