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Creating Notations, Templated Structures, and Tensors

Jason Harris
Organization: Wolfram Research, Inc.
Department: User Interface Group

2001 Mathematica Developer Conference
Conference location

Champaign, IL

This talk will cover creating notations in Mathematica. It will progress from creating basic notations to details on creating templated structures via TagBoxes and the corresponding notations to use for these structures. With these techniques a "proper" implementation of Dirac's Bra Ket Notation will be presented. Several other advanced features of the notation package, such as adding input aliases and the Action option, will be mentioned. These techniques will culminate in a presentation of a notation for Tensors, which fully works in both input and output. Finally, a highly efficient algorithm to canonicalize tensorial expressions will be demonstrated. Functioning with the created tensorial notation, by an innovative technique this algorithm circumvents the dummy index relabeling problem of tensor calculus. The complete algorithm handles linear symmetries such as the Bianchi identities as well as fully accommodating partial derivatives and mixed index classes.

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