MorseGraph

© 2015 Mario Albert
GNU Free Documentation License, Version 1.2



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Examples

User documentation for Morse Graph

Via the Morse Graph we are able to compute a free resolution of a polynomial ideal via the JBMill. We can compute a free resolution and, if the ideal is homogeneous, the minimal free resolution and the graded Betti numbers of the ideal.

Using the Morse Graph

In the following let mill a JBMill with degrevlex order The following command computes a free resolution as vector<matrix>

Maintainer documentation for TmpMorseGraph.C, TmpMorseBetti.C, TmpMorseResolution.C, TmpPartialMorseBetti.C TmpMorseElement.C, TmpMorsePaths.C, TmpResolutionMinimization.C

For computing free resolutions and graded Betti diagramms with a Janet basis we using algebraic discrete Morse theory. (More information about the mathematical background the user can find in "On the free resolution induced by a Pommaret basis").

MorseElement and JBElem

The basic datastructure is a, so called, MorseGraph. The nodes are represented by the class MorseElement. A MorseElement consists of three main data members: