[Axiom-math] partialFraction behavior in Axiom

[Tim Daly]

Yes, 

aa:UP(x,FRAC INT):=2*x^3
partialFraction(aa,1-x^2)

also fails in the NAG version. I'm almost certain it is an issue of 
the interpreter walking itself into some corner of the type system
and failing to find a good resolution. The usual answer is to give
it more information as you did by declaring the types. I'll have to
contemplate the "painful" output and see where it goes astray.

However, this is related to the general issue of automatic coercions,
types, and simplifications. Somebody needs to write a complete type
graph independent of systems like Axiom (which would be a PhD thesis
or two). Then we could code it up in a less adhoc form. We could
answer questions like "under what conditions can you coerce from a 
fraction of polynomials over integers to polynomials over fractions
of integers?" for knarly things like multivariate polynomials. What
is not apparent on the surface is that some of these coercions go thru
intermediate types before reaching the final output (basically a walk
of the type lattice). The problem is very hard.

Tim