For given matrix $A\in\Z^{ d\times n}$, the set $P_{ b}=\{ z:Az=b,z\in\Z^n_+\}$ describes the preimage or fiber of $b\in\Z^d$ under the $\Z$-linear map $f_A:\Z^n_+\to\Z^d$, $x\mapsto Ax$. The fiber $P_{ b}$ is called atomic, if $P_{ b}=P_{ b_1}+P_{ b_2}$ implies $b=b_1$ or $b=b_2$. In this paper we present a novel algorithm to compute such atomic fibers. An algorithmic solution to appearing subproblems, computational examples and applications are included as well.
Categories: math.CO