AlgebraSignature

The signature vector: what each of the algebra's generators squares to, in order — $-1$, $+1$ or $0$.

WikipediaMetric signature↗MathWorldMatrixSignature↗WikidataQ1142562↗

AlgebraSignature(algebra)each generator's square, as a list

Typed signatures

Type	Package	Applies
(clifford_algebra) -> list	hypercomplex	always

Domain: Hypercomplex algebra

Details

• Together with the commutation rule this is all that defines the algebra
• $\mathrm{Cl}(p,q)$ reads as $p$ entries of $+1$ then $q$ of $-1$
• A $0$ entry marks a nilpotent generator — the dual and Grassmann families

Examples

Basic #

live ↗

In$\mathrm{AlgebraSignature}(\mathrm{Quaternions})$Out$\bigl\lbrack-1, -1\bigr\rbrack$

$\mathrm{Cl}(2,1)$

live ↗

In$\mathrm{AlgebraSignature}(\mathrm{CliffordAlgebra}(2, 1))$Out$\bigl\lbrack1, 1, -1\bigr\rbrack$

Scope #

nilpotent

live ↗

In$\mathrm{AlgebraSignature}(\mathrm{DualNumbers})$Out$\bigl\lbrack0\bigr\rbrack$

About

Examples	3
Crosswalk	WikipediaMathWorldWikidata

See also: Basis, AlgebraDimension, Quaternions, PowerModList