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FastLinAlg :: chooseSubmatrixSmallestDegree

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

Synopsis

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 rows, and then a list of columns. 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.

The option PeriodicCheckFunction can be set to a function which will periodically compare partially computed ideal of minors via the given function. For instance, one can set it to periodically check whether the dimension of the ideal is at most zero via PeriodicCheckFunction => (J -> dim J <= 0).

Ways to use chooseSubmatrixSmallestDegree :

For the programmer

The object chooseSubmatrixSmallestDegree is a method function with options.