Top
Back: Graded commutative algebras (SCA)
Forward: Examples of use of Letterplace
FastBack:
FastForward:
Up: Singular Manual
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

7.7 LETTERPLACE

Singular:Letterplace logo

A Subsystem for Non-commutative Finitely Presented Associative Algebras

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

All algebras are assumed to be associative 53#53-algebras for 53#53 being a field 50#50

or a ring 30#30.

What is and what does LETTERPLACE?

What is LETTERPLACE? It is a subsystem of SINGULAR, providing the manipulations and computations within free associative algebras over rings 53#53 300#300,..., 301#301, where the coefficient domain 53#53 is either a ring 30#30 or a field, supported by SINGULAR.

LETTERPLACE can perform computations also in the factor-algebras of the above (via data type qring) by two-sided ideals.

Free algebras are internally represented in SINGULAR as so-called Letterplace rings.

Each such ring is constructed from a commutative ring 53#53[ 302#302,..., 303#303 ] and a degree (length) bound 171#171.

This encodes a sub- 50#50-vector space (also called a filtered part) of 50#50 300#300,..., 301#301, spanned by all monomials of length at most 171#171. Analogously for free 53#53-subbimodules of a free 53#53-bimodule of a fixed rank.

Within such a construction we offer the computations of Groebner (also known as Groebner-Shirshov) bases, normal forms, syzygies and many more.

We address both two-sided ideals and subbimodules of the free bimodule of the fixed rank.

A variety of monomial and module orderings is supported, including elimination orderings for both variables and bimodule components. A monomial ordering has to be a well-ordering.

LETTERPLACE works with every field, supported by SINGULAR, and with the coefficient ring 30#30.

Note, that the elements of the coefficient field (or a ring) mutually commute with all variables.

7.7.1 Examples of use of LETTERPLACE  
7.7.2 Example of use of LETTERPLACE over Z  
7.7.3 Functionality and release notes of LETTERPLACE  
7.7.4 References and history of LETTERPLACE  
7.8 Functions (letterplace)  
7.10 LETTERPLACE libraries  
7.11 Release Notes (letterplace)  


Top Back: Graded commutative algebras (SCA) Forward: Examples of use of Letterplace FastBack: FastForward: Up: Singular Manual Top: Singular Manual Contents: Table of Contents Index: Index About: About this document
            User manual for Singular version 4.4.0, 2024, generated by texi2html.