Differences between revisions 8 and 13 (spanning 5 versions)

Sage Days 24 Coding Sprint Projects

This is a list of projects suitable for Sage Days 24. Feel free to add your favourite ideas/wishes, and to put your name down for something you're interested in (you'll need to get an account on the wiki to do this).

Contents

Sage Days 24 Coding Sprint Projects

GIAC Factoring

People: Thomas, Burcin, Richard, William Stein (total anarchy, no leader!)

Kovacic's Algorithm

People: Burcin, Erocal, Felix

Implement Kovacic's algorithm in Sage.

Hypergeometric Functions

People: Flavia Stan, Karen Kohl, Fredrik Johansson, Zaf

Add a hypergeometric function class + simplifications

Plural support

$/!\$ Edit conflict - other version:

People: Burcin Erocal, Simon King, Oleksandr, Alex D., Burkhard

$/!\$ Edit conflict - your version:

People: Burcin Erocal, Simon King, Alex, Alex D., Burkhard (total anarchy!)

$/!\$ End of edit conflict

Add support for Singular's noncommutative component Plural, finish #4539.

Parallel Integration

People: Stefan Boethner, Ralf, Burkhard, Burcin Erocal

Integrate Stefan Boettner's parallel integration code in Sage. There are several prerequisites for this, such as

algebraic function fields (transcendence degree > 1)
differential rings/fields
proper to_polynomial(), to_rational() functions for symbolic expressions

Function Fields

The goal of this project is to get the basic infrastructure for function fields into Sage. See Hess's papers and talks.

People: William Stein, Sebastian P.

Trac 9054: Create a class for basic function_field arithmetic for Sage
Trac 9069: Weak Popov Form (reduction algorithm)
Trac 9094: is_square and sqrt for polynomials and fraction fields
Trac 9095: Heights of points on elliptic curves over function fields

Make sure to see this page for more links.

Fast linear algebra over small extensions of GF(2)

People: Martin Albrecht, Ciaran Mullan, Robert Miller, Sebastian P., Thomas

Here is how long Sage currently takes to compute the reduced row echelon form over GF(2^4) on a Macbook Pro (2nd generation):

n	Sage	NTL *2	Magma	M4RIE
1000	49.49	18.84	0.090	0.097
2000	429.05	149.11	0.510	0.529
3000	1494.33	526.57	1.640	2.315

Note that over GF(2^8) this code is already faster than Magma

> K<a> := GF(2^8);
> for i := 1000 to 10001 by 1000 do
for> A:=RandomMatrix(K,i,i);
for> t:=Cputime();
for> E:=EchelonForm(A);
for> print i, Cputime(t);
for> end for;
1000 1.290
2000 9.870
3000 33.560

gf(2^8), 1000 x 1000: wall time: 0.865
gf(2^8), 2000 x 2000: wall time: 4.306
gf(2^8), 3000 x 3000: wall time: 14.029

Generating Stuff

People: Robert Miller (self-determination!)

Fix sage.functions

People: Frederik, William Stein, Harald

Easy ripping apart of symbolic expression trees

People: Burcin, Thomas, Stefan, Frederik

-  ⇤ ← Revision 8 as of 2010-07-17 15:54:42 → 
  Size: 4907
  Editor: MartinAlbrecht
  Comment:
+   ← Revision 13 as of 2010-07-17 16:06:30 → ⇥
  Size: 3463
  Editor: MartinAlbrecht
  Comment:
-Deletions are marked like this.
+Additions are marked like this.
 Line 7:
+== GIAC Factoring ==

'''People:''' Thomas, Burcin, Richard, William Stein (total anarchy, no leader!)
-Line 9:
+Line 13:
-'''People:''' Burcin Erocal, Felix
+'''People:''' '''Burcin''', Erocal, Felix
-Line 15:
+Line 19:
-'''People:''' Flavia Stan, Karen Kohl, Fredrik Johansson, Zaf
+'''People:''' Flavia Stan, Karen Kohl, '''Fredrik Johansson''', Zaf

Add a hypergeometric function class + simplifications
-Line 19:
+Line 25:
-'''People:''' Burcin Erocal, Simon King, Alex, Alex D., Burkhard
+---- /!\ '''Edit conflict - other version:''' ----
'''People:''' Burcin Erocal, Simon King, Oleksandr, Alex D., Burkhard

---- /!\ '''Edit conflict - your version:''' ----
'''People:''' Burcin Erocal, Simon King, Alex, Alex D., Burkhard (total anarchy!)

