# AlgebraicSplines : Index

• AlgebraicSplines -- a package for working with splines on simplicial complexes, polytopal complexes, and graphs
• BaseRing -- compute matrix whose kernel is the module of $C^r$ splines on $\Delta$
• ByFacets -- compute matrix whose kernel is the module of $C^r$ splines on $\Delta$
• ByLinearForms -- compute matrix whose kernel is the module of $C^r$ splines on $\Delta$
• cellularComplex -- create the cellular chain complex whose homologies are the singular homologies of the complex $\Delta$ relative to its boundary
• cellularComplex(List) -- create the cellular chain complex whose homologies are the singular homologies of the complex $\Delta$ relative to its boundary
• cellularComplex(List,List) -- 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
• courantFunctions(List,List) -- 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.
• formsList(List,List,ZZ) -- 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
• generalizedSplines(List,List) -- the module of generalized splines associated to a simple graph with an edge labelling
• GenVar -- 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
• hilbertComparisonTable -- a table to compare the values of the hilbertFunction and hilbertPolynomial of a graded module
• hilbertComparisonTable(ZZ,ZZ,Module) -- a table to compare the values of the hilbertFunction and hilbertPolynomial of a graded module
• Homogenize -- compute matrix whose kernel is the module of $C^r$ splines on $\Delta$
• idealsComplex -- creates the Billera-Schenck-Stillman chain complex of ideals
• idealsComplex(List,List,ZZ) -- creates the Billera-Schenck-Stillman chain complex of ideals
• IdempotentVar -- 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
• InputType -- compute matrix whose kernel is the module of $C^r$ splines on $\Delta$
• postulationNumber -- computes the largest degree at which the hilbert function of the graded module M is not equal to the hilbertPolynomial
• postulationNumber(Module) -- 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
• ringStructure(Module) -- 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
• RingType -- the module of generalized splines associated to a simple graph with an edge labelling
• splineComplex -- creates the Billera-Schenck-Stillman chain complex
• splineComplex(List,List,ZZ) -- creates the Billera-Schenck-Stillman chain complex
• splineDimensionTable -- a table with the dimensions of the graded pieces of a graded module
• splineDimensionTable(ZZ,ZZ,List,ZZ) -- a table with the dimensions of the graded pieces of a graded module
• splineDimensionTable(ZZ,ZZ,Module) -- 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 $\Delta$
• splineMatrix(List,List,List,ZZ) -- compute matrix whose kernel is the module of $C^r$ splines on $\Delta$
• splineMatrix(List,List,ZZ) -- compute matrix whose kernel is the module of $C^r$ splines on $\Delta$
• splineMatrix(List,ZZ) -- 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
• splineModule(List,List,List,ZZ) -- compute the module of all splines on partition of a space
• splineModule(List,List,ZZ) -- 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.
• stanleyReisner(List,List) -- 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 $\Delta$.
• stanleyReisnerPresentation(List,List,ZZ) -- 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 $\Delta$.
• Trim -- 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
• VariableGens -- 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
• VariableName -- compute matrix whose kernel is the module of $C^r$ splines on $\Delta$