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∈\Zd×n, the set Pb={z:Az=b,z∈\Z+n} describes the preimage or fiber of b∈\Zd under the \Z-linear map fA:\Z+n→\Zd, x↦Ax. The fiber Pb is called atomic, if Pb=Pb1+Pb2 implies b=b1 or b=b2. 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

Vol. 6 No. 2 (2011)

Section

Articles

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