clifford.MultiVector

class clifford.MultiVector(layout, value=None, string=None)

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

blades_list	ordered list of blades present in this MV
even	Even part of this mulivector
odd	Odd part of this mulivector

Methods

__init__	Constructor.
adjoint	Adjoint / reversion _ ~M –> M (any one of several conflicting notations) ~(N * M) –> ~M * ~N adjoint() –> MultiVector
anticommutator	Returns the anti-commutator product of two multivectors.
basis	Finds a vector basis of this subspace.
clean	Sets coefficients whose absolute value is < eps to exactly 0.
commutator	Returns the commutator product of two multivectors.
conjugate	Returns the Clifford conjugate (reversion and grade involution).
dual	Returns the dual of the multivector against the given subspace I.
gradeInvol	Returns the grade involution of the multivector.
grades	Return the grades contained in the multivector.
inv	Return right-inverse using a computational linear algebra method proposed by Christian Perwass.
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.
join	Returns the join of two blades.
lc	Returns the left-contraction of two multivectors.
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 2 |M| mag2() –> PyFloat | PyInt
meet	Returns the meet of two blades.
normal	Return the (mostly) normalized multivector.
normalInv	Returns the inverse of itself if M*~M == |M|**2.-1 M = ~M / (M * ~M) normalInv() –> MultiVector.
project	Projects the multivector onto the subspace represented by this blade.
pseudoScalar	Returns a MultiVector that is the pseudoscalar of this space.
rightInv	Return right-inverse using a computational linear algebra method proposed by Christian Perwass.
rightLaInv	Return right-inverse using a computational linear algebra method proposed by Christian Perwass.
round	Rounds all coefficients according to Python’s rounding rules.
x	Returns the commutator product of two multivectors.