I have been reading a bit about nonstandard analysis. It seems like a
topic likely to be very useful for automating certain mathematical
constructions in something like maxima. For example, there is a very
nice way to construct the ito integral as a hyperfinite riemann
integral, and there has been a variety of work on things like calculus
of variations or formal constructions of the Feynman path integration
approach to quantum mechanics.
In particular, I think it might be very useful for deriving differential
equations from physical principles if one could express the differential
equation in terms of a hyperfinite difference equation and then tell
maxima to convert the system into a differential equation by taking the
standard part. Furthermore, it might be useful for calculating a greater
variety of limits than what the current code can do, or for doing
asymptotic approximations and soforth.
My question is whether anyone knows of packages for carrying out
nonstandard calculations in maxima?
Thanks,
Dan