Computation of atomic fibers of Z-linear maps

Authors

  • Elke Eisenschmidt
  • Raymond Hemmecke
  • Matthias Köppe

DOI:

https://doi.org/10.11575/cdm.v6i2.62106

Abstract

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 $f_A:\Z^n_+\rightarrow\Z^d$, $x\mapsto Ax$. 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.

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Published

2011-10-20

Issue

Section

Articles