Singular

7.6.5 Release notes of LETTERPLACE

With this functionality it is possible to compute two-sided Groebner basis of a graded two-sided ideal (that is, an ideal, generated by homogeneous polynomials) in a free associative algebra up to a given degree. It is assumed, that each variable has degree $1$.

Restrictions of the LETTERPLACE package:

• At the moment we provide stable implementation for the homogeneous input only, computations with quasi-homogeneous and general inhomogeneous ideals are under development. (There are no automatic checks.)
• Since free algebra is not Noetherian, one has to define an explicit degree bound, up to which a partial Groebner basis will be computed. Note, that makeLetterplaceRing procedure stores the bound in the structure of the ring it creates. Thus running letplaceGBasis in such a ring does not require the degree bound in its argument.
• the options option(redSB); option(redTail); must be always activated
• we advise to run the computations with the options option(prot);option(mem); in order to see the activity journal as well as the memory usage

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 memnership test.

The fpadim_lib contains procedures for computations with vector space basis of a factor algebra including finiteness check and dimension computation.