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
• courantFunctions -- returns the Courant functions of a simplicial complex
• 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 Billera-Schenck-Stillman 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 sub-module of a free module (viewed as a ring with direct sum structure) which is also a sub-ring, creates a ring map whose image is the module with its ring structure
• splineComplex -- creates the Billera-Schenck-Stillman chain complex
• splineDimensionTable -- a table with the dimensions of the graded pieces of a graded module
• 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 sub-ring of $C^0(\Delta)$ generated by $C^r(\Delta)$. If $\Delta$ is simplicial, $C^0(\Delta)$ is the Stanley Reisner ring of $\Delta$.