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From: Axel Vogt <&noreply@axelvogt.de>
Newsgroups: comp.soft-sys.math.maple
Subject: Re: Mod
Date: Mon, 23 May 2011 14:59:24 +0200
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Xref: x330-a1.tempe.blueboxinc.net comp.soft-sys.math.maple:162

Peter Pein wrote:
> Am 23.05.2011 08:14, schrieb Axel Vogt:
>> Thomas D. Dean wrote:
>>> Maple 11
>>>
>>> 1/3 mod 7
>>>   5
>>> (1/3) mod 7
>>>   5
>>> -2 mod 7
>>>   5
>>>
>>> How do I explain 1/3 mod 7 in terms of the definition?
>>>
>>> r = a mod n
>>>
>>> a = n*q + r
>>>
>>>
>>> tomdean
>> Your input 1/3 is interpreted as "multiplicative inverse
>> of 3" and Maple answers that: 3*5 = 15 = 2*7 + 1 = 1 (7).
>>
>> Try to enter 1/2 mod 14. You will get "Error, the modular
>> inverse does not exist"
> 
> 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.

Or view at it as G A Edgar said it.