Re: Mixing variables in Mod expressions

[John Cremona <john.cremona@gmail.com>]

The link does explain the first output in a way that makes sense to
me:   the two moduli are coprime so the common quotient is mod 1 hence
0.

For a beginner, a run-time error might be more informative though,
along the lines of "invalid summands" or "incompatible moduli" -- but
I think that the policy might be to always allow addition between
objects of the same type?

John

On 20 January 2015 at 09:53, Karim Belabas
<Karim.Belabas@math.u-bordeaux.fr> wrote:
> Dear John,
>
> * John Cremona [2015-01-20 10:20]:
>> I am trying to understand the following.  The answer might well be
>> something like "if you try to do something stupid then you must expect
>> a stupid answer"
>>
>> ? Mod(x,x^2-3) + Mod(x,x^2-5)
>> %1 = 0
>
> This is by design. And (IMHO) impossible to fix to get "expected"
> results (e.g. POLMOD variables being treated as "mute" variables).
>
> Does the following FAQ explain the situation in a satisfactory way ?
>
>   http://pari.math.u-bordeaux1.fr/faq.html#modular
>
>> -- but I was pretending to be a student trying to find the polynomial
>> satisfied by sqrt(3)+sqrt(5) and doing what seemed natural.
>
> There are various ways to achieve this:
>
> (10:42) gp > algdep(sqrt(3)+sqrt(5), 4)
> %1 = x^4 - 16*x^2 + 4
>
> (10:43) gp > polcompositum(x^2-3, x^2-5)
> %2 = [x^4 - 16*x^2 + 4]
>
> (10:43) gp > rnfequation(y^2-3, x^2-5)
> %3 = x^4 - 16*x^2 + 4
>
> [ all 3 methods can break in various ways, but they can all be made to
> work (provably) with extra effort ]
>
>> This version works:
>>
>> ? Mod(x,x^2-3) + Mod(y,y^2-5)
>> %2 = Mod(x + Mod(y, y^2 - 5), x^2 - 3)
>> ? a = Mod(x,x^2-3) + Mod(y,y^2-5)
>> %3 = Mod(x + Mod(y, y^2 - 5), x^2 - 3)
>> ? a^2-8
>> %4 = Mod(Mod(2*y, y^2 - 5)*x, x^2 - 3)
>> ? (a^2-8)^2
>> %5 = Mod(Mod(60, y^2 - 5), x^2 - 3)
>> ? (a^2-8)^2-60
>> %6 = 0
>> but that is not the point;  result %1 is surely going to confuse people.
>
> Cheers,
>
>     K.B.
> --
> Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
> Universite de Bordeaux         Fax: (+33) (0)5 40 00 69 50
> 351, cours de la Liberation    http://www.math.u-bordeaux1.fr/~kbelabas/
> F-33405 Talence (France)       http://pari.math.u-bordeaux1.fr/  [PARI/GP]
> `