Cheta with base-change: preliminary results

[jaydfox]

I also just see that there is a function lagrange_polynomial in sage
e.g.
# using the definition of Lagrange interpolation polynomial
sage: R = PolynomialRing(QQ, 'x')
sage: R.lagrange_polynomial([(0,1),(2,2),(3,-2),(-4,9)])

I mean this should be super easy now. Just plug in your argument-value-pairs and you have the interpolating polynomial (no matrix fuzz).
Then you can apply this interpolating polynomial to non-real values.
Or extract the coefficients as you like.
However I didnt check how long it takes

Well that takes all the fun out of it, now doesn't it?

But seriously, I'll try both approaches and see which is faster.