I'm running Sage 5.3 on a MacBook Pro with OS X version 10.7.5, and I don't 
understand why the modulo operator % works so differently on reals and on 
integers or how I can work around it.

For instance,   4 % 10 = 4  and 6 % 10 = 10, just as I would expect.

But while 4.9 % 10 = 4.9 as expected, 5.1 % 10 = -4.9 instead of 5.1.  

And as far as I can tell, for any positive integer or real modulus n and 
any positive integer m and positive noninteger x < n, 

(mn + x) % n = x  if x < n/2,

but 

(mn + x) % n = x-n if x > n/2.

I don't understand this AT ALL.

(Apologies if it's a simple question that I'm failing to understand because 
I'm a relative novice: I would go to the ask-sage-math forum as recommended 
but the posting feature there seems to be currently disabled for low-karma 
posters.)

Thanks for any enlightenment,
Kim

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