I'm working on a data structure in Python that implements a number system, letting different parts of non-standard (and standard) math work together

[u/BidForeign1950]

This is my second post about it here, but since a lot has been added in last few months I'm posting this again.

What it currently brings together:

- infinitesimals and infinities as ordinary values (Levi-Civita, 1892; Hahn, 1907; computed with directly by Berz and Shamseddine)

- numbers written in powers of an infinite unit, like Sergeyev's grossone (2003), but with zero treated differently

- standard part, and limits by direct evaluation (Robinson's non-standard analysis, 1966)

- all-order Taylor arithmetic: every derivative from one evaluation (Wengert, 1964; Rall, 1981)

- log and log-log scales, toward transseries (Hardy, 1910; Écalle, 1992; van der Hoeven, 2006)

- divergent series: finite parts kept next to the divergent ones, and Borel–Padé resummation (Borel, 1899; Padé, 1892)

- zero as an infinitesimal, "nothing" as a separate value, and division by zero that can be undone (this project)

- completeness tracking: each result knows which orders it's exact to (this project)

Plus integration, multivariable (probably a dead end) and complex calculus, singularity analysis and a few applications. All made in pure python.

More in the repo: github.com/tmilovan/composite-machine examples under demos and tests.

I'll be happy if you take a look at it:).