clifford.MultiVector

class clifford.MultiVector(layout, value=None, string=None, *, dtype: numpy.dtype = <class 'numpy.float64'>)

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:

• A * B : geometric product

• A ^ B : outer product

• A | B : inner product

• A << B : left contraction

• ~M : reversion

• M(N) : grade or subspace projection

• M[N] : blade projection

Attributes

I	Returns a MultiVector that is the pseudoscalar of this space.
blades_list	ordered list of blades present in this MV
even	Even part of this multivector
odd	Odd part of this mulitvector
pseudoScalar	Returns a MultiVector that is the pseudoscalar of this space.

Methods

__init__	Constructor.
adjoint	Adjoint / reversion, \(\tilde M\)
anticommutator	The anti-commutator product of two multivectors, \((MN + NM)/2\)
as_array
astype	Change the underlying scalar type of this vector.
basis	Finds a vector basis of this subspace.
clean	Sets coefficients whose absolute value is < eps to exactly 0.
commutator	The commutator product of two multivectors.
conjugate	The Clifford conjugate (reversion and grade involution).
dual	The dual of the multivector against the given subspace I, \(\tilde M = MI^{-1}\)
exp
factorise	Factorises a blade into basis vectors and an overall scale.
gradeInvol	The grade involution of the multivector.
grades	Return the grades contained in the multivector.
inv
invPS	Returns the inverse of the pseudoscalar of the algebra.
isBlade	Returns true if multivector is a blade.
isScalar	Returns true iff self is a scalar.
isVersor	Returns true if multivector is a versor.
join	The join of two blades.
lc	The left-contraction of two multivectors, \(M\rfloor N\)
leftInv	Return left-inverse using a computational linear algebra method proposed by Christian Perwass.
leftLaInv	Return left-inverse using a computational linear algebra method proposed by Christian Perwass.
mag2	Magnitude (modulus) squared, \({|M|}^2\)
meet	The meet of two blades.
normal	Return the (mostly) normalized multivector.
normalInv	The inverse of itself if \(M \tilde M = |M|^2\).
project	Projects the multivector onto the subspace represented by this blade.
rightInv	Return left-inverse using a computational linear algebra method proposed by Christian Perwass.
right_complement
round	Rounds all coefficients according to Python’s rounding rules.
vee	The vee product aka.
x	The commutator product of two multivectors.