Diff for "daysff/pms"

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.