---- /!\ '''End of edit conflict''' ----
-Line 23:
+Line 36:
-== Locapal support ==

'''People:''' Burcin Erocal

There is experimental support for computing Groebner bases over certain localizations of operator algebras in Singular. See [[http://www.math.rwth-aachen.de/~Viktor.Levandovskyy/filez/singular/levandovskyy_kl.pdf|this presentation]] for more details. Support for arithmetic needs to be provided in Sage.
-Line 31:
+Line 38:
-'''People:''' Stefan Boethner, Ralf, Burkhard, Burcin Erocal
+'''People:''' '''Stefan Boethner''', Ralf, Burkhard, Burcin Erocal
-Line 38:
+Line 45:
-== Algorithmic/Automatic Differentiation ==

'''People:''' William Stein

I never thought much of this topic, but there is [[http://www.euroscipy.org/talk/2045|a talk at Euroscipy]] suggesting it could be useful.    [[/ad|More details here.]]

== Upgrade Pari to version 2.4.3 ==

'''People:''' William Stein

See [[http://trac.sagemath.org/sage_trac/ticket/9343|trac 9343]].  This has little to do with symbolic computation though...
-Line 54:
+Line 49:
-People: William Stein, Sebastian P.
+People: '''William Stein''', Sebastian P.
-Line 65:
+Line 60:
-People: Martin Albrecht, Ciaran Mullan, Robert Miller, Sebastian P., Thomas
+'''People''': '''Martin Albrecht''', Ciaran Mullan, Robert Miller, Sebastian P., Thomas
-Line 69:
+Line 64:
-{{{
----------------------------------------------------------------------
| Sage Version 4.4.3, Release Date: 2010-06-04                       |
| Type notebook() for the GUI, and license() for information.        |
----------------------------------------------------------------------
sage: for i in range(1000,3001,1000):
    A = random_matrix(GF(2^4,'a'),i,i)
    t = cputime()
    E = A.echelon_form()
    print i, cputime(t)
....:
1000 49.49
2000 429.05
3000 1494.33
}}}

Here's how much NTL could improve things (only upper triangular not RREF):

{{{
sage: K.<a> = GF(2^4)
sage: for i in (1000,2000,3000):
    A = ntl.mat_GF2E(K,i,i)
    A.randomize()
    t = cputime()
    _ = A.gauss()
    print "%5d, %7.2f"%(i,cputime(t))
....:     
 1000,   18.84
 2000,  149.11
 3000,  526.57
}}}

Here is how long Magma takes for the same task on a Xeon:

{{{
Magma V2.16-11    Sat Jul 17 2010 05:06:30 on eno      [Seed = 1246196891]
Type ? for help.  Type <Ctrl>-D to quit.
> K<a> := GF(2^4);
> for i := 1000 to 10001 by 1000 do
for> A:=RandomMatrix(K,i,i);
for> t:=Cputime();
for> E:=EchelonForm(A);
for> print i, Cputime(t);
for>
for> end for;
1000 0.090
2000 0.510
3000 1.640
}}}

Finally, here is how long some proof of concept code (written on the train ride to Linz) takes (cf. http://bitbucket.org/malb/m4rie ):

{{{
gf(2^4), 1000 x 1000: wall time: 0.097
gf(2^4), 2000 x 2000: wall time: 0.529
gf(2^4), 3000 x 3000: wall time: 2.315
}}}
+|| n    || Sage    || NTL *2  || Magma || M4RIE ||
|| 1000 ||   49.49 ||   18.84 || 0.090 || 0.097 ||
|| 2000 ||  429.05 ||  149.11 || 0.510 || 0.529 ||
|| 3000 || 1494.33 ||  526.57 || 1.640 || 2.315 ||
-Line 150:
+Line 92:
-'''People:''' Robert Miller
+'''People:''' Robert Miller (self-determination!)

=== Fix sage.functions ===

'''People:''' '''Frederik''', William Stein, Harald

== Easy ripping apart of symbolic expression trees ==

'''People:''' '''Burcin''', Thomas, Stefan, Frederik

Diff for "days24/projects"