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
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i3 : chooseSubmatrixLargestDegree(2, M)
o3 = {{0, 1}, {2, 0}}
o3 : List
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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.
The object chooseSubmatrixLargestDegree is a method function with options.