# 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) => , default value true,
• CoefficientRing (missing documentation) => a ring, default value QQ,
• VariableName (missing documentation) => , default value t,
• InputType (missing documentation) => , 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

This method returns a list of (affine) linear forms cutting out codimension one faces, raised to the power (r+1).

 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

## Ways to use formsList :

• "formsList(List,List,ZZ)"

## For the programmer

The object formsList is .