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Message from discussion Combining finite/rational fields
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Dima Pasechnik  
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 More options Nov 18 2012, 12:22 pm
From: Dima Pasechnik <dimp...@gmail.com>
Date: Sun, 18 Nov 2012 17:22:43 +0000 (UTC)
Local: Sun, Nov 18 2012 12:22 pm
Subject: Re: Combining finite/rational fields
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On 2012-11-18, Nils Bruin <nbr...@sfu.ca> wrote:

> On Nov 17, 9:28 pm, Robert Bradshaw <rober...@math.washington.edu>
> wrote:
>> How about doing

>> sage: f = legendre_P(3, GF(11)['x'].gen()); f
>>  8*x^3 + 4*x
>> sage: parent(f)
>>  Univariate Polynomial Ring in x over Finite Field of size 11
>> sage: f(5)
>>  8

>> However, the implementation (manipulating strings) is pretty horrid.

> That can be cleaned up quite a bit if this were rewritten to use
> maxima_lib. In that case the multiplications would probably be actual
> sage multiplications too, so would likely lead to the same errors as
> in Sage, though.

> The issue really is whether "rational number"*"finite field element"
> should be supported. The problem is of course that there is no common
> parent for *all* possible element pairs, so the coercion framework
> rightfully refuses. It would be awfully convenient if it were allowed
> when it makes sense (and just throw a ZeroDivision otherwise).

How different is "rational number"*"finite field element"
from division, which is also a partial operation?
(Well, I admit I don't know Sage's coersion model at all...)

Dima


 
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