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D.4.4.2 belongSemigroup

Procedure from library cisimplicial.lib (see cisimplicial_lib).

Usage:
belongSemigroup(v,A[,k]); v is an integral vector, A is an integral matrix, n is a positive integer.

Return:
counters, a vector with nonnegative entries such that A*counters = v. If it does not exist such a vector, it returns 0. If a third parameter k is introduced, it will only consider the first k columns of A.

Assume:
A is a matrix with nonnegative entries, nonzero colums, v is a nonnegative vector and nrows(v) = nrows(A).

Example:
 
LIB "cisimplicial.lib";
intmat A[3][4] = 10,3,2,1,2,1,1,3,5,0,1,2;
print(A);
==>     10     3     2     1
==>      2     1     1     3
==>      5     0     1     2
intvec v = 23,12,10;
belongSemigroup(v,A);
==> 1,3,1,2
"// A * (1,3,1,2) = v";
==> // A * (1,3,1,2) = v
belongSemigroup(v,A,3);
==> 0
"// v is not a combination of the first 3 columns of A";
==> // v is not a combination of the first 3 columns of A
intvec w = 12,4,1;
belongSemigroup(w,A);
==> 0
"// w is not a combination of the columns of A";
==> // w is not a combination of the columns of A