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BoijSoederberg -- Betti diagram routines

Description

BoijSoederberg is a package designed to help with the investigation of the Boij-Soederberg conjectures and theorems. For the definitions and conjectures, see math.AC/0611081, "Graded Betti numbers of Cohen-Macaulay modules and the Multiplicity conjecture", by Mats Boij, Jonas Soederberg.

Manipulation of Betti diagrams

Pure Betti diagrams

  • pureBetti -- list of smallest integral Betti numbers corresponding to a degree sequence
  • pureBettiDiagram -- pure Betti diagram given a list of degrees
  • isPure -- is a Betti diagram pure?

Cohomology tables

Decomposition into pure diagrams

Three constructions for pure resolutions. These routines provide the zero-th betti number given a degree sequence.

  • pureTwoInvariant -- first betti number of specific exact complex
  • pureWeyman -- first betti number of specific exact complex
  • pureCharFree -- first betti number of specific exact complex
  • pureAll -- Vector of first betti number of our three specific exact complexes

Constructions often leading to pure resolutions

  • randomModule -- module with random relations in prescribed degrees
  • randomSocleModule -- random finite length module with prescribed number of socle elements in single degree

Facet equation and the dot product between Betti diagrams and cohomology tables

  • facetEquation -- The upper facet equation corresponding to (L,i)
  • dotProduct -- entry by entry dot product of two Betti diagrams
  • supportFunctional (missing documentation)
  • BettiTally * CohomologyTally (missing documentation)

Authors

Version

This documentation describes version 1.2 of BoijSoederberg.

Source code

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

Exports