# Does this notation have a name?

This:
$$a + bx + cx^2 +dx^3 + ex^4 + ...$$
where $$x$$ is a unit, like $$i$$ or $$1$$ or $$\pi$$. ($$1 + 2\pi + 3\pi^2$$)

Algebraic Notation? I don't understand what you're trying to get at here...

Let's say you have $$1 + 0t + 1t^2 + 1t^3$$ where $$t=2$$, and you take the coefficients in reverse, you get $$1101$$, which, in binary, (base $$t$$) is the same number, 13. But the notation I used can have something like $$2 + 5t + 3t^2 + 3t^3$$, which can be simplified if you know that $$t$$ is 2, but you can't write "3352" when you're writing in binary.

polynomal

You're right, except I'm writing them in the reverse of standard notation, it seems. (standard notation being $$3t^3+3t^2+5t+2$$)

("it seems" because I just now looked up "polynomial notation".)

Yeah, for finite polynomials you are, but not for ones with infinitely many terms. (Look up Taylor series.)