# STENSOR

## a System for Tensor- and Noncommutative Algebra

Stensor is a computer algebra system devoted to tensors with symbolic indices and noncommuting objects. The folowing features have evolved during the many years of development:
Full Simplification of Symbolic Tensor Expressions.
i.e. with symbolic indices on tensors. Any index symmetries are allowed, and consequences undestood, eg that A_{ij}S^{ij}-0, if (A) S are (anti) symmetric, respectively.

Noncommutative- and Operator Algebra
Handling octonians, Clifford/Grassman algebra, Poisson brackets, variations, difforms,...

Kaluza-Klein, Supergravity, Spinors.
Splitting into any number of spubspaces, multiple indextypes/conventions for these subspaces, Fiertz-transformations, gamma algebra and trace for any dimension/metric, ...

Sum-Substitutor fully Exploit Trig- and other Sumrelations.
Eg -cos^6x sin^2x + cos^6x - cos^2x sin^7x + sin^7x -> sin^9x +cos^8x Other systems tend towards pure sin (or cos) results, while STENSOR returns the minimal mixture! From this cyclic Riemann symmetry (sumrelation) STENSOR derived the seemingly new identities: R_{ijkl}R_{klmn}R_{mnij} = 4R_{ijkl}R_{ikmn}R_{jmln} = 2R_{ijkl}R_{ikmn}R_{jlmn} from the (accidental) LHS input.

Generate Tensor Algorithms for Component Computation
From symbolic formulae, algorithms are generated that compute tensor components often faster than handcoded algorithms. Especially this is done in symbiosis with the relativity system SHEEP.

Disk-Bucketing for Multi-Million Term Calculations.
Expression parts (buckets) can be automatically shuffled to/from disk at need. So was the general Ricci-tensor in 5 dimensions computed: R_{00} had 263,598 terms, exceeding eg Reduce/Macsyma capability by orders of magnitude. Time was a reasonable 100 h. with a negligible part spent in disk i/o, so much larger computations than this are possible. Schoonschip and FORM offer this facility as well.

User Interface.
• Formulae input close to textbook conventions
• History and modification mechanism a la unix shell
• On line help that looks up appropriate documentation
• Extensively commented lectues/demos that yoy step through interactively
• A TeX mode cause STENSOR create a session file you can send directly to TeX
• User guide, which ahs been produced by STENSOR in its TeX mode
• Reference Manual, 120 pages.
• STENSOR/SHEEP can run alone or inside Reduce, fully exploiting its features like GCD and factoring.

Machines
VAX(VMS/U-ix), Orion (HLH ltd), SUN, DEC/VAX workstations, IBM 3090, ATARI ST, AMIGA, Desktops IBM 386, 486, and MacIntosh.

Lars Hornfeldt
Institute of Theoretical Physics
University of Stockholm