Well, I'm not 100% certain, but *someone* must have written a paper *sometime* about positional number systems using an *algebraic* and/or *algebraic integer* radix and integer numerals. Knuth? Knuth? Anyone? Anyone? Several interesting things: If p(r) is the minimal polynomial for r, and deg(p)=n, then we can express r^n in terms of lower powers of r, and thus there is some possible redundancy in the representations. Also, if n>1, then there are multiple r's satisfying p(r)=0, so we have to relate representations using r and r', s.t. p(r)=p(r')=0. Clearly, complex number systems of the 1+i type qualify, but I don't recall any such systems with n>2. Also, cyclotomic polynomials have the same unfortunate property that base-(e^i) numbers have -- namely, it is a lot more difficult to represent large numbers.