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).

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

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

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):

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

Matrix group actions on polynomials

People: Simon

(review needed for 4513) So far, a matrix group could act on, e.g., vectors. If it tried to act on something else, it always tried to do a matrix multiplication - which is not what we want for an action on polynomials! The patch in trac allows to do:

sage: M = Matrix(GF(3),[[1,2],[1,1]])
sage: N = Matrix(GF(3),[[2,2],[2,1]])
sage: G = MatrixGroup([M,N])
sage: m = G.0
sage: n = G.1
sage: R.<x,y> = GF(3)[]
# left action on polynomial
sage: m*x
x + y
# right action on polynomial
sage: x*m
x - y
# it really is left/right action!
sage: (n*m)*x == n*(m*x)
True
sage: x*(n*m) == (x*n)*m
True

# Action on vectors and matrices still works as it used to do
sage: x = vector([1,1])
sage: x*m
(2, 0)
sage: m*x
(0, 2)
# again, verify left/right action
sage: (n*m)*x == n*(m*x)
True
sage: x*(n*m) == (x*n)*m
True
sage: x = matrix([[1,2],[1,1]])
sage: x*m
[0 1]
[2 0]
sage: m*x
[0 1]
[2 0]
sage: (n*m)*x == n*(m*x)
True
sage: x*(n*m) == (x*n)*m
True