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symbolic constant in clifford algebra

asked 2016-06-13 15:01:50 +0100

davidvanovereem gravatar image

updated 2022-10-06 20:15:29 +0100

FrédéricC gravatar image

Dear all,

First of all I'd like to state that I am far from a SageMath expert. Right now, I am working on Clifford algebra's and I would like to do some computations with SageMath Cloud. Unfortunately, I experience the problem that when I define a symbolic constant, Sage doesn't know how to multiply this with elements in the Clifford algebra. This is the code that I'm using.


C = ComplexField();

sage: Q = QuadraticForm(C, 3, [0,0,1,1,0,0])

sage: Cl.<x,y,z> = CliffordAlgebra(Q)




I get an error for ex: ''unsupported operand parent(s) for '': 'Symbolic Ring' and 'The Clifford algebra of the Quadratic form in 3 variables over Complex Field with 53 bits of precision with coefficients:''

Does anyone maybe know how to work around this? Maybe I am defining the variable all wrong?

Thank you very much!

Kind regards,


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Could you tell who is supposed to be e (mathematically) ?

tmonteil gravatar imagetmonteil ( 2016-06-13 16:32:11 +0100 )edit

thanks for your comment tmonteil! e is supposed to be just some constant in C.

davidvanovereem gravatar imagedavidvanovereem ( 2016-06-13 18:49:29 +0100 )edit

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answered 2016-06-13 23:43:15 +0100

tmonteil gravatar image

It is not clear to me what do you plan to do with such product, so i fear there is no good answer to your question, perhaps could you try to be more precise on your goals.

That said, when dealing with algebraic objects, a classical trick is to use polynomial indeterminates instead of symbols. In your case, it could be something like:

sage: R.<e> = PolynomialRing(C)
sage: R
Univariate Polynomial Ring in e over Complex Field with 53 bits of precision
sage: e*x
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Asked: 2016-06-13 15:01:50 +0100

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Last updated: Jun 13 '16