> | ## 7.7 LETTERPLACE ### 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 -algebras for some field . What is LETTERPLACE? It is a subsystem of SINGULAR, providing the manipulations and computations within free associative algebras ,..., 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 [ ,..., ] and a degree (length) bound . This encodes a sub- -vector space (also called a filtered part) of ,..., , spanned by all monomials of length at most . 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 |  |

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