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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

Dynamic attributes for classes derived from Function

People: Simon, Burcin

Let f be an instance of a subclass of BuiltinFunction, and let t be obtained by calling f(a,b,c). According to Burcin, for implementing hypergeometric functions it would be useful to be able to access the methods (say, 'foo') of f that are not methods of BuiltinFunction, so that calling t.foo() is the same as f.foo(a,b,c).

Of course, it would be nice to have 'foo' show up in tab completion and in dir(t). The code we wrote seems to solve it, and should be posted to trac after adding some doctests. Here is an example. Let ExampleBuiltin(BuiltinFunction) be a class that defines a method

    def some_function_name(self, *args):
        print self
        print args
        return len(args)

Then, one can do

sage: ex_func = ExampleBuiltin()
sage: t = ex_func(x,x+1, x+2)
# introspection:
sage: 'some_function_name' in dir(t)
True
# tab completion
sage: import sagenb.misc.support as s
sage: s.completions('t.some', globals(), system='python')
['t.some_function_name']
# intended usage
sage: t.some_function_name()
ex_func
(x, x + 1, x + 2)
3

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

Implement fast-ish linear algebra over GF(2^n) for n small. Here are some preliminary benchmarks.

project page

Generating Stuff

People: Robert Miller (self-determination!)

For a somewhat recent snapshot of what I'm doing (as recent as the last time I updated it...), look:

PATCH

Fix sage.functions

People: Frederik, William Stein, Harald

Easy ripping apart of symbolic expression trees

People: Burcin, Thomas, Stefan, Frederik

(done) 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