Michael Monagan,
Center for Experimental and Computational Mathematics,
Simon Fraser University.

Some problems in general purpose computer algebra systems design.

In this talk I will present three probems of interest to the computer algebra community. The first is the problem of implementing modular algorithms efficiently. Application of the Chinese remainder theorem to solve the GCD and Grobner bases problems leads to a big loss of efficiency because the data structure overhead overwhelm's the cost of the modular arithmetic. The second problem is how to build a system so that all the components interact well. I will take as an example a problem of automatic differentation from astrophysics where the function to be differentiated involves the solution of a non-linear equation. Can the CAS differentiate commands like fsolve(f=0,x=a); in a program? The third problem is a problem of trying to implement generic algorithms, efficiently. I will take as an example a linear p-adic Newton iteration. A generic version of this algorithm would work over Z mod p^k and over F[x] mod x^k for example.