Modular Abelian Varieties
Todo on March 16
- (william) Move functions out of abvar_modsym_factor into abvar and delete that file.
- (william) Torsion subgroups:
- Refactor base class
- Get implementation to work with defining data being (lattice, abvar); compute generators.
- Quotients by finite subgroup
- (william) Decomposition:
- three types:
- ungrouped as simple abvars (default)
- groups abvars
- over End(A)
- label function
- create from label
- three types:
(craig) Compute the Hecke algebra image in End(A) and find a good clean way to represent for Hecke stable. New object that is a subring of End(A). Have methods like R.index_in(S).
- (craig) Compute End(A):
for simple
Af - in general.
- (craig) Degeneracy maps
- (william/craig) Morphisms:
- Kernels
- Cokernels
- (william/craig) Isogenies:
- Complementary -- invert matrix, clear denom.
- Dual
- (william) Intersection pairing
- (?) Poincare Reducibility:
- projection
- quotients by abelian subvariety
- (craig/william) Minimal isogeny degree for A, B simple.
- (craig/william) Create a small mock database
Todo on Monday, March 17
- Write doctests, etc., for everything above.
- Optimize everything
Todo on Tuesday, March 18
- Write paper
Todo on Wednesday, March 19
- Write paper