Andreas Enge on Fri, 28 Nov 2014 15:09:22 +0100

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Re: New GP functions for modular polynomials

On Mon, Nov 17, 2014 at 05:24:03PM +0100, Bill Allombert wrote:
> We have recently added three new GP functions in PARI GIT 2.8, implemented
> by Hamish Ivey-Law, using Sutherland algorithm:

These are very good news indeed!

> polmodular(l): return the canonical modular polynomial of level l prime.
> (unfortunately limited to l<=31 in 32bit)

Actually, in Magma terms, these are the "classical" ones, the canonical
ones are for the simple eta quotients (I also mix them up all the time...).

Following Karim's latest git commit, I noticed that the library function
is called polmodular, with additional specially typed functions
modpoly_ZXX etc.; should these not also be renamed polmodular_ZXX etc.?

> polclass(D): return the Hilbert class polynomial for the imaginary order.

How about allowing here as an optional parameter a prime p modulo which
the polynomial is reduced? Then internally a special kind of CRT could be

The same could be useful for modular polynomials (without evaluating in
a j-invariant), but I fear we are running out of optional parameters there.