# 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.

## 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 .