The Canon package: a fast kernel for tensor manipulators

Abstract

This paper describes the Canon package written in the Maple programming language. Canon's purpose is to work as a kernel for complete Maple tensor packages or any Maple package for manipulating indexed objects obeying generic permutation symmetries and possibly having dummy indices. Canon uses Computational Group Theory algorithms to efficiently simplify or manipulate generic tensor expressions. We describe the main command to access the package, give examples, and estimate typical computation timings. Program summary Title of program: Canon Catalogue identifier: ADSP Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADSP Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computers: any machine running Maple versions 6 to 9 Operating systems under which the program has been tested: Microsoft Windows, Linux Programming language used: Maple Memory required to execute with typical data: up to 10 Mb No. of bits in word: 32 or 64 No. of processors used: 1 Has the code been vectorized or parallelized?: No No. of bytes in distributed program, including test data, etc.: 45 910 Distribution format: tar gzip file Nature of physical problem: Manipulation and simplification of tensor expressions (or any expression in terms of indexed objects) in explicit index notation, where the indices obey generic permutation symmetries and there may exist dummy (summed over) indices. Method of solution: Computational Group Theory algorithms have been used, specially algorithms for finding canonical representations of single and double cosets, and algorithms for creating strong generating sets. Restriction on the complexity of the problem: Computer memory. With current equipment, expressions with hundreds of indices have been manipulated successfully. Typical running time: Simplification of expressions with 15 Riemann tensors was done in less than one minute in a personal computer. Unusual features: The use of Computational Group Theory algorithms allows the package to manipulate objects with a few hundreds of indices.