clifford.conformalize

clifford.conformalize(layout, added_sig=[1, -1], **kw)

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)