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FiniteFittingIdeals :: FiniteFittingIdeals

FiniteFittingIdeals -- Computing Fitting ideals and Quot schemes of points

Description

This package implements an algorithm for computing Fitting ideals of finite modules from the paper Gotzmann's persistence theorem for finite modules arXiv:1411.7940 by Gustav Sædén Ståhl.

The following is an example illustrating the main functions provided in the package.

Author

Version

This documentation describes version 1.0 of FiniteFittingIdeals.

Source code

The source code from which this documentation is derived is in the file FiniteFittingIdeals.m2.

Exports

  • Functions and commands
    • affinePart -- Replaces columns in a matrix with an identity matrix
    • co1Fitting -- Calculates the (n-1)'th Fitting ideal of a finite module
    • gaussCol -- Makes column reductions of a matrix
    • gotzmannTest -- Checks if a set of monomials is a Gotzmann set
    • nextDegree -- Lifts the kernel to the next degree
    • quotScheme -- Calculates the defining equations for Quot schemes of points
  • Methods
    • "affinePart(Matrix,List)" -- see affinePart -- Replaces columns in a matrix with an identity matrix
    • "affinePart(Matrix,ZZ)" -- see affinePart -- Replaces columns in a matrix with an identity matrix
    • "co1Fitting(Matrix)" -- see co1Fitting -- Calculates the (n-1)'th Fitting ideal of a finite module
    • "co1Fitting(Module)" -- see co1Fitting -- Calculates the (n-1)'th Fitting ideal of a finite module
    • "gaussCol(Matrix)" -- see gaussCol -- Makes column reductions of a matrix
    • "gaussCol(MutableMatrix)" -- see gaussCol -- Makes column reductions of a matrix
    • "gotzmannTest(List,RingElement)" -- see gotzmannTest -- Checks if a set of monomials is a Gotzmann set
    • "gotzmannTest(Module,ZZ,List)" -- see gotzmannTest -- Checks if a set of monomials is a Gotzmann set
    • "nextDegree(Matrix,ZZ,Ring)" -- see nextDegree -- Lifts the kernel to the next degree
    • "nextDegree(Module,ZZ,Ring)" -- see nextDegree -- Lifts the kernel to the next degree
    • "quotScheme(Module,ZZ,List)" -- see quotScheme -- Calculates the defining equations for Quot schemes of points

For the programmer

The object FiniteFittingIdeals is a package.