W0036

Power of Notation. Malgorzata Rowicka, Zbyszek Otwinowski, Andrzej Kudlicki, Depty of Biochemistry, Univ. of Texas, Southwestern Medical Center, 5323 Harry Hines Blvd, Dallas, TX 75390-903.

Crystallographers deal with different types of objects defined in various coordinate systems. To simplify the description of affine transformation, ubiquitous in crystallography, 4-vectors are used as base objects. Upper and lower indices of Einstein convention are used to distinguish between objects that transform differently. Einstein notation, once applied, works uniformly in real and reciprocal space, including the calculation of derivatives. The Einstein notation can be used in the modern, object-oriented programming style to enforce the correctness of algorithms that deal with different coordinate systems in crystallography. Examples of non-obvious use of the presented notation are: memory access calculations, calculations involving anisotropic vibration tensor (B factor) and translation-libration-screw (TLS) rigid-body description of vibrations.