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 anti-commutator 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 left-contraction of two multivectors, \(M\rfloor N\) |
|
Return left-inverse using a computational linear algebra method proposed by Christian Perwass. |
|
Return left-inverse 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 left-inverse 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. |