D.2.4.3 freerank
................
Procedure from library poly.lib (see poly_lib).

Usage:
freerank(M[,any]); M=poly/ideal/vector/module/matrix

Compute:
rank of module presented by M in case it is free.

By definition this is vdim(coker(M)/m*coker(M)) if coker(M)
is free, where m = maximal ideal of the variables of the
basering and M is considered as matrix.

(the 0-module is free of rank 0)

Return:
rank of coker(M) if coker(M) is free and -1 else;

in case of a second argument return a list:

L[1] = rank of coker(M) or -1

L[2] = minbase(M)

Note:
freerank(syz(M)); computes the rank of M if M is free (and -1 else)

Example:
LIB "poly.lib";
ring r;
ideal i=x;
module M=[x,0,1],[-x,0,-1];
freerank(M);          // should be 2, coker(M) is not free
==> 2
freerank(syz (M),"");
==> [1]:
==>    1
==> [2]:
==>    _[1]=gen(2)+gen(1)
// [1] should be 1, coker(syz(M))=M is free of rank 1
// [2] should be gen(2)+gen(1) (minimal relation of M)
freerank(i);
==> -1
freerank(syz(i));     // should be 1, coker(syz(i))=i is free of rank 1
==> 1

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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,
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