5.1.127 rank

Syntax:

rank ( matrix_expression ) #*rank ( matrix_expression ,1)

Type:

int

Purpose:

returns the rank of a given matrix which is filled with elements of the ground field.
The first variant uses a LU-decomposition, the second a row-echelon form.

Note:

The function works by computing the row echelon form of the matrix using the same algorithm as for ludecomp.

Example:

ring s = 0, x, dp; matrix A[100][100]; int i; int j; int r; for (i = 1; i <= 100; i++) { for (j = 1; j <= 100; j++) { A[i, j] = random(-10, 10); } } r = rank(A); r; ==> 100