clifford.ConformalLayout

class clifford.ConformalLayout(*args, layout=None, **kwargs)

A layout for a conformal algebra, which adds extra constants and helpers.

Typically these should be constructed via clifford.conformalize().

New in version 1.2.0.

ep

The first added basis element, \(e_{+}\), usually with \(e_{+}^2 = +1\)

Type

MultiVector

en

The first added basis element, \(e_{-}\), usually with \(e_{-}^2 = -1\)

Type

MultiVector

eo

The null basis vector at the origin, \(e_o = 0.5(e_{-} - e_{+})\)

Type

MultiVector

einf

The null vector at infinity, \(e_\infty = e_{-} + e_{+}\)

Type

MultiVector

E0

The minkowski subspace bivector, \(e_\infty \wedge e_o\)

Type

MultiVector

I_base

The pseudoscalar of the base ga, in cga layout

Type

MultiVector

Attributes

I	the psuedoScalar
basis_names
basis_vectors
basis_vectors_lst
blades
blades_list	List of blades in this layout matching the order of self.bladeTupList
metric
pseudoScalar	the psuedoScalar
rotor_mask
scalar	the scalar of value 1, for this GA (a MultiVector object)

Methods

MultiVector	create a multivector in this layout
__init__	Initialize self.
bases	Returns a dictionary mapping basis element names to their MultiVector instances, optionally for specific grades
blades_of_grade	return all blades of a given grade,
dict_to_multivector	Takes a dictionary of coefficient values and converts it into a MultiVector object
down	down-project a vector from CGA to GA
gen_dual_func	Generates the dual function for the pseudoscalar
gen_vee_func	Generates the vee product function
get_grade_projection_matrix	Returns the matrix M_g that performs grade projection via left multiplication eg.
get_left_gmt_matrix	This produces the matrix X that performs left multiplication with x eg.
get_right_gmt_matrix	This produces the matrix X that performs right multiplication with x eg.
gmt_func_generator
grade_mask
homo	homogenize a CGA vector
imt_func_generator
lcmt_func_generator
load_ga_file	Takes a ga file Checks it is the same signature as this layout Loads the data into an MVArray
omt_func_generator
parse_multivector	Parses a multivector string into a MultiVector object
randomMV	Convenience method to create a random multivector.
randomRotor	generate a random Rotor.
randomV	generate n random 1-vector s
up	up-project a vector from GA to CGA