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deformMCMModule(...,DegreeLimit=>...) -- Compute only up to this exponent

Description

This parameter is an integer $ n $ such that in the result of the computation the versality criterion holds only after reducing the relevant rings modulo the maximal homogeneous ideal to the power $ n+1 $. Concretely, this means that the output may have incorrect terms with total exponent greater than $ n $. If the input is positively graded, all deformation parameters have strictly positive degree, and $ n $ is sufficiently large, then no terms of degree greater than $ n $ appear in the output, and the result is versal. In this case, the maximum of $ d / deg x $ where $ d $ is the degree of the equation of the hypersurface and $ x $ ranges over all variables in the ring of the hypersurface and all deformation parameters, should suffice.

Functions with optional argument named DegreeLimit:

  • compose(Module,Module,Module,DegreeLimit=>...) -- see compose -- composition as a pairing on Hom-modules
  • deformMCMModule(...,DegreeLimit=>...) -- Compute only up to this exponent
  • End(...,DegreeLimit=>...) -- see End -- module of endomorphisms
  • gb(...,DegreeLimit=>...) -- see gb -- compute a Gröbner basis
  • Hom(...,DegreeLimit=>...) -- see Hom -- module of homomorphisms
  • homomorphism'(...,DegreeLimit=>...) -- see homomorphism' -- get the element of Hom from a homomorphism
  • minimalBetti(...,DegreeLimit=>...) -- see minimalBetti -- minimal betti numbers of (the minimal free resolution of) a homogeneous ideal or module
  • pushForward(...,DegreeLimit=>...) -- see pushForward(RingMap,Module) -- compute the pushforward of a module along a ring map
  • quotient(...,DegreeLimit=>...) (missing documentation)
  • saturate(...,DegreeLimit=>...) (missing documentation)
  • syz(...,DegreeLimit=>...) -- see syz(Matrix) -- compute the syzygy matrix

Further information

  • Default value: 10
  • Function: deformMCMModule -- versal deformation of MCM-module on hypersurface
  • Option key: DegreeLimit -- an optional argument

The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/ModuleDeformations.m2:530:0.