AlgebraicSplines : Table of Contents

AlgebraicSplines  a package for working with splines on simplicial complexes, polytopal complexes, and graphs

cellularComplex  create the cellular chain complex whose homologies are the singular homologies of the complex $\Delta$ relative to its boundary


formsList  list of powers of (affine) linear forms cutting out a specified list of codimension one faces.

generalizedSplines  the module of generalized splines associated to a simple graph with an edge labelling

hilbertComparisonTable  a table to compare the values of the hilbertFunction and hilbertPolynomial of a graded module

idealsComplex  creates the BilleraSchenckStillman chain complex of ideals

postulationNumber  computes the largest degree at which the Hilbert function of the graded module M is not equal to the hilbertPolynomial

ringStructure  given a submodule of a free module (viewed as a ring with direct sum structure) which is also a subring, creates a ring map whose image is the module with its ring structure

splineComplex  creates the BilleraSchenckStillman chain complex


splineMatrix  compute matrix whose kernel is the module of $C^r$ splines on $\Delta$

splineModule  compute the module of all splines on partition of a space

stanleyReisner  Creates a ring map whose image is the ring of piecewise continuous polynomials on $\Delta$. If $\Delta$ is simplicial, the Stanley Reisner ring of $\Delta$ is returned.

stanleyReisnerPresentation  creates a ring map whose image is the subring of $C^0(\Delta)$ generated by $C^r(\Delta)$. If $\Delta$ is simplicial, $C^0(\Delta)$ is the Stanley Reisner ring of $\Delta$.