Hi Sam.
> I'd like to know what you all consider landmark
> papers/dissertations in computer algebra.
When I was reading on this stuff in the mid-nineties I found these four
writings about polynomials to be fundamental (I guess that Richard Fateman
would be able to tell you whether they were landmark or not):
1. Knuth's "Art of Computer Programming" (the volume on Semi-numerical
Algorithms) is a great starting point for polynomial arithmetic and
factorisation.
2. Moses and Yun "The EZ-GCD Algorithm".
3. Wang "The EEZ-GCD Algorithm"
4. Wang and Trager "New Algorithms for polynomial Squarefree Decomposition
over the Integers"
The following papers were also worthwhile reading:
- Smedley "A New Modular Algorithm for Computation of Algebraic Number
Polynomial GCD's"
- Sasaki and Suzuki "Three New Algorithms for Multivariate Polynomial GCD"
If you can, browse back issues of the "Journal of Symbolic Computation".
I found that Geddes, Czapor and Labahn's "Algorithms for Computer Algebra"
and Davenport, Siret and Tournier's "Computer Algebra Systems and Algorithms
for Algebraic Computation" were very helpful in getting started.
When you understand this stuff, move on to the Risch integration algorithm -
i never made it that far!
Cheers
Mike Thomas.