Bill Allombert on Thu, 24 Nov 2005 09:59:02 +0100

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Re: priority

On Wed, Nov 23, 2005 at 11:43:23PM +0100, Robert Gerbicz wrote:
> Hi!
> Is -5%3=1 correct? In all languages ( c++, basic... ) -5%3 is the
> additive inverse of 5%3 so this is -2

This is correct, PARI return the Euclidean remainder which is always

C/C++ follows the FORTRAN convention whereas the sign of x%n
is the product of the sign x and n.  This is mathematically a very
strange convention, because this make the following implication false:
(x-y)%n==0 => x%n==y%n

(for example x=-5, y=1, n=3)

You call look up he documentation for % using ??%
? ??%

   The  expression  x % y evaluates to the modular Euclidean remainder of x and
y, which we now define.   If y is an integer, this is the smallest non-negative
integer congruent to x modulo y.