Heh, that's got me worried now! I'll be more careful. Is your thesis a 
reference for what is being computed? I suppose I could also read the code.

What I think I'm computing is specialization mod p of modular symbols over 
Zp and mod p specializations of Hecke algebras over Zp, and, by extension, 
specializations of Hida's ordinary p-adic Hecke algebras localized at 
maximal ideals. Does that sound reasonable?

Rob

On Tuesday, July 5, 2016 at 8:34:29 PM UTC-6, William stein wrote:
>
> On Tue, Jul 5, 2016 at 3:25 PM, Rob Harron <[email protected] 
> <javascript:>> wrote: 
> > Kiran, thanks for getting on this so quickly! 
> > 
> > Maarten and Vincent, it would be a shame to not be able to do mod p 
> > computations; they are pretty essential when doing anything p-adic. It 
> is 
> > true that I've found several problems when working mod p, but also with 
> Qp. 
> > Do note that sage only allows base rings that are fields, so that one 
> can't 
> > literally work over ZZ, and also note that magma does allow finite 
> fields, I 
> > wonder if William wrote that part. 
>
> I wrote the code in both Magma and Sage.  It's the same algorithm with 
> the same shortcomings.  There's no difference in what each program 
> allows in this regard, except the bug involving the P1list 
> implementation in this thread. 
>
> You can work with the modulo symbols presentation modulo p, but you 
> had better clearly understand what is really being computed if you 
> want to draw any conclusions from the results you get. 
>
>  -- William 
>
> -- 
> William (http://wstein.org) 
>

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