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* Sage has a rather old version of eclib in it. It should be easy to upgrade the spkg. | * Sage has a rather old version of eclib in it. It should be easy to upgrade the spkg. DONE: http://trac.sagemath.org/sage_trac/ticket/10993 is ready for review -- in fact has just received a positive review! |
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* People: Martin L., Simon K., Flint developers == Linear algebra mod p, for log_2 p = 64 == * People: Martin A., if it is still going to happen |
* People: Martin L., Simon K., Burcin E., Flint developers Updated my (mlee) experimental interface from Flint2 to Singular, to make use of the new polynomial factorization over Z/p. This sped up some of Singular's tests by a factor of 2 (compared to the regular Singular which uses NTL). However there are still some issues related to maybe mpir and/or the lack of a half gcd in Flint2 which need to be investaged. You can have a look at the Singular FLINT interface here: https://github.com/mmklee/Sources/wiki/Singular-With-Flint2. And hopefully this will be extended soon (use FLINT multiplication, division etc. during multivariate polynomial factorization) In the near future it would be great if FLINT supported: * asymptotically fast GCD for Z[x] * build system improvements * version number in header file (to help auto* decide if we have the right version) To replace NTL completely, we need: * factorization over Z[x] * factorization over GF(p^k)[x] * LLL == --(Linear algebra mod p, for log_2 p = 64)-- == * People: Martin A. |
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'''Update (2011-12-20 11:10):''' Okay, project cancelled, none of the tricks I could think of make sense. |
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Gives a ratio of about 4.5. | Gives a ratio of about 4.5. But then, some of it is due to load/store times, so it might still make sense to try. |
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* People: Martin A., Simon K., Johan B. 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. |
* 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 [[http://trac.sagemath.org/sage_trac/ticket/12177|#12177]] |
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* People: mysterious people who added this project, Andy N. | * People: Martin A., Andy N. |
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* People: David L., John C., Jan V., Frithjof, Johan B., Maarten D., Martin R., Simon K., Marco S. | * People: David L., John C., Jan V., Frithjof, Johan B., Maarten D., Martin R., Simon K. |
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* #5048: Johan B. has done this one. * #11601: depends on #5048; needs rebase: DL working on this * #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 |
* [[http://trac.sagemath.org/sage_trac/ticket/5048|#5048]]: Johan B. has done this one. (reviewed positivly) * [[http://trac.sagemath.org/sage_trac/ticket/11601|#11601]]: depends on #5048; now rebased; Johan working on this. Done. (reviewed positivly) * [[http://trac.sagemath.org/sage_trac/ticket/10546|#10546]]: depends on #11601; Jan V to take a look (reviewed positivly) * [[http://trac.sagemath.org/sage_trac/ticket/12043|#12043]]: DL to work on this (needs review) * [[http://trac.sagemath.org/sage_trac/ticket/10658|#10658]]: Martin R and Frithjof will have a look at this (reviewed positivly) * [[http://trac.sagemath.org/sage_trac/ticket/12124|#12124]]: Martin R and Frithjof will have a look at this (reviewed positivly) * Start working towards putting Edixhoven's algorithm into Sage. The meta-ticket for this is [[http://trac.sagemath.org/sage_trac/ticket/12132|#12132]]. * Implement the upper half plane: [[http://trac.sagemath.org/sage_trac/ticket/9439|#9439]] * Add a LLL for matrices over QQ and RR: [[http://trac.sagemath.org/sage_trac/ticket/12051|#12501]]. Andy Novocin proposed some other methods to use LLL to handle Johan's problem. |
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* People: Francis C., Monique v B., Florian B., Sam S., Michiel K, Bogdan B., Colton, Jan, Marco S. | * People: Francis C., Monique v B., Florian B., Sam S., Michiel K, Bogdan B., Colton, Jan, Marco S., Paul Z., Johan B., Daniel B. |
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#4283 |
