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D.2.6.4 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 is the maximal ideal of the variables of the basering and M is considered to be a 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:
 


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