D.3.2.12 gaussred_pivot
.......................
Procedure from library linalg.lib (see linalg_lib).

Usage:
gaussred_pivot(A); A any constant matrix

Return:
list Z: Z[1]=P , Z[2]=U , Z[3]=S , Z[4]=rank(A)

gives n row reduced matrix S, a permutation matrix P and a
normalized lower triangular matrix U, with P*A=U*S

Note:
with row pivoting

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;
list Z=gaussred_pivot(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

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&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; User manual for <a href="http://www.singular.uni-kl.de/"><i>Singular</i></a> version 2-0-4, October 2002,
generated by <a href="http://www.gnu.org/software/texinfo/"><i>texi2html</i></a>.
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