EliminationMatrices : Table of Contents

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