On Thursday, April 10, 2014 8:23:06 PM UTC-7, Privasie Invazhian wrote:
>
> 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
>
sage: 5.1 % 10
-4.90000000000000
sage: a=5.1
sage: a.__mod__? #unfortunately, you have to know that "%" eventually
calls "__mod__", but that's just python
Type: method-wrapper
String Form:<method-wrapper '__mod__' of sage.rings.real_mpfr.RealLiteral
object at 0x70986e0>
Definition: a.__mod__(left, right)
Docstring:
Return the value of "left - n*right", rounded according to the
rounding mode of the parent, where "n" is the integer quotient of
"x" divided by "y". The integer "n" is rounded toward the nearest
integer (ties rounded to even).
EXAMPLES:
sage: 10.0 % 2r
0.000000000000000
sage: 20r % .5
0.000000000000000
sage 1.1 % 0.25
0.100000000000000
This is just how "%" is implement in MPFR (the main floating point library
in sage)
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