Dual

The Poincaré dual $!x$ in algebra: each blade of $x$ replaced by the blade on the generators it does not contain, signed so $b \wedge {!b} = I$.

Dual(x, algebra)$!x$, the Poincaré dual of $x$ in algebra

Typed signatures

Type	Package	Applies
(number, clifford_algebra) -> number	geometric	always

Domain: Geometric algebra

Examples

Basic #

The dual of a vector in 3D is the bivector on the other two generators

live ↗

In$\mathrm{Dual}(e_1, \mathrm{CliffordAlgebra}(3, 0))$Out$e_2e_3$

live ↗

In$\mathrm{Dual}(e_1e_2, \mathrm{CliffordAlgebra}(3, 0))$Out$e_3$

About

Examples	2

See also: Pseudoscalar