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A Subsystem for Non-commutative Finitely Presented Algebras

This section describes mathematical notions and definitions used in the LETTERPLACE subsystem of SINGULAR.

All algebras are assumed to be associative $K$-algebras for some field $K$.

What is LETTERPLACE? It is a subsystem of SINGULAR, providing the manipulations and computations within free associative algebras

$K$ $<x_1$,..., $x_n >$

as well as in the factor-algebras of those by two-sided ideal.

Free algebras are represented in SINGULAR as so-called Letterplace rings. Each such ring is constructed from a commutative ring $K$[ $x_1$,..., $x_n$ ] and a degree (length) bound $d$.

This encodes a sub- $K$-vector space (also called a filtered part) of $K$ $<x_1$,..., $x_n >$, spanned by all monomials of length at most $d$.

Within such a construction we offer the computations of Groebner bases, normal forms and many more. A variety of monomial orderings is supported.

7.7.1 Examples of use of LETTERPLACE  
7.7.2 Functionality and release notes of LETTERPLACE  
7.7.3 References and history of LETTERPLACE