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
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 mulivector 
odd 
Odd part of this mulivector 
pseudoScalar 
Returns a MultiVector that is the pseudoscalar of this space. 
Methods
__init__ 
Constructor. 
adjoint 
Adjoint / reversion 
anticommutator 
Returns the anticommutator 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. 
factorise 
Factorises a blade into basis vectors and an overall scale Uses Leo Dorsts algorithm from 21.6 of GA for Computer Science 
gradeInvol 
Returns 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 
Returns the join of two blades. 
lc 
Returns the leftcontraction of two multivectors. 
leftInv 
Return leftinverse using a computational linear algebra method proposed by Christian Perwass. 
leftLaInv 
Return leftinverse using a computational linear algebra method proposed by Christian Perwass. 
mag2 
Magnitude (modulus) squared 
meet 
Returns the meet of two blades. 
normal 
Return the (mostly) normalized multivector. 
normalInv 
Returns the inverse of itself if M*~M == M**2. 
project 
Projects the multivector onto the subspace represented by this blade. 
rightInv 
Return leftinverse 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. 