Combinatorial_Algebra

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title: Combinatorial Algebra permalink: wiki/Combinatorial_Algebra/ layout: wiki

Graphs Extras--add any desired extra features:

Interpolation Work:

Written(Gitted):

-method for polynomial interpolation (Lagrange) -method for rational interpolation using Chebyshev algorithm -implemented floater-horman algorithm for rational interpolation -method for linear regression -cubic hermite splines and their evaluation

Written(unGitted):

Being Written:

Lattice Coordinatization Work:

Written(Gitted):

Written(unGitted):

-minimalSQFIdeal - produces the minimal square free monomial ideal associated to an input finite attomic lattice.

-labeling - assigns monomial labels to input lattice

-possCoord - produces the monomial ideal associated to a labeling of an input finite atomic lattice

-squareFullIdeal - produces the most non square free monomial ideal for an input finite atomic lattice

BeingWritten:

-isCoord - checks whether a labeling of a finite atomic lattice is a coordinatization

Graphs and Ideals Work:

BeingWritten:

-random functions/methods for creating toric edge rings and random graphs (user specifies probability of presence of an edge) both will call functions/methods from graphs package.

(note: it seems there is SIGNIFICANT overlap between Graphs package and Edge Ideals package. should an interface or subcategory relationship be established between these?)

-Now thinking about writing a GraphsPlus package to incorporate functions/methods included in EdgeIdeals not in new Graphs (written by J. Burkart, D. Cook II, and C. Jansen). Also want to include functions for facet ideals of simplicial complexes.

Misc. monomial ideal functions:

BeingWritten: b-pol