clifford.conformalize¶
-
clifford.
conformalize
(layout, added_sig=[1, -1], **kw)[source]¶ Conformalize a Geometric Algebra
Given the Layout for a GA of signature (p, q), this will produce a GA of signature (p+1, q+1), as well as return a new list of blades and some stuff. stuff is a dict containing the null basis blades, and some up/down functions for projecting in/out of the CGA.
- Parameters
layout (clifford.Layout) – layout of the GA to conformalize (the base)
added_sig (list-like) – list of +1, -1 denoted the added signatures
**kw (kwargs) – passed to Cl() used to generate conformal layout
- Returns
layout_c (clifford.Layout) – layout of the base GA
blades_c (dict) – blades for the CGA
stuff (dict) –
- dict containing the following:
ep - first basis vector added (usually positive)
en - second basis vector added (usually negative)
eo - zero vector of null basis (=.5*(en-ep))
einf - infinity vector of null basis (=en+ep)
E0 - minkowski bivector (=einf^eo)
base - pseudoscalar for base ga, in cga layout
up - up-project a vector from GA to CGA
down - down-project a vector from CGA to GA
homo - homogenize a CGA vector
Examples
>>> from clifford import Cl, conformalize >>> G2, blades = Cl(2) >>> G2c, bladesc, stuff = conformalize(G2) >>> locals().update(bladesc) >>> locals().update(stuff)