clifford.MultiVector¶

class
clifford.
MultiVector
(layout, value=None, string=None)[source]¶ An element of the algebra
 Parameters
layout (instance of clifford.Layout) – the layout of the algebra
value (sequence of length layout.gaDims) – the coefficients of the base blades
Notes
The following operators are overloaded as follows:
: geometric product
^ : outer product
 : inner product
~ : reversion
: abs value, this is sqrt(abs(~M*M))
sequence method
M(N) : grade or subspace projection
M[N] : blade projection
Attributes
Returns a MultiVector that is the pseudoscalar of this space. 

ordered list of blades present in this MV 

Even part of this mulivector 

Odd part of this mulivector 

Returns a MultiVector that is the pseudoscalar of this space. 
Methods
Constructor. 

Adjoint / reversion 

Returns the anticommutator product of two multivectors. 

Finds a vector basis of this subspace. 

Sets coefficients whose absolute value is < eps to exactly 0. 

Returns the commutator product of two multivectors. 

Returns the Clifford conjugate (reversion and grade involution). 

Returns the dual of the multivector against the given subspace I. 

Factorises a blade into basis vectors and an overall scale Uses Leo Dorsts algorithm from 21.6 of GA for Computer Science 

Returns the grade involution of the multivector. 

Return the grades contained in the multivector. 

Returns the inverse of the pseudoscalar of the algebra. 

Returns true if multivector is a blade. 

Returns true iff self is a scalar. 

Returns true if multivector is a versor. 

Returns the join of two blades. 

Returns the leftcontraction of two multivectors. 

Return leftinverse using a computational linear algebra method proposed by Christian Perwass. 

Return leftinverse using a computational linear algebra method proposed by Christian Perwass. 

Magnitude (modulus) squared 

Returns the meet of two blades. 

Return the (mostly) normalized multivector. 

Returns the inverse of itself if M*~M == M**2. 

Projects the multivector onto the subspace represented by this blade. 

Return leftinverse using a computational linear algebra method proposed by Christian Perwass. 

Rounds all coefficients according to Python’s rounding rules. 

The vee product aka. 

Returns the commutator product of two multivectors. 