AlgebraDimension

The dimension of a finite-dimensional algebra: the length of its basis.

WikipediaDimension (vector space)↗WikidataQ929302↗

AlgebraDimension(algebra)for a Clifford algebra, $2^n$ for $n$ generators

Oscardim(algebra)

Typed signatures

Type	Package	Applies
untyped	hypercomplex	always
(any) -> unknown	structures	always

Domain: Structures

Details

• Every subset of the generators is one basis blade, so the dimension doubles per generator
• A separate head from compute-engine's Dimension, which is defined for lists and matrices and is deliberately left alone

Examples

Basic #

live ↗

In$\mathrm{AlgebraDimension}(\mathrm{Quaternions})$Out$4$

live ↗

In$\mathrm{AlgebraDimension}(\mathrm{CliffordAlgebra}(2, 1))$Out$8$

$\mathbb{C}_4$

live ↗

In$\mathrm{AlgebraDimension}(\mathrm{MulticomplexAlgebra}(4))$Out$16$

About

Examples	3
Crosswalk	WikipediaWikidataOscar

Implementation

mappedwolframpackages/oracle/src/mappings.ts

No built-in algebra-object type to take a dimension of: Quaternions is a domain symbol with no generic dimension function, and CliffordAlgebra/MulticomplexAlgebra aren't Wolfram heads at all. There is a Wolfram/GeometricAlgebra paclet (resources.wolframcloud.com/PacletRepository) but it's a separate installable paclet, not a ResourceFunction, and this environment has no Wolfram Cloud connection to install or check it against our examples -- also its generator-count convention is unconfirmed against ours. Left unmapped.

mappedsagepackages/oracle/src/mappings.ts

mappedoscarpackages/oracle/src/mappings.ts

See also: Basis, AlgebraSignature