D.3.2.11 gaussred

Procedure from library linalg.lib (see linalg_lib).

Usage:

gaussred(A); A any constant matrix

Return:

list Z: Z[1]=P , Z[2]=U , Z[3]=S , Z[4]=rank(A)
gives a row reduced matrix S, a permutation matrix P and a normalized lower triangular matrix U, with P*A=U*S

Note:

This procedure is designed for teaching purposes mainly. The straight forward implementation in the interpreted library is not very efficient (no standard basis computation).

Example:

LIB "linalg.lib";
ring r=0,(x),dp;
matrix A[5][4]=1,3,-1,4,2,5,-1,3,1,3,-1,4,0,4,-3,1,-3,1,-5,-2;
print(A);
list Z=gaussred(A);   //construct P,U,S s.t. P*A=U*S
print(Z[1]);          //P
print(Z[2]);          //U
print(Z[3]);          //S
print(Z[4]);          //rank
print(Z[1]*A);        //P*A
print(Z[2]*Z[3]);     //U*S