# chooseSubmatrixLargestDegree -- returns coordinates for higher degree submatrix of a matrix

## Synopsis

• Usage:
chooseSubmatrixLargestDegree(n1, M1)
• Inputs:
• Outputs:

## Description

This returns a list containing two entries, the row and column coordinates in the original matrix for a specified sized submatrix. In this case, the terms of that submatrix are likely higher 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 : chooseSubmatrixLargestDegree(2, M) o3 = {{0, 1}, {2, 0}} o3 : List

It returns a list with two entries, first a list of row indices, and then a list of column indices. In this case, x^4 is the biggest element, and after removing that row and column from consideration, y^4 is biggest. Thus we want rows 0 and 1 and columns 2 and 0.

## Ways to use chooseSubmatrixLargestDegree :

• "chooseSubmatrixLargestDegree(ZZ,Matrix)"

## For the programmer

The object chooseSubmatrixLargestDegree is .