%0 Book Section %1 Miller1989 %A Miller, William David %B Algorithms and Order %C Dordrecht %D 1989 %E Rival, Ivan %I Springer Netherlands %K algorithms lattices orthomodular semigroups test %P 59--102 %R 10.1007/978-94-009-2639-4_3 %T A Computer Program for Orthomodular Lattices %U https://doi.org/10.1007/978-94-009-2639-4_3 %X This paper describes a computational approach to studying certain aspects of small finite orthomodular lattices (OML's). The program has two main parts: one, to construct a representation of an OML L, and to perform some simple analyses on L; and two, to construct at least a portion of S 0 (L), the Foulis semigroup (or Baer *-semigroup) of the Sasaki projection functions on L. The representation is constructed from an input which represents the Greechie diagram of L. Such a diagram depicts an orthoposet as a collection of maximal Boolean subalgebras, and if an input does not represent a lattice, the program indicates why not. While the operations of the program are not asserted to be optimal, extensive efforts have been made to use information about the problem area to find efficient methods of performing the various tasks of the program. The methods used and some results are described, and some remarks about possible future work are also given. %@ 978-94-009-2639-4

@inbook{Miller1989, abstract = {This paper describes a computational approach to studying certain aspects of small finite orthomodular lattices (OML's). The program has two main parts: one, to construct a representation of an OML L, and to perform some simple analyses on L; and two, to construct at least a portion of S 0 (L), the Foulis semigroup (or Baer *-semigroup) of the Sasaki projection functions on L. The representation is constructed from an input which represents the Greechie diagram of L. Such a diagram depicts an orthoposet as a collection of maximal Boolean subalgebras, and if an input does not represent a lattice, the program indicates why not. While the operations of the program are not asserted to be optimal, extensive efforts have been made to use information about the problem area to find efficient methods of performing the various tasks of the program. The methods used and some results are described, and some remarks about possible future work are also given.}, added-at = {2018-06-27T00:39:42.000+0200}, address = {Dordrecht}, author = {Miller, William David}, biburl = {https://www.bibsonomy.org/bibtex/274930c1e82e8916afc85b1c8ef93dfcb/typo3tester}, booktitle = {Algorithms and Order}, doi = {10.1007/978-94-009-2639-4_3}, editor = {Rival, Ivan}, interhash = {4161396c06d618fb17bbd02d2b538240}, intrahash = {74930c1e82e8916afc85b1c8ef93dfcb}, isbn = {978-94-009-2639-4}, keywords = {algorithms lattices orthomodular semigroups test}, pages = {59--102}, publisher = {Springer Netherlands}, timestamp = {2018-08-14T12:42:37.000+0200}, title = {A Computer Program for Orthomodular Lattices}, url = {https://doi.org/10.1007/978-94-009-2639-4_3}, year = 1989 }