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"Just run for t,c in A+B*i: print(t,c) and you'll see." Oh that's fancy.. I'm gonna like this software :)

Hello, I am trying to take the exponential of A+B*i in Clifford algebra (isomorphic to the complex numbers) .

Code is:

sage: R.<A,B> = PolynomialRing(ZZ);
sage: Q = QuadraticForm(R,1,[-1]);
sage: Cl.<i> = CliffordAlgebra(Q);
sage: exp(A+B*i)*exp(A-B*i)

I would expect it to output exp(2*A), but it produces this error:

TypeError: cannot coerce arguments: no canonical coercion from The Clifford algebra of the Quadratic form in 1 variables over Multivariate Polynomial Ring in A, B over Integer Ring with coefficients: 
[ 1 ] to Symbolic Ring

Can you explain what c and t means in the function, and what for t,c in x do, with respect to x=A+B*i?

Can you explain what c and t means in the function, and what for t,c in x do?

Can you explain what t means in the function, and what for t,c in x do?

Can you explain what t means in the function, and what for t,c in x do?

Can you explain the function. I gather that you are using E as a 'dummy' variable and utilize the fact that A, Bi commut

Can you explain the function. I gather that you are using E as a 'dummy' variable and utilize the fact that A, Bi commut

Works wonderfully... thank you. reset();Q = QuadraticForm(SR,1,[-1]);Cl.<i> = CliffordAlgebra(Q);a,b = var('a b')

reset();Q = QuadraticForm(SR,1,[-1]);Cl. = CliffordAlgebra(Q);a,b = var('a b');a+b*i Works wonderfully... thank you. A

reset();Q = QuadraticForm(SR,1,[-1]);Cl. = CliffordAlgebra(Q);a,b = var('a b');a+b*I Works wonderfully... thank you. A

@MaxAlekseyez this guy... https://www.euclideanspace.com/maths/algebra/clifford/algebra/functions/exponent/index.htm giv

@MaxAlekseyez Its definable using the matrix exponential: https://en.wikipedia.org/wiki/Matrix_exponential (and the isom

@MaxAlekseyez Its definable using the matrix exponential: https://en.wikipedia.org/wiki/Matrix_exponential (and the isom

@MaxAlekseyez Its defined using the matrix exponential: https://en.wikipedia.org/wiki/Matrix_exponential (and the isomor

@MaxAlekseyez Its defined the same way as the matrix exponential: https://en.wikipedia.org/wiki/Matrix_exponential Als

@MaxAlekseyez Its defined the same way as the matrix exponential.https://en.wikipedia.org/wiki/Matrix_exponential Also

@MaxAlekseyez Its defined the same way as the matrix exponential.https://en.wikipedia.org/wiki/Matrix_exponential Also,

@MaxAlekseyez Its defined the same way as the matrix exponential.https://en.wikipedia.org/wiki/Matrix_exponential Also,

@MaxAlekseyez Its defined the same way as the matrix exponential.https://en.wikipedia.org/wiki/Matrix_exponential Also,

@MaxAlekseyez Its defined the same way as the matrix exponential.https://en.wikipedia.org/wiki/Matrix_exponential Also,

@MaxAlekseyez Its defined the same way as the matrix exponential.https://en.wikipedia.org/wiki/Matrix_exponential Also,

@MaxAlekseyez Its defined the same way as the matrix exponential.https://en.wikipedia.org/wiki/Matrix_exponential Also,

Hello, a similar question was asked previously, but I am unable to use multiple symbolic variables with the answer. What I would like to do is the following:

sage: Q = QuadraticForm(ZZ,2,[1,1,1])                                                                                                                              
sage: Cl.<x,y> = CliffordAlgebra(Q)

Then, I would like to define two symbolic a and b variables

sage: a*x+b*y

such that this output is produced:

sage: (a*x+b*y)*(a*x+b*y)
a^2+b^2

How do I declare a and b so that this is possible?

I have tried a, b = var('a b') but a*x gives an error

sage: a*x
TypeError: unsupported operand parent(s) for *: 'Symbolic Ring' and 'The Clifford algebra of the Quadratic form in 2 variables over Integer Ring with coefficients: 
[ 1 1 ]
[ * 1 ]'

I have also tried R.<a> = PolynomialRing(ZZ) and it works for 1 variable. But if I also tried to add b, it fails

sage: R.<a,b> = PolynomialRing(ZZ)
sage: a*x+b*y
TypeError: unsupported operand parent(s) for +: 'Multivariate Polynomial Ring in a, b over Integer Ring' and 'The Clifford algebra of the Quadratic form in 2 variables over Integer Ring with coefficients: 
[ 1 1 ]
[ * 1 ]'

@MaxAlekseyez Well, I just want A and B to be symbolic variables. In my mind A and B are elements of the reals. Using po

@Max Well, I just want A and B to be symbolic variables. In my mind A and B are elements of the reals. Using polynomial

@Max Well, I just want A and B to be symbolic variables. In my mind A and B are elements of the reals. Using polynomial

@Max Well, I just want A and B to be symbolic variables. Using polynomial ring was suggested by a colleague on this site

@Max Well, I just want A and B to be symbolic variables. Using polynomial ring was suggested by a colleague on this site

@Max Well, I just want A and B to be symbolic variables. Using polynomial ring was suggested by a colleague on this site

Well, I just want A and B to be symbolic variables. Using polynomial ring was suggested by a colleague on this site to m

Exponential in Clifford algebra Hello, I am trying to take the exponential of A+B*i in Clifford algebra (isomorphic to t

Exponential in Clifford algebra Hello, I am trying to take the exponential of A+B*i in Clifford algebra (isomorphic to t

Exponential in Clifford algebra Hello, I am trying to take the exponential of A+B*i in Clifford algebra (isomorphic to t

@MaxAlekseyez Good question. What I want, really, is for this exp(A+B*i)*exp(A-B*i) to give exp(2*A) (I've edited the qu

@MaxAlekseyez Good question. What I want, really, is for this exp(A+Bi)*exp(A-Bi) to give exp(2A) (I've edited the quest

Exponential in Clifford algebra Hello, I am trying to take the exponential of A+B*i in Clifford algebra (isomorphic to t

Exponential in Clifford algebra Hello, I am trying to take the exponential of A+B*i in Clifford algebra (isomorphic to t

@MaxAlekseyez Good question. What I want, really, is for this exp(A+Bi)exp(A-Bi) to give exp(2A) (I've edited the questi

@MaxAlekseyez Good question. What I want, really, is for this exp(A+Bi)exp(A-Bi) to give exp(2A)

@MaxAlekseyez Good question. Want I want, really, is for this exp(A+Bi)exp(A-Bi) to give exp(2A)

@MaxAlekseyez Good question. Want I want, really, is for this exp(A+Bi)exp(A-Bi) to give exp(2A): sage: exp(A+Bi)exp

@MaxAlekseyez Good question. Want I want, really, is for this exp(A+Bi)exp(A-Bi) to give exp(2A).

Good question. Want I want, really, is for this exp(A+Bi)exp(A-Bi) to give exp(2A).

Exponential in Clifford algebra Hello, I am trying to take the exponential of A+B*i in Clifford algebra (isomorphic to t