mixedSubdivision -- computes a coherent mixed sub-division

Usage:

cell = mixedSubdivision( grad, Lift )
Inputs:
- grad, a list, of matrices with coordinates of lattice points in its rows
- Lift, a matrix, additional coordinate to lift these points
Outputs:
- cell, a list, list of cells of the coherent mixed sub-division (CMD)

Description

Determine the tight mixed coherent subdivision (TCMD) of sparse system given in 'On the Newton Polytope of the Resultant' by Sturmfels [1994]. We get 7 cells, each containing a vertex.

i1 : grad = { {{0,2,1},{0,2,3}}, {{0,2,1},{0,0,2}}, {{3,1},{0,1}} } / matrix

o1 = {| 0 2 1 |, | 0 2 1 |, | 3 1 |}
      | 0 2 3 |  | 0 0 2 |  | 0 1 |

o1 : List

i2 : Lift = {{-1, 0, 0},{-7, -13, 0},{0, 0}};

i3 : cell = mixedSubdivision( grad, matrix {flatten Lift} )

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

o3 : List

Ways to use mixedSubdivision:

mixedSubdivision(List,Matrix) (missing documentation)

For the programmer

The object mixedSubdivision is a method function.

The source of this document is in ResultantComplexes.m2:479:0.