Work with non-commutative variables in the reduce-2 system for analytical calculations

Abstract

A brief description and examples of using a program package for handling non-commutative variables in the REDUCE-2 system are presented. The package facilitates work with arbitrary commutation rules. The user may declare operators, variables, and procedures to be non-commutative, and introduce the rules for their rearrangement. Tools are included for reducing delta functions and Kronecker symbols in expressions involving non-commutative variables. During calculation, expressions are rearranged according to the rules introduced by the user, and similar terms are grouped together with explicit singling out of the non-commutative part.

Computation of covariant derivatives of the geodetic interval with coincident arguments

“…[ V , V , ~I = g, ( 6 ) [ V , V , V k a ] = 0 (7) [ V r V , V k V l ~l =NL,/ + RIIJk) (8) where the brackets mean that the bilocal quantity is taken with coincident arguments.…”

“…To satisfy this requirement we have prepared a collecting program taking into account the summation indices. This program uses the non-commutative algebra package of the system REDUCE [ 6 ] . Previously, the Kronecker symbol simplification has been realised in this package.…”

“…This paper presents calculations of Z,(x) and Z,(x). The main calculations were performed by means of the program REDUCE [ 5 ] using an additional package for the non-commutative variables [6]. In 0 2 the recurrence formula for Z,(x) is presented.…”