Free Algebra Ontology
An informal description of the Ontology of the Free Algebra Knowledge Base developed so far.
All Free Algebra instances belong to the owl:Class sd:FreeAlgebra with predicates
- sd:hasVariables Literal - comma separated list of (non commuting) variables
- sd:hasParameters Literal - comma separated list of (commuting) parameters
- sd:uptoDegree Literal - integer, semantics to be fixed
- sd:relatedXMLResource URI - the Resource file
- standard predicates sd:createdAt, sd:createdBy, rdfs:comment
The free algebra is the factor of the non commutative polynomial ring Q(a1,…,ak)<x1,…,xn> over the commtative field Q(a1,…,ak) of rational functions in a1,…,ak by the twosided ideal generated by the given non commutative polynomials.
The XML-Resource contains mainly the following tags
- a list x1,...,xn of (non commuting) variables,
- (optionally) - a list a1,...,ak of (commuting) parameters
- (optionally) - an integer (meaning has to be specified)
- a sequence of entries of non commutative polynomials
For details see the XSchema description FreeAlgebras.xsd.