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Simplification of Complex Tensor Expressions

Ryszard A. Walentynski
Organization: Silesia University of Technology, Poland
Department: Department of Building Structures’ Theory, Faculty of Civil Engineering

2002 Applications of Computer Algebra Conference (ACA '2002)
Conference location

Volos, Greece

The system of computer algebra Mathematica contains advanced tools of algebraic ex-pressions simplification (Simplify and a newer one FullSimplify). Its external package MathTensor for doing tensor analysis has got possibilities to simplify tensor ex-pression (Tsimplify). They are very effective but if the expression is very complicated not necessarily a simplest (shortest) expression is obtained if they are applied directly (automatically). Moreover the terms may be not sorted in the most elegant form.

The paper presents how the process of the simplification can be moderated by a user. There are some additional tools both of Mathematica and MathTensor that can help in this process. Among algebraic tools we can specify mapping (Map or /@), replacement (Replace or /. and ReplaceAll or //.), expansion (Expand) and collection (Collect). MathTensor functions like finding (Dum) or absorption (Absorb, Absorbg or AbsorKdelta) of dummy indices and canonicalization (Canonicalize) helps to find the simplest form of tensor expressions.

There is shown how to effectively use these commands on examples of tensor expressions simplification. They has been obtained during some research conducted in the theory of shells. Application of the “user moderates” simplification allows to find much shorter and elegant final expression. Moreover some symmetry features of the expressions can be observed.

The aim of the contribution is to show how the system of computer algebra can be applied more effectively and what the user can do to exploit more deeply its symbolic possibilities.

*Mathematics > Algebra
*Wolfram Technology > Application Packages > Applications from Independent Developers > MathTensor

Simplify, FullSimplify, MathTensor, algebraic tools