clifford.conformalize¶
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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.
Parameters: layout (clifford.Layout) – layout of the GA to conformalize (the base) Returns: - 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
Examples
>>> from clifford import Cl, conformalize >>> G2, blades = Cl(2) >>> G2c, bladesc, stuff = conformalize(G2) >>> locals().update(bladesc) >>> locals().update(stuff)