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DeterminantalRepresentations : Index
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bivariateDiagEntries
-- computes diagonal entries and eigenvalues for a determinantal representation of a bivariate polynomial
bivariateDiagEntries(...,Tolerance=>...)
-- computes diagonal entries and eigenvalues for a determinantal representation of a bivariate polynomial
bivariateDiagEntries(RingElement)
-- computes diagonal entries and eigenvalues for a determinantal representation of a bivariate polynomial
cholesky
-- computes the Cholesky decomposition of a positive semidefinite matrix
cholesky(...,Tolerance=>...)
-- computes the Cholesky decomposition of a positive semidefinite matrix
cholesky(Matrix)
-- computes the Cholesky decomposition of a positive semidefinite matrix
coeffMatrices
-- gets coefficient matrices for a matrix of linear forms
coeffMatrices(Matrix)
-- gets coefficient matrices for a matrix of linear forms
companionMatrix
-- companion matrix of a univariate polynomial
companionMatrix(RingElement)
-- companion matrix of a univariate polynomial
Determinantal representations of bivariate polynomials
Determinantal representations of hyperbolic plane cubics
Determinantal representations of quadrics
DeterminantalRepresentations
-- computing determinantal representations of polynomials
detRep
-- compute determinantal representations
detRep(...,HyperbolicPt=>...)
detRep(...,Software=>...)
detRep(...,Tolerance=>...)
-- compute determinantal representations
detRep(RingElement)
-- compute determinantal representations
generalizedMixedDiscriminant
-- computes generalized mixed discriminant of a list of matrices
generalizedMixedDiscriminant(List)
-- computes generalized mixed discriminant of a list of matrices
hadamard
-- computes the Hadamard product of two matrices
hadamard(Matrix,Matrix)
-- computes the Hadamard product of two matrices
HyperbolicPt
isDoublyStochastic
-- whether a matrix is doubly stochastic
isDoublyStochastic(...,Tolerance=>...)
-- whether a matrix is doubly stochastic
isDoublyStochastic(Matrix)
-- whether a matrix is doubly stochastic
isOrthogonal
-- whether a matrix is orthogonal
isOrthogonal(...,Tolerance=>...)
-- whether a matrix is orthogonal
isOrthogonal(Matrix)
-- whether a matrix is orthogonal
orthogonalFromOrthostochastic
-- computes orthogonal matrices for a given orthostochastic matrix
orthogonalFromOrthostochastic(...,Tolerance=>...)
-- computes orthogonal matrices for a given orthostochastic matrix
orthogonalFromOrthostochastic(Matrix)
-- computes orthogonal matrices for a given orthostochastic matrix
randomIntegerSymmetric
-- constructs a random integer symmetric matrix
randomIntegerSymmetric(ZZ)
-- constructs a random integer symmetric matrix
randomIntegerSymmetric(ZZ,Ring)
-- constructs a random integer symmetric matrix
randomOrthogonal
-- constructs a random special orthogonal matrix
randomOrthogonal(ZZ)
-- constructs a random special orthogonal matrix
randomOrthogonal(ZZ,Thing)
-- constructs a random special orthogonal matrix
randomPSD
-- constructs a random positive semidefinite matrix
randomPSD(ZZ)
-- constructs a random positive semidefinite matrix
randomPSD(ZZ,RR)
-- constructs a random positive semidefinite matrix
randomPSD(ZZ,ZZ)
-- constructs a random positive semidefinite matrix
randomPSD(ZZ,ZZ,RR)
-- constructs a random positive semidefinite matrix
randomUnipotent
-- constructs a random unipotent matrix
randomUnipotent(ZZ)
-- constructs a random unipotent matrix
randomUnipotent(ZZ,Thing)
-- constructs a random unipotent matrix
realPartMatrix
-- real part of a matrix over CC
realPartMatrix(Matrix)
-- real part of a matrix over CC
roundMatrix
-- lifts matrix over RR to matrix over QQ
roundMatrix(ZZ,Matrix)
-- lifts matrix over RR to matrix over QQ