chooseSubmatrixSmallestDegree -- returns coordinates for low degree submatrix of a matrix

Synopsis

Usage:

chooseSubmatrixSmallestDegree(n1, M3)
Inputs:
- n1, an integer,
- M3, a matrix,
Outputs:
- a list,

Description

Returns a list containing the row and column coordinates in the original matrix for a specified sized submatrix of terms lower in degree than other terms of the matrix.

i1 : R = QQ[x,y,z];

i2 : M=matrix{{x^2,x^3,x^4},{y^4,y^2,y^3},{z^3,z^4,z^2}}

o2 = | x2 x3 x4 |
     | y4 y2 y3 |
     | z3 z4 z2 |

             3      3
o2 : Matrix R  <-- R

i3 : chooseSubmatrixSmallestDegree(2, M)

o3 = {{2, 1}, {2, 1}}

o3 : List

This returns a list with two entries, first a list of row indices, and then a list of column indices. In this case, z^2 is the smallest element, and after removing that row and column from consideration, y^2 is smallest. Thus we want rows 2 and 1 and columns 2 and 1.

Ways to use chooseSubmatrixSmallestDegree :

chooseSubmatrixSmallestDegree(ZZ,Matrix)

For the programmer

The object chooseSubmatrixSmallestDegree is a method function with options.