Test Sets Ontology

All TestSets are stored according to notational conventions of the Normaliz group that provides a tool for computations in affine monoids, vector configurations, lattice polytopes, and rational cones. They are represented by a list of integer vectors (of length m = number of rows) in an ambient affine space (of dimension n = number of columns).

The Test Sets Ontology is based upon the Normaliz model conventions:

A TestSet instance belongs to the owl:Class sd:TestSet and can belong to one of the subclasses

• sd:Equations - Test Set of Equations Type
• sd:Polytope - Test Set of Polytope Type
• sd:Normalization - Test Set of Normalization Type
• sd:IntegralClosure - Test Set of Integral Closure Type
• sd:Hyperplanes - Test Set of Hyperplanes Type

A TestSet instance has

• common standard predicates rdfs:comment, rdfs:label, sd:hasOrigin
• pointers to the related resource
  • sd:hasNormalizSDBase URI - input file in Normaliz format stored at http://symbolicdata.org/OtherResources/TestSets/
  • sd:hasNormalizPrimaryBase URI - (optional) result file stored at http://www.home.uni-osnabrueck.de/wbruns/normaliz/InterChallenge.html. Such a file may contain more than one example.
• fingerprint predicates (meaning has to be clarified)
  • sd:numberOfColumns xsd:integer - number of columns
  • sd:numberOfRows xsd:integer - number of rows

The different subclasses provide different additional information:

• sd:Normalization, sd:Hyperplanes, sd:IntegralClosure, sd:Equations
  • sd:hasNumberOfExtremeRays xsd:integer
  • sd:hasSupportingHyperplanes xsd:integer
  • sd:hasNumberOfHilbertBasisElements xsd:integer
  • sd:hasRank xsd:integer
• sd:Polytope
  • sd:hasSupportingHyperplanes xsd:integer - number of supporting hyperplanes
  • sd:hasDimension xsd:integer - dimension within the ambient space
  • sd:hasNumberOfLatticePoints xsd:integer
  • sd:hasNumberExtremePoints xsd:integer

TestSets Resources

TestSets resources are provides as zip-files according to the Normaliz conventions.