Projects

Please feel free to add more

Put flint2 into Sage

• People: Bill H., Mike H., Fredrik J., Andy N., Sebastian P.
• Building flint2 in Sage

  1. Update MPFR to 3.1.0 - http://trac.sagemath.org/sage_trac/ticket/11666

     • http://sage.math.washington.edu/mpfr-3.1.0.spkg (Mike Hansen)

  2. Update MPFI to 1.5.0 - http://trac.sagemath.org/sage_trac/ticket/12171

     • http://sage.math.washington.edu/home/mhansen/mpfi-1.5.0.spkg (Mike Hansen)

  3. Reinstall http://sagemath.org/packages/standard/libfplll-3.0.12.p1.spkg

  4. Install flint2 spkg (beware, this will break Sage)

     • http://sage.math.washington.edu/flint-2.3.spkg

  5. touch SAGE_ROOT/devel/sage/sage/combinat/partitions.*
  6. Run "sage -b"

Switch some of the /eclib/mwrank code to use flint2, and upgrade the eclib spkg in Sage

• People: John C., David H., Martin R., Maarten D., Flint developers
• Sage has a rather old version of eclib in it. It should be easy to upgrade the spkg.

Help the Singular developers make better use of flint2

• People: Martin L., Simon K., Burcin E., Flint developers

Linear algebra mod p, for log_2 p = 64

• People: Martin A., if it is still going to happen

Flint2 has an implementation for asymptotically fast linear algebra mod p for p up to 2^64. I (malb) am curious whether it can be improved using ideas inspired by M4RIE, i.e., replace multiplications by additions using pre-computation tables. Whether this is beneficial will depend on how much slower multiplication is than additions.

Update (2011-12-15 10:57): It seems the difference between scalar multiplication and addition is too small for these tricks to make sense.

#include <flint.h>
#include <nmod_mat.h>
#include <profiler.h>
#include <stdio.h>

#include "cpucycles-20060326/cpucycles.h"

int main(int argc, char *argv[]) {
  nmod_mat_t A,B,C;
  flint_rand_t state;
  unsigned long long cc0 = 0, cc1 = 0;
  unsigned long i,j;

  unsigned long long p = 4294967311ULL;

  flint_randinit(state);

  nmod_mat_init(A, 2000, 2000, p);
  nmod_mat_init(C, 2000, 2000, p);
  nmod_mat_randfull(A, state);

  cc0 = cpucycles();
  nmod_mat_scalar_mul(C, A, 14234);
  cc0 = cpucycles() - cc0;
  printf("scalar multiplication: %llu\n",cc0);

  cc1 = cpucycles();
  for (i = 0; i < A->r; i++) {
    for (j = 0; j < A->c; j++) {
      C->rows[i][j] =  A->rows[i][j] + A->rows[i][j];
    }
  }
  cc1 = cpucycles() - cc1;
  printf("addition: %llu\n",cc1);

  printf("ratio: %lf\n",((double)cc0)/(double)cc1);

  nmod_mat_clear(A);
  nmod_mat_clear(C);
  flint_randclear(state);
  return 0;
}

Gives a ratio of about 4.5.

Linear algebra mod p^n, for log_2 p small-ish

• People: Martin A., Simon K., Johan B., Burcin E.

Linear algebra over GF(p^k) can be reduced to linear algebra over GF(p) and for GF(2^k) the performance is very nice. Hence, it would be a good project to develop some somewhat generic infrastructure for dense matrices over GF(p^k), or even *any* extension field? The natural place to put this would be LinBox but perhaps we can start stand-alone and then integrate it with LinBox if LinBox is too scary to start with. Some references (concerning prime slicing) are given at trac ticket #12177

BKZ 2.0

• People: mysterious people who added this project, Andy N.

At AsiaCrypt 2011 Chen and Nguyen presented their new BKZ implementation which is much much more efficient than that in NTL. As far as I understand, the main improvements are due to "extreme pruning" as presented in a paper at EuroCrypt 2010 and perhaps careful parameter choice. As far as I understand, they do not plan to make their code available. I don't know how much work it would be, but perhaps it would be a nice idea to patch NTL's BKZ to include extreme pruning and/or to port it to Flint2?

Improve polynomial factoring mod p in flint2

• People: Fredrik J., Andy N., David H.

The Cantor-Zassenhaus implementation in the flint2 nmod_poly module could be optimized:

• Make exponentiation faster by precomputing a Newton inverse of the modulus
• Use sliding window exponentiation
• Use the von zur Gathen / Shoup algorithm (adapt the fast power series composition code for modular composition)

Modular forms code in Sage

• People: David L., John C., Jan V., Frithjof, Johan B., Maarten D., Martin R., Simon K., Marco S.
• review patches
  • (#5048: Johan B. has done this one.)
  • (#11601: depends on #5048; now rebased; Johan working on this. Done.)
  • #10546: depends on #11601; Jan V to take a look
  • #12043: DL to work on this
  • #10658: Martin R and Frithjof will have a look at this
  • #12124: Martin R and Frithjof will have a look at this

Open MP and FLINT

• People: David H., Fredrik J., Bogdan B., Julian R.,

Miscellaneous Sage Algebra and Number Theory patches

• People: Francis C., Monique v B., Florian B., Sam S., Michiel K, Bogdan B., Colton, Jan, Marco S.
• Suggested patch numbers:
  • #4283
  • #12176

Simon and ComputeL GP scripts

• People: John C., Martin R., Marco S.

• Revive work of March Sage Days: see http://trac.sagemath.org/sage_trac/ticket/11005

Elliptic curve isogenies

• People: Kimi T., John C., François Morain., Monique v B., Özge Ç., Marco S.

• Sage has a fast implementation of l-isogenies for l=2,3,5,7,13 (for which X_0(l) has genus zero). Kimi has a similarly fast algorithm for those l for which X_0(l) is hyperelliptic (l up to 71), implemented in Sage, which need to be made into a patch for Sage.

Mestre's algorithm for constructing hyperelliptic curves from their invariants

• People: Florian B., people from projects 10 and 12, Marco S.

• Trac ticket: http://trac.sagemath.org/sage_trac/ticket/6341

• Florian has code for Mestre's algorithm, make this into a patch
• Florian has code for the covariant z_0, put that in the same patch

• Code for covariant z is not written, write that (optional), reference for the invariant: http://www.warwick.ac.uk/~masgaj/papers/redp1.pdf

• Reduction of points for SL_2 is also needed. It is
  • easy for QQ, put that in the patch as well
  • very interesting for number fields: Hilbert fundamental domain, bad code that works surprisingly well (Marco), improve that (optional)

Tate's Algorithm over function fields

• People: Frithjof S, John C., Marco S., Julian R.

There is a Magma implementation based on John's number field implementation here.