# Isomorphism -- Probabalistic test for isomorphism

## Description

Two modules are isomorphic if there is a surjection in each direction. These routines produce random combinations of the generators of Hom and test whether these are surjections.

## Contributors

Mike Stillman

• isIsomorphic -- Probabalistic test for isomorphism of modules
• checkDegrees -- compares the degrees of generators of two modules

## Version

This documentation describes version 1.0 of Isomorphism.

## Source code

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

## Exports

• Functions and commands
• checkDegrees -- compares the degrees of generators of two modules
• isIsomorphic -- Probabalistic test for isomorphism of modules
• Methods
• "checkDegrees(Matrix,Matrix)" -- see checkDegrees -- compares the degrees of generators of two modules
• "checkDegrees(Module,Module)" -- see checkDegrees -- compares the degrees of generators of two modules
• "isIsomorphic(Matrix,Matrix)" -- see isIsomorphic -- Probabalistic test for isomorphism of modules
• "isIsomorphic(Module,Module)" -- see isIsomorphic -- Probabalistic test for isomorphism of modules
• Symbols
• Strict -- Forces strict equality of degrees

## For the programmer

The object Isomorphism is .