Introduction, Curve Algorithm

[Brad Klee <bradklee@gmail.com>]

Hi Pari users,

Thank you for making this language publicly available.
It seems we have many fun programming hours ahead.

For starters, I wrote a "Salut au Monde!" program, which
calculates a certified Picard-Fuchs equation for any family
of Hyperelliptic level curves,

C_z ={ (x,y) : z = 2*H(x,y) = y^2 + 2*V(x) } ,
V(x) = c_1*x + c_2*x^2 + ... + c_d*x^d .

The algorithm is easy to analyse, and leads readily to
the genus-degree formula for non-singular curves C_z:

https://github.com/bradklee/Hyperelliptic .

The code is also extremely simple and lightweight.
Perhaps we could consider working this into a future
revision of PARI/GP?

Since this is my first time coding PARI/GP, there may
very well be typos or non-optimal statements. Any
suggestions, stylistic or otherwise, are welcome.

One more issue, ATTN. JOHN CREMONA:

A few elliptic / hypergeometric examples are given
to reiterate my earlier point about 500K+ periods
in the LMFDB (Cf. https://oeis.org/A113424 ).

Cheers,

Brad