Re: Mod

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From	Joe Riel <joer@san.rr.com>
Newsgroups	comp.soft-sys.math.maple
Subject	Re: Mod
Date	Tue, 31 May 2011 15:26:33 -0700
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Ilmari Karonen <usenet2@vyznev.invalid> writes:

> On 2011-05-23, Axel Vogt <&noreply@axelvogt.de> wrote:
>> Peter Pein wrote:
>>> 
>>> so "mod" is not the "mod" I know? I would expect for any x < 14 that mod
>>> (x,14)=x and not an error-message. Should my professor for numbertheory
>>> be set on fire?
>>
>> Nice :-) But may be he is faster, if anyone dares to write
>> 1/3 over the integers :-))
>>
>> Maple is more or less clear in its help:
>>
>> "The mod operator evaluates the expression e over the integers
>> modulo m.  It incorporates facilities for doing finite field
>> arithmetic and polynomial and matrix arithmetic over finite
>> fields, including factorization."
>>
>> So 'mod' means to work in the ring Z/7Z, being a field here.
>
> Admittedly, one sometimes _does_ want to work in the ring R/mZ of
> reals modulo m.
>
> Sometimes, one might even find use for the "division" operation in
> R/mZ inherited from R by identifying the equivalence classes of R/mZ
> with their lowest non-negative members, even if said operation does
> not actually always yield a multiplicative inverse in R/mZ.
>
> Perhaps more to the OP's point, sometimes one, while nominally working
> in R, might nonetheless desire an operator which returns the remainder
> of dividing x by y.  Curiously, I couldn't immediately find such a
> function in Maple, although of course it's easy enough to define, e.g.
>
>   fmod := (x,m) -> x - m * floor(x/m);

frem is a builtin that is similar, but minimizes the norm, 
so will return negative values.

-- 
Joe Riel

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Mod "Thomas D. Dean" <tomdean@speakeasy.org> - 2011-05-22 19:10 -0700
  Re: Mod Peter Pein <petsie@dordos.net> - 2011-05-23 07:39 +0200
  Re: Mod Axel Vogt <&noreply@axelvogt.de> - 2011-05-23 08:14 +0200
    Re: Mod "G. A. Edgar" <edgar@math.ohio-state.edu.invalid> - 2011-05-23 06:04 -0600
    Re: Mod Peter Pein <petsie@dordos.net> - 2011-05-23 14:07 +0200
      Re: Mod Axel Vogt <&noreply@axelvogt.de> - 2011-05-23 14:59 +0200
        Re: Mod Ilmari Karonen <usenet2@vyznev.invalid> - 2011-05-28 22:04 +0000
          Re: Mod Joe Riel <joer@san.rr.com> - 2011-05-31 15:26 -0700
      Re: Mod "G. A. Edgar" <edgar@math.ohio-state.edu.invalid> - 2011-05-23 10:08 -0600
  Re: Mod "Nasser M. Abbasi" <nma@12000.org> - 2011-05-23 16:04 -0700

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