ExtensionsAndTorsWithLimitedDegree -- computation of the homogeneous components of the graded modules Ext^i(M,N) and Tor^i(M,N) with a fixed degree limit

Description

We compute, for a given pair of graded modules M, N and an integer d, the homogeneous components in degree less or equal than d of the graded modules Ext^i(M,N) and Tor^i(M,N). Functoriality is also implemented. Moreover, we construct explicitly the Yoneda extension corresponding to a homogeneous element belonging to a previously computed Ext^1(M,N)_{<=d}.

Graded Ext-modules with a degree limit

ExtDegreeLimit -- Computes the components in degree <=d of Ext^i(M,N)

Yoneda extensions

extension -- Construct the Yoneda extension corresponding to an element in Ext^1(M,N)_deg for deg<=d

Graded Tor-modules with a degree limit

TorDegreeLimit -- Computes the components in degree <=d of Tor^i(M,N)

Caveat

This package requires Macaulay2 Version 1.8 or newer.

Authors

Version

This documentation describes version 0.5 of ExtensionsAndTorsWithLimitedDegree.

Source code

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

Exports

Functions and commands
- ExtDegreeLimit -- Computes the components in degree <=d of Ext^i(M,N)
- extension -- Construct the Yoneda extension corresponding to an element in Ext^1(M,N)_deg for deg<=d
- TorDegreeLimit -- Computes the components in degree <=d of Tor^i(M,N)
Symbols
- printTimings -- a Boolean value, default value false, whether to print timings of the key steps of the function.