Reversion

Reversion $\tilde{x}$: reverse the order of generators in every blade of $x$, costing sign $(-1)^{k(k-1)/2}$ per grade $k$.

Reversion(x)$\tilde{x}$, the reverse of $x$

Typed signatures

Type	Package	Applies
(number) -> number	geometric	always

Domain: Geometric algebra

Examples

Basic #

Reversing the order of the generators in a bivector flips its sign

live ↗

In$\mathrm{Reversion}(e_1e_2)$Out$-(e_1e_2)$

Grade 3 flips too

live ↗

In$\mathrm{Reversion}(e_1e_2e_3)$Out$-(e_1e_2e_3)$

About

Examples	2

See also: GradeInvolution, CliffordConjugate, Sandwich