EliminationMatrices : Index
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bezoutianMatrix -- returns a matrix associated to generalized resultants
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bezoutianMatrix(List,Matrix) -- returns a matrix associated to generalized resultants
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byResolution -- Strategy for eliminationMatrix.
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ciResDeg -- compute a regularity index and partial degrees of the residual resultant over a complete intersection
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ciResDegGH -- compute a regularity index used for the residual resultant over a complete intersection
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ciResidual -- Strategy for eliminationMatrix.
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CM2Residual -- Strategy for eliminationMatrix.
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degHomPolMap -- given a subset of variables 'var' of the polynomial ring R, it returns the base of monomials on these variables, and the matrix of coefficients of a morphism of free modules f:R(d1)+...+R(dn)->R_d with respect to these variables
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degHomPolMap(Matrix,List,List,ZZ) -- given a subset of variables 'var' of the polynomial ring R, it returns the base of monomials on these variables, and the matrix of coefficients of a morphism of free modules f:R(d1)+...+R(dn)->R_d with respect to these variables
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degHomPolMap(Matrix,List,ZZ) -- given a subset of variables 'var' of the polynomial ring R, it returns the base of monomials on these variables, and the matrix of coefficients of a morphism of free modules f:R(d1)+...+R(dn)->R_d with respect to these variables
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detComplex -- This function calculates the determinant of a graded ChainComplex with respect to a subset of the variables of the polynomial ring in a fixed degree.
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detComplex(..., Strategy => ...) -- choose between Exact and Numeric algorithms
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detComplex(ZZ,List,ChainComplex) -- This function calculates the determinant of a graded ChainComplex with respect to a subset of the variables of the polynomial ring in a fixed degree.
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determinantal -- Strategy for eliminationMatrix.
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detResDeg -- compute a regularity index and partial degrees of the determinantal resultant
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EliminationMatrices -- resultants
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eliminationMatrix -- returns a matrix that represents the image of the map
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eliminationMatrix(..., Strategy => ...) -- returns a matrix that represents the image of the map
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eliminationMatrix(List,Matrix) -- returns a matrix associated to the Macaulay resultant
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eliminationMatrix(List,Matrix,Matrix) -- returns a matrix corresponding to a residual resultant
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eliminationMatrix(ZZ,List,Matrix) -- returns a matrix corresponding to the determinantal resultant, in particular the Macaulay resultant
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Exact -- Strategy for functions that uses rank computation.
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listDetComplex -- This function calculates the list with the determinants of some minors of the maps of a graded ChainComplex with respect to a subset of the variables of the polynomial ring in a fixed degree.
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listDetComplex(..., Strategy => ...) -- choose between Exact and Numeric algorithms
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listDetComplex(ZZ,List,ChainComplex) -- This function calculates the list with the determinants of some minors of the maps of a graded ChainComplex with respect to a subset of the variables of the polynomial ring in a fixed degree.
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Macaulay -- Strategy for eliminationMatrix.
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macaulayFormula -- returns two matrices such that the ratio of their determinants is the Macaulay resultant
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macaulayFormula(List,Matrix) -- returns two matrices such that the ratio of their determinants is the Macaulay resultant
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mapsComplex -- This function calculates the maps of a graded ChainComplex with respect to a subset of the variables of the polynomial ring in a fixed degree.
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mapsComplex(ZZ,List,ChainComplex) -- This function calculates the maps of a graded ChainComplex with respect to a subset of the variables of the polynomial ring in a fixed degree.
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maxCol -- Returns a submatrix form by a maximal set of linear independent columns.
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maxCol(..., Strategy => ...) -- choose between Exact and Numeric algorithms
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maxCol(Matrix) -- Returns a submatrix form by a maximal set of linear independent columns.
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maxMinor -- Returns a maximal minor of the matrix of full rank.
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maxMinor(..., Strategy => ...) -- choose between Exact and Numeric algorithms
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maxMinor(Matrix) -- Returns a maximal minor of the matrix of full rank.
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minorsComplex -- This function calculates some minors of the maps of a graded ChainComplex with respect to a subset of the variables of the polynomial ring in a fixed degree. The choice of the minors is according to the construction of the determinant of a complex
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minorsComplex(..., Strategy => ...) -- choose between Exact and Numeric algorithms
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minorsComplex(ZZ,List,ChainComplex) -- This function calculates some minors of the maps of a graded ChainComplex with respect to a subset of the variables of the polynomial ring in a fixed degree. The choice of the minors is according to the construction of the determinant of a complex
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Numeric -- Strategy for functions that uses rank computation.
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regularityVar -- computes the Castelnuovo-Mumford regularity of homogeneous ideals in terms of Betti numbers, with respect to some of the variables of the ring
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regularityVar(List,Ideal) -- computes the Castelnuovo-Mumford regularity of homogeneous ideals in terms of Betti numbers, with respect to some of the variables of the ring
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Sylvester -- Strategy for eliminationMatrix.