Is there a hyperreal datatype implementation for doing computations in non-standard analysis?

Question

Non-standard mathematical analysis extends the real number line to include "hyperreals" -- infinitesimals and infinite numbers. Is there (specification for an) implementation of a data type to implement computations using hyperreals? I'm looking for something analogous to the complex number data type you find in Python and Fortran and elsewhere. I actually don't know if such computations are useful: I'm just curious. I've played around with this concept a bit, but since I probably made errors I will spare you-all the details. Reference wikipedia page on hyperreals.

Answer 1

I think you could do that with the following construction:

Hyperreal numbers are quotients of polynomials with real coefficients over the variable w where w denotes the "smallest" infinity (i.e. not a product of smaller infinite numbers).

The polynomials are ordered lexicographically, i.e. the highest power where the polynomials differ determines the ordering. This can be extended in the standard way to quotients of polynomials (like the order on rational numbers, which are quotients of integers).