clifford.MultiVector¶

class
clifford.
MultiVector
(layout, value=None, string=None, *, dtype: numpy.dtype = <class 'numpy.float64'>)[source]¶ An element of the algebra
 Parameters
layout (instance of
clifford.Layout
) – the layout of the algebravalue (sequence of length
layout.gaDims
) – the coefficients of the base blades
Notes
The following operators are overloaded:
A * B
: geometric productA ^ B
: outer productA  B
: inner productA << B
: left contraction~M
: reversionM(N)
: grade or subspace projectionM[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 multivector 

Odd part of this mulitvector 

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

Adjoint / reversion, \(\tilde M\) 

The anticommutator product of two multivectors, \((MN + NM)/2\) 

Change the underlying scalar type of this vector. 

Finds a vector basis of this subspace. 

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

The commutator product of two multivectors. 

The Clifford conjugate (reversion and grade involution). 

The dual of the multivector against the given subspace I, \(\tilde M = MI^{1}\) 

Factorises a blade into basis vectors and an overall scale. 

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. 

The join of two blades. 

The leftcontraction of two multivectors, \(M\rfloor N\) 

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, \({M}^2\) 

The meet of two blades. 

Return the (mostly) normalized multivector. 

The inverse of itself if \(M \tilde M = M^2\). 

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. 

Vee product \(A \vee B\). 

The commutator product of two multivectors. 