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

## Synopsis

• Usage:
chooseSubmatrixSmallestDegree(n1, M3)
• Inputs:
• Outputs:

## 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 .