LinearTruncations : Table of Contents

• LinearTruncations -- truncations of a multigraded module that give linear resolutions

  • multigradedPolynomialRing -- produces polynomial rings with standard multigradings
  • irrelevantIdeal -- gives the irrelevant ideal of the coordinate ring of a product of projective spaces
  • diagonalMultidegrees -- t-tuples of non-negative integers with sum equal to d
  • findMins -- calculates the minimal elements of a subset of ZZ^r
  • findRegion -- finds minimal multidegree(s) in a given region where an ideal or module satisfies a Boolean function
  • partialRegularities -- calculates Castelnuovo-Mumford regularity in each component of a multigrading
  • isLinearComplex -- tests whether a complex of graded modules is linear
  • linearTruncations -- finds minimal multidegree(s) in a given range where the resolution of a truncated module is linear
  • supportOfTor -- computes multidegrees in the support of Tor_i(M,k), where k is the residue field
  • linearTruncationsBound -- bounds the region where truncations of a module have linear resolutions
  • regularityBound -- bounds the multigraded regularity of a module
  • isQuasiLinear -- checks whether degrees in the resolution of a truncation are at most those of the irrelevant ideal
  • compMin -- takes componentwise minimum or maximum of a list of lists