Charles Greathouse on Tue, 26 Jul 2011 10:03:24 +0200

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Re: [sage-devel] Sage & Pari

> We badly need feedback at a higher level, from developpers or would-be
> developpers, regarding the features they think are lacking in Pari, and
> are preventing them from developping in Pari the way they would like to.

I have some thoughts.

1. Let forprime() take large arguments.
2. New types, possibly "special" types as in TODO: t_FACTORED and
maybe t_FILE and t_BITS (bit array -- hard to implement efficiently in
3. New loop forfactored that uses a sieve to factor all the numbers
from a to b.  Equivalent to
 for(k=a,b,n=factor(k); closure(n))
but faster.  (Useful for evaluating number-theoretic functions over
large ranges.)
4. Lambert's W.
5. Ability to read from arbitrary files, as opposed to reading a file
as a GP script
6. Recognizing cyclotomic polynomials and products of same
7. Extension of squarerootint to other roots, including library
versions for ulongs.
8. Let primepi() take large arguments (various algorithms are possible).

I have a working version of #1 which takes two approaches: for wide
intervals it uses a segmented sieve and for narrow intervals it
removes small factors and tests primality (as suggested in TODO).  I'd
be happy to share the code, though perhaps it would be better to take
code from one of the GPL-compatible fast sieves out there.

I also have code for #4, though a better version would increase
precision incrementally, roughly doubling performance.

I'm working on #6 using the Bradford-Davenport algorithm.

Generally, I have 5700 lines of C/PARI code which I'd be happy to
share but I'm not sure how much of it you would find useful.  (Would
anyone want an optimized function for finding terms of Stern's
diatomic series, Jeff Erickson's algorithm for finding maximal
arithmetic progressions, or normally-distributed random numbers?)

Charles Greathouse
Case Western Reserve University