WIP: Elliptic curve

[shikil]

• Add docstring
• Add test case
• Calculate torsion points

[asmeurer]

Doesn't characteristic 2 have to be treated separately?

[shikil]

I am studying, the book does not specifically mention characteristic 2 yet, if you have paper/code regarding this, please post here.

[shikil]

@asmeurer, I guess that you mean this

http://www.certicom.com/index.php/40-elliptic-curve-groups-over-f2m

This kind of prime power field, Galois field, may be implemented in other pull request.

[asmeurer]

Even over the two element field it is different. If I remember correctly, the nonsingular condition changes in that case.

[shikil]

EC y^2 = x^3 + ax +b must be singular in char 2 or 3. So the curve need to be y^2 + a1y + a3xy = x^3 + a2x^2 + a4x + a6 in this form.

[jrioux]

SymPy Bot Summary: 🔴 Failed after merging shikil/ec (6ae5c68) into master (dad12ba).
@shikil: Please fix the test failures.
🔴 PyPy 2.0.0-beta-1; 2.7.3-final-42: fail
🔴 Python 2.7.2-final-0: fail
🔴 Python 3.2.1-final-0: fail
✅ Sphinx 1.1.3: pass
Doc Coverage: decreased
36.711% of functions have doctests (compared to 36.678% in master)
41.853% of functions are imported into Sphinx (compared to 41.930% in master)

[hargup]

@shikil any news?

[shikil]

Sorry, I am busy and cannot continue work on this.

[jksuom]

This is almost complete. It should probably be placed in polys/agca instead of ntheory.

[abh2k]

I am taking this over.