# Exponential in Clifford algebra

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
```

What do you expect as a result? Is it a polynomial in

`A`

,`B`

,`i`

?@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 question).There are no such things in the polynomial ring.

@MaxAlekseyez Well, I just want A and B to be symbolic variables. In my mind A and B are elements of the reals. Using polynomial ring was suggested by a colleague on this site to make A and B work as symbolic variables in Clifford algebras. I am willing to look at other things. Specifically I would like to set up a Clifford algebra, such that both

`(A+B*i)*(A-B*i)=A^2+B^2`

and`exp(A+B*i)*exp(A-B*i)=exp(2*A)`

are realized. I don't mind playing around with the definitions of the setup of the algebra to make this possible.You can define

`A`

and`B`

as symbolic variables, and`exp(2A)`

would be a legitimate object, however`exp(B*i)`

would still not make sense as exponentiation of the generator of the Clifford algebra is not defined.