Singular Manual: belongSemigroup

| #### 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

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