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

Synopsis

• Usage:

  L = formsList(V,E,r)

• Inputs:
  • V, a list, list of coordinates of vertices
  • E, a list, list of codimension 1 faces (each codimension 1 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:
  • L, a list, L = list of (affine) linear forms cutting out codimension one faces specified by E, raised to the power (r+1)

Description

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

i2 : E = {{0,1},{0,2},{0,3},{1,2},{2,3}};

i3 : formsList(V,E,0)

o3 = {t , t  - t , t , t  - t , t  - t }
       1   0    1   0   0    2   1    2

o3 : List

i4 : S=QQ[x,y];--can specify the polynomial ring to use, and whether to homogenize

i5 : formsList(V,E,0,BaseRing=>S,Homogenize=>false)

o5 = {y, x - y, x, x - 1, y - 1}

o5 : List