1 | initial version |
You can see how division polynomial is implemented using E.division_polynomial??. With just one ? you can see its parameters. The second optional paramater defaults to a variable x. The documentation (which I wrote, I think) says
"x" - optional ring element to use as the "x" variable. If x is
None, then a new polynomial ring will be constructed over the
base ring of the elliptic curve, and its generator will be used
as x. Note that x does not need to be a generator of a polynomial
ring; any ring element is ok. This permits fast calculation of
the torsion polynomial *evaluated* on any element of a ring.
i.e. in your code you could compute E.division_polynomial(N,z) for each z.