OK:
(%i41) radcan(exp(((t-2*%i)*x^2)/(4*t-2*%i))), gcd : 'red;
(%o41) %e^(((t-2*%i)*x^2)/(4*t-2*%i))
OK (I think) but messy:
(%i42) radcan(exp(((t-2*%i)*x^2)/(4*t-2*%i))), gcd : 'spmod;
(%o42) %e^(((32*t^6-144*%i*t^5-240*t^4+200*%i*t^3+90*t^2-21*%i*t-2)*x^2)/(128*t^6-384*%i*t^5-480*t^4+320*%i*t^3+120*t^2-24*%i*t-2))
I wasn't able to transform (%o42) back to exp(((t-2*%i)*x^2)/(4*t-2*%i)).
--Barton