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


layout (clifford.Layout) – layout of the GA to conformalize (the base)


  • layout_c (clifford.Layout) – layout of the base 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)

    • 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


>>> from clifford import Cl, conformalize
>>> G2, blades = Cl(2)
>>> G2c, bladesc, stuff = conformalize(G2)
>>> locals().update(bladesc)
>>> locals().update(stuff)