Mathematics/computer algebra

So SFTP under Perl requires Net::SSH::Perl, which in turn relies on Math::Pari, which interfaces to PARI [wiki], a computer algebra system that implements a lot of number theory algorithms.  PARI is a library that is normally accessed through GP/PARI, a scripting language specifically written for it.

Here's the thing.  Math::Pari doesn't install on Windows (nothing I tried tonight installed on Windows) and, reading into it, the implementer of Math::Pari seems like a real ... ahem, doesn't seem to play well with others.  Math::Pari will only install if you have built PARI on your own machine; it requires the build directory to build the Perl.  Period.  Unfortunately, it doesn't react at all well to the current version.  Like, "Perl dies" levels of poor reactions.

I'd like to wrap PARI a little better.  Maybe Inline::GP or something, I don't know, but there is most definitely room for improvement.

But that aside, I ran across Sage again.  Sage is essentially an open-source mathematics Swiss Army chainsaw.  What it is, is Mathematica re-implemented on open-source, and it includes PARI, SymPy, and a boatload of other open-source tools of that nature.

There's a whole comparison list here.

There, my friend, is a domain crying out.

Math: sympy

A symbolic manipulation library for Python.

Here's what I want to do:

• Handwriting recognition on a tablet PC to be translated into OpenMath and thence TeX.
• Selection of portions of a large mathematical formula and specification of specific operations to be carried out (e.g. "solve for this" or "call this theta" or what have you, said operations to be discovered by observation of my private theoretical physicist)
• Maintenance of a log of the trajectory through formula space
• n-fold productivity increases for theoretical physicists
• Public perception of my private theoretical physicist as highly productive physics genius
• Live on p.t.p.'s CERN salary while enjoying Geneva

It's freaking brilliant!