
7.7.2 Functionality and release notes of LETTERPLACEWith the present functionality it is possible to compute twosided Groebner basis of an arbitrary twosided ideal in a free associative algebra up to a given degree. The weights of variables are determined by the current monomial ordering. Restrictions/conventions of the LETTERPLACE subsystem:
Operations for polynomials in Letterplace rings are Functions for objects from Letterplace rings are: twostd (letterplace), rightstd (letterplace), reduce (letterplace). Also, the functions bracket, maxideal and std (an alias for twostd (letterplace)) work within letterplace rings:
Further functionality is provided in the libraries for the LETTERPACE subsystem. In the freegb_lib one finds e.g. Letterplace arithmetics procedures, conversion tools, procedures for creating some common ideals of relations as well as the normal form procedure, providing effective ideal membership test. The fpadim_lib contains procedures for computations with vector space basis of a factor algebra including finiteness check and dimension computation. The fpaprops_lib contains procedures for determining important ringtheoretic properties including GelfandKirillov dimension. The fpalgebras_lib contains procedures for the generation of various algebras, including group algebras of finitely presented groups in the Letterplace ring.
The ncfactor_lib contains the procedure See bracket; maxideal; reduce (letterplace); rightstd (letterplace); std (letterplace); twostd (letterplace). 