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

Synopsis

• Usage:

  M = splineModule(V,F,E,r)

  M = splineModule(V,F,r)

• Inputs:
  • V, a list, list of coordinates of vertices of $\Delta$
  • F, a list, list of facets of $\Delta$; each facet is recorded as a list of indices of vertices taken from V
  • E, a list, list of codimension one faces of $\Delta$ (interior or not); each codimension one face is recorded as a list of indices of vertices taken from V
  • r, an integer, desired degree of smoothness
• Optional inputs:
  • BaseRing (missing documentation) => a ring, default value null,
  • Homogenize (missing documentation) => a Boolean value, default value true,
  • CoefficientRing (missing documentation) => a ring, default value QQ,
  • VariableName (missing documentation) => a symbol, default value t,
  • InputType (missing documentation) => a string, default value "ByFacets",
• Outputs:
  • M, a module, module of splines on $\Delta$

Description

i1 : V = {{0,0},{1,0},{1,1},{0,1}}

o1 = {{0, 0}, {1, 0}, {1, 1}, {0, 1}}

o1 : List

i2 : F = {{0,1,2},{0,2,3}}

o2 = {{0, 1, 2}, {0, 2, 3}}

o2 : List

i3 : E = {{0,1},{0,2},{0,3},{1,2},{2,3}}

o3 = {{0, 1}, {0, 2}, {0, 3}, {1, 2}, {2, 3}}

o3 : List

i4 : splineModule(V,F,E,1)

o4 = image | 1 t_0^2-2t_0t_1+t_1^2 |
           | 1 0                   |

                                                 2
o4 : QQ[t ..t ]-module, submodule of (QQ[t ..t ])
         0   2                            0   2

See also

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