Top
Back: Exterior
Forward: superCommutative
FastBack: ncfactor_lib
FastForward: perron_lib
Up: nctools_lib
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document
7.7.13.0. findimAlgebra
Procedure from library nctools.lib (see nctools_lib).

Usage:
findimAlgebra(M,[r]); M a matrix, r an optional ring

Return:
ring

Purpose:
define a finite dimensional algebra structure on a ring

Note:
the matrix M is used to define the relations x(i)*x(j) = M[i,j] in the basering (by default) or in the optional ring r.
The procedure equips the ring with the noncommutative structure.
The procedure exports the ideal (not a two-sided Groebner basis!), called fdQuot, for further qring definition.

Theory:
finite dimensional algebra can be represented as a factor algebra of a G-algebra modulo certain two-sided ideal. The relations of a f.d. algebra are thus naturally divided into two groups: firstly, the relations on the variables of the ring, making it into G-algebra and the rest of them, which constitute the ideal which will be factored out.

Example:
 


Top Back: Exterior Forward: superCommutative FastBack: ncfactor_lib FastForward: perron_lib Up: nctools_lib Top: Singular Manual Contents: Table of Contents Index: Index About: About this document
            User manual for Singular version 3-1-6, Dec 2012, generated by texi2html.