# clifford.ConformalLayout¶

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

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