clifford.conformalize

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

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 Returns:

• layout_c (clifford.Layout) – layout of the conformalized GA
• blades_c (dict) – blades for the CGA
• stuff (dict) –

  dict containing the following:

  • ep - postive basis vector added
  • en - negative basis vector added
  • eo - zero vector of null basis (=.5*(en-ep))
  • einf - infinity vector of null basis (=en+ep)
  • E0 - minkowski bivector (=einf^eo)
  • I_ga - pseudoscalar for conformalized GA in new 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)