* [[http://trac.sagemath.org/sage_trac/ticket/4283|#4283]] A Speed-up Patch for NTL's ZZXFactoring.c * [[http://trac.sagemath.org/sage_trac/ticket/12176|#12176]] Compute Minkowski bound for relative number fields (positive review) * [[http://trac.sagemath.org/sage_trac/ticket/11521|#11521]] Memleak with elliptic curves * [[http://trac.sagemath.org/sage_trac/ticket/11838|#11838]] Multivariate factorization over non-prime finite fields hangs (positive review) * [[http://trac.sagemath.org/sage_trac/ticket/11673|#11673]] is_unit not properly implemented for algebraic integers (needs review) * [[http://trac.sagemath.org/sage_trac/ticket/11930|#11930]] Function to check if hyperelliptic curve is singular in the sense of hyperelliptic curves(almost ready for review) * [[http://trac.sagemath.org/sage_trac/ticket/12182|#12182]] Calculate the trace dual of an order in a number field (needs review) * [[http://trac.sagemath.org/sage_trac/ticket/12185|#12185]] Bug in norm for orders of relative number fields (needs review) * [[http://trac.sagemath.org/sage_trac/ticket/12186|#12186]] Faster norm calculations (needs review) * [[http://trac.sagemath.org/sage_trac/ticket/12183|#12183]] Absolute and relative norm functions for number field elements (positive review) * [[http://trac.sagemath.org/sage_trac/ticket/11319|#11319]] Cannot create homomorphism from prime residue field to finite field (positive review) * [[http://trac.sagemath.org/sage_trac/ticket/12191|#12191]] is_squarefree for integer polynomials (needs review) * [[http://trac.sagemath.org/sage_trac/ticket/11417|#11417]] binomial of polynomial is not polynomial (needs review) * [[http://trac.sagemath.org/sage_trac/ticket/12179|#12179]] Binomial of integer (mod n) returns integer (positive review) * [[http://trac.sagemath.org/sage_trac/ticket/12196|#12196]] Improve latex for quadratic fields (positive review) * [[http://trac.sagemath.org/sage_trac/ticket/12210|#12210]] GP(p) constructor should check primality of p only once (needs review) |
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* People: John C., Martin R., Marco S. * Revive work of March Sage Days |
* People: John C., Martin R. * Revive work of March Sage Days: see http://trac.sagemath.org/sage_trac/ticket/11005 |
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* People: Florian B., people from projects 10 and 12, Marco S. * Trac ticket: http://trac.sagemath.org/sage_trac/ticket/6341 |
* People: Florian B., Marco S., Lassina D. * Trac ticket: http://trac.sagemath.org/sage_trac/ticket/6341. |
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* The two above has been put in a patch on #6341. Needs reviewing | |
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As a side effect, implementation of reducing the defining polynomial of hyperelliptic curves [[http://trac.sagemath.org/sage_trac/ticket/12204|#12204]] Need review | |
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== Fix some memory leak that was found using elliptic curves == * People: Simon K., Jean-Pierre F., Paul Z. The solution is to use weak references for caching homsets. Little problem: Up to now, it was possible to have category objects that are no instances of CategoryObject and thus do not support weak references. But people seem to agree that this should be strongly deprecated. '''[[http://trac.sagemath.org/sage_trac/ticket/11521|#11521]] needs review!''' == Implement finite algebras == * People: Johan B., Michiel K. The trac ticket for this is [[http://trac.sagemath.org/sage_trac/ticket/12141|12141]]. == Things related to PARI/GP == * People: Jeroen D. * [[http://trac.sagemath.org/sage_trac/ticket/12203|#12203]]: Implement is_PariGpElement * [[http://trac.sagemath.org/sage_trac/ticket/12158|#12158]]: Segfault in PARI's err_init() during pari_init_opts(): '''positive_review''' * [[http://trac.sagemath.org/sage_trac/ticket/9948|#9948]]: Conversion between p-adics and PARI/GP |
Projects
Please feel free to add more
Contents
-
Projects
- Put flint2 into Sage
- Switch some of the /eclib/mwrank code to use flint2, and upgrade the eclib spkg in Sage
- Help the Singular developers make better use of flint2
- --(Linear algebra mod p, for log_2 p = 64)--
- Linear algebra mod p^n, for log_2 p small-ish
- BKZ 2.0
- Improve polynomial factoring mod p in flint2
- Modular forms code in Sage
- Open MP and FLINT
- Miscellaneous Sage Algebra and Number Theory patches
- Simon and ComputeL GP scripts
- Elliptic curve isogenies
- Mestre's algorithm for constructing hyperelliptic curves from their invariants
- Tate's Algorithm over function fields
- Fix some memory leak that was found using elliptic curves
- Implement finite algebras
- Things related to PARI/GP
Put flint2 into Sage
- People: Bill H., Mike H., Fredrik J., Andy N., Sebastian P.
