Goal--get the examples from the thesis to work
Pointsearch
- height zero or one, easy, since we just need a point, we can possibly just do this ourselves
- eventually need the whole thing, since points might have larger height
- in the examples they are all height zero or one
ConcisFF(Kevin)
- square roots in residue fields and lifts, also conic solving over QQ (auxiliary,i.e. useful in general)
DescentFF(Kevin and Jen)
- in the process of being decomposed and doctested/tested
- need to find intersections of curves (points) -restrict to hight zero or one?
- find all the singular points? make this case work?
LocSol(Aly)
- needs testing and debugging
Independent(Jen)
- needs is_linear_independent method on elliptic curves (mwrank from number field to function field--ask Cremona?)
- this is dependent on heights
PointSearchFF
- immediate goal is height zero and one cases
QuartMin(Gerriet) (current implementation
- finished but not tested
Other
- Need to put the following functions into ell_function_field:
- * gens()
- * rank()
- * torsion_subgroup() (need Mazur's theorem!!!!)
Typos in Examples
- compile and fix these
- p. 34: (3.15) T+36 should be T+56
- p. 35: should be (d_1, d_2) = ((T+17)(T+25),1) (not (T+17)(T+35))
p. 35: should be (1) (T+17)(T+25)Z12 - Z22 + ...
p. 35: should be (2) (T+17)(T+25)Z12 - (T+17)(T+25)Z32 + ...
Comments:
- p. 34: quadric intersection in (3.16) depends on the labeling of two torsion as in (3.14). See TD_full comment at the top of the code.