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
Returns a MultiVector that is the pseudoscalar of this space. |
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ordered list of blades present in this MV |
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Even part of this mulivector |
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Odd part of this mulivector |
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Returns a MultiVector that is the pseudoscalar of this space. |
Methods
Constructor. |
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Adjoint / reversion |
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Returns the anti-commutator product of two multivectors. |
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Finds a vector basis of this subspace. |
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Sets coefficients whose absolute value is < eps to exactly 0. |
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Returns the commutator product of two multivectors. |
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Returns the Clifford conjugate (reversion and grade involution). |
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Returns the dual of the multivector against the given subspace I. |
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Factorises a blade into basis vectors and an overall scale Uses Leo Dorsts algorithm from 21.6 of GA for Computer Science |
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Returns the grade involution of the multivector. |
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Return the grades contained in the multivector. |
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Returns the inverse of the pseudoscalar of the algebra. |
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Returns true if multivector is a blade. |
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Returns true iff self is a scalar. |
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Returns true if multivector is a versor. |
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Returns the join of two blades. |
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Returns the left-contraction of two multivectors. |
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Return left-inverse using a computational linear algebra method proposed by Christian Perwass. |
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Return left-inverse using a computational linear algebra method proposed by Christian Perwass. |
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Magnitude (modulus) squared |
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Returns the meet of two blades. |
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Return the (mostly) normalized multivector. |
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Returns the inverse of itself if M*~M == |M|**2. |
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Projects the multivector onto the subspace represented by this blade. |
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Return left-inverse using a computational linear algebra method proposed by Christian Perwass. |
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Rounds all coefficients according to Python’s rounding rules. |
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The vee product aka. |
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Returns the commutator product of two multivectors. |