- Building flint2 in Sage
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)
Update MPFI to 1.5.0 - http://trac.sagemath.org/sage_trac/ticket/12171
Reinstall http://sagemath.org/packages/standard/libfplll-3.0.12.p1.spkg
- Install flint2 spkg (beware, this will break Sage)
- touch SAGE_ROOT/devel/sage/sage/combinat/partitions.*
- 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. DONE: http://trac.sagemath.org/sage_trac/ticket/10993 is ready for review -- in fact has just received a positive review!
Help the Singular developers make better use of flint2
- People: Martin L., Simon K., Burcin E., Flint developers
Updated my (mlee) experimental interface from Flint2 to Singular, to make use of the new polynomial factorization over Z/p. This sped up some of Singular's tests by a factor of 2 (compared to the regular Singular which uses NTL). However there are still some issues related to maybe mpir and/or the lack of a half gcd in Flint2 which need to be investaged.
You can have a look at the Singular FLINT interface here: https://github.com/mmklee/Sources/wiki/Singular-With-Flint2. And hopefully this will be extended soon (use FLINT multiplication, division etc. during multivariate polynomial factorization)
In the near future it would be great if FLINT supported:
- asymptotically fast GCD for Z[x]
- build system improvements
- version number in header file (to help auto* decide if we have the right version)
To replace NTL completely, we need:
- factorization over Z[x]
- factorization over GF(p^k)[x]
- LLL
--(Linear algebra mod p, for log_2 p = 64)--
- People: Martin A.
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.
Update (2011-12-20 11:10): Okay, project cancelled, none of the tricks I could think of 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. But then, some of it is due to load/store times, so it might still make sense to try.
Linear algebra mod p^n, for log_2 p small-ish
- People: Martin A., Simon K., Johan B., Burcin E.
Linear algebra over GF(pk) can be reduced to linear algebra over GF(p) and for GF(2k) 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: Martin A., 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.
- review patches
#5048: Johan B. has done this one. (reviewed positivly)
#11601: depends on #5048; now rebased; Johan working on this. Done. (reviewed positivly)
#10546: depends on #11601; Jan V to take a look (reviewed positivly)
#12043: DL to work on this (needs review)
#10658: Martin R and Frithjof will have a look at this (reviewed positivly)
#12124: Martin R and Frithjof will have a look at this (reviewed positivly)
Start working towards putting Edixhoven's algorithm into Sage. The meta-ticket for this is #12132.
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., Paul Z., Johan B., Daniel B.
- Suggested patch numbers:
#4283 A Speed-up Patch for NTL's ZZXFactoring.c
#12176 Compute Minkowski bound for relative number fields (positive review)
#11521 Memleak with elliptic curves
#11838 Multivariate factorization over non-prime finite fields hangs (positive review)
#11673 is_unit not properly implemented for algebraic integers (needs review)
#11930 Function to check if hyperelliptic curve is singular in the sense of hyperelliptic curves(almost ready for review)
#12182 Calculate the trace dual of an order in a number field (needs review)
#12185 Bug in norm for orders of relative number fields (needs review)
#12186 Faster norm calculations (needs review)
#12183 Absolute and relative norm functions for number field elements (positive review)
#11319 Cannot create homomorphism from prime residue field to finite field (positive review)
#12191 is_squarefree for integer polynomials (needs review)
#11417 binomial of polynomial is not polynomial (needs review)
#12179 Binomial of integer (mod n) returns integer (positive review)
#12196 Improve latex for quadratic fields (positive review)
#12210 GP(p) constructor should check primality of p only once (needs review)
Simon and ComputeL GP scripts
- People: John C., Martin R.
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., Marco S., Lassina D.
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
- The two above has been put in a patch on #6341. Needs reviewing
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)
As a side effect, implementation of reducing the defining polynomial of hyperelliptic curves #12204 Need review
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.
Fix some memory leak that was found using elliptic curves
- People: Simon K., Jean-Pierre F., Paul Z.
The solution is to use weak references for caching homsets. Little problem: Up to now, it was possible to have category objects that are no instances of CategoryObject and thus do not support weak references. But people seem to agree that this should be strongly deprecated. #11521 needs review!
Implement finite algebras
- People: Johan B., Michiel K.
The trac ticket for this is 12141.
Things related to PARI/GP
- People: Jeroen D.
#12203: Implement is_PariGpElement
#12158: Segfault in PARI's err_init() during pari_init_opts(): positive_review
#9948: Conversion between p-adics and PARI/GP