clifford.ConformalLayout

class clifford.ConformalLayout(*args, layout=None, **kwargs)[source]

Bases: clifford._layout.Layout

A layout for a conformal algebra, which adds extra constants and helpers.

Typically these should be constructed via clifford.conformalize().

New in version 1.2.0.

ep

The first added basis element, \(e_{+}\), usually with \(e_{+}^2 = +1\)

Type

MultiVector

en

The first added basis element, \(e_{-}\), usually with \(e_{-}^2 = -1\)

Type

MultiVector

eo

The null basis vector at the origin, \(e_o = 0.5(e_{-} - e_{+})\)

Type

MultiVector

einf

The null vector at infinity, \(e_\infty = e_{-} + e_{+}\)

Type

MultiVector

E0

The minkowski subspace bivector, \(e_\infty \wedge e_o\)

Type

MultiVector

I_base

The pseudoscalar of the base ga, in cga layout

Type

MultiVector

up(x: clifford._multivector.MultiVector) → clifford._multivector.MultiVector[source]

up-project a vector from GA to CGA

homo(x: clifford._multivector.MultiVector) → clifford._multivector.MultiVector[source]

homogenize a CGA vector

down(x: clifford._multivector.MultiVector) → clifford._multivector.MultiVector[source]

down-project a vector from CGA to GA