Singular Manual: Release notes

| ### 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 `std` 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 Operations for polynomials in letterplace rings are `+` (addition), `-` (subtraction), `*` (multiplication) and `^` (power). Functions for objects from letterplace rings are: std, maxideal, reduce. 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 fpalgebras_lib contains procedures for the generation of various algebras, including group algebras of finitely presented groups in the Letterplace ring. See maxideal; reduce; std.

User manual for Singular version 4-1-1p4, 2018, generated by texi2html.