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
- makePureBetti -- list of Betti numbers corresponding to a degree sequence
- pureBettiDiagram -- pure Betti diagram given a list of degrees
- makePureBettiDiagram -- makes a pure Betti diagram given a list of degrees
- isPure -- is a Betti diagram pure?
Cohomology tables
Decomposition into pure diagrams
- decompose(BettiTally) -- write a Betti diagram as a positive combination of pure integral diagrams
- decomposeBetti -- write a Betti diagram as a positive combination of pure integral diagrams
- decomposeDegrees -- Find the degree sequences of pure diagrams occuring in a Boij-Soederberg decomposition of B
- eliminateBetti -- elimination table for a Betti diagram
- isMassEliminate -- determines whether the Boij-Soederberg decomposition algorithm eliminates multiple Betti numbers at the same time
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)