The book by von zur Gathen et al "Modern Computer Algebra" has
a great deal of material, with bibliographic references to a lot
more. On the down side, they fall into almost all the traps
of theorists writing about algorithms and software. Like believing
asymptotic complexity theory when inputs could not possibly be
"asymptotically" large. They also dispense with much of what
I consider interesting by not getting beyond polynomials in 1 variable
for hundred of pages. (and hardly mentioning Risch.)
There are books by Chee Yap and by Richard Zippel that are worth
looking at, too. I suspect that the individual papers listed below
have been superceded by material Zippel's book, which also talks
about sparse algorithms.
Davenport's book is out of print and has a number of mistakes, especially
when discussing macsyma!
Knuth's vol 2 is still good, but doing big-number arithmetic by FFT,
regardless of how neat it is, doesn't make for holiday reading.
RJF
Mike Thomas wrote:
> 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.
>
>
>
> _______________________________________________
> Maxima mailing list
> Maxima@www.math.utexas.edu
> http://www.math.utexas.edu/mailman/listinfo/maxima