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D.4.4.2 belongSemigroup
Procedure from librarycisimplicial.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 columns,
v is a nonnegative vector and nrows(v) = nrows(A).
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 |