An informal description of the Ontology of the G-Algebra Knowledge Base developed so far.
All G-Algebra instances belong to the owl:Class sd:GAlgebra with predicates
The G-Algebra is the factor of the “almost” commutative polynomial rings, i.e. polynomial rings R=k[x_1,…,x_n] with commutator relations
x_j*x_i=c_ij*x_i*x_j+d_ij for i<j, c_ij in k, d_ij in R, with default c_ij=1, d_ij=0 (x_i and x_j commute in this case),
by the left(?) ideal generated by the given basis.
For a G-Algebra all polynomials in R can be uniquely rewritten as sum of standard monimials in ordered distributive form, the Poincaré standard form.
The base domain k is a field, either Q or Q(a1,…,ak) for (commuting) parameters a1,…,ak
The XML-Resource contains mainly the following tags
A commutator rule