A system for automatic generation of tensor algorithms and indicial tensor calculus, including substitution of sums
SHEEP is an algebraic system written by I. Frick [1,2] that is specialized for manipulating components of tensors. On top of this language another system has been built treating a new data type "indicial formula" representing formulas containing tensors or spinors with symbolic (letter) indices. Such formulas can be used in two ways:
1. There are routines for manipulating indicial formulas, such as evaluation, differentiation, simplification using symmetries, substitution of products and sums, etc.
Also scalar sums can be efficiently substituted, e.g. sin2x+cos2x−1=>0
2. There is a compiler which for any indicial formula generates a corresponding program that actually performs the contractions etc. indicated in the formula. Thus the components of a tensor can be computed as soon as an indicial formula for its computation has been typed.
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