# Why is sage behaving weird when rounding rational numbers?

I might be doing something stupid, but Sage's int() and round() functions seem to be buggy to me.

I'm trying to use these with rational numbers to round towards zero. I'd expect -7/4 to round to -1 and +7/4 to round to 1. Instead I get different behavior for rationals and their decimal representation:

┌────────────────────────────────────────────────────────────────────┐
│ SageMath Version 7.1, Release Date: 2016-03-20                     │
│ Type "notebook()" for the browser-based notebook interface.        │
│ Type "help()" for help.                                            │
└────────────────────────────────────────────────────────────────────┘
sage: int(-1.75)              # Correctly rounds towards zero
-1
sage: int(-7/4)               # Does not round towards zero
-2
sage: (-7/4).round("toward")  # Does not round towards zero (despite what the documentation claims!)
-2
sage: -7/4 + 0.0              # The numbers are in fact the same!
-1.75


How do I round rational numbers towards zero in Sage?

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1

t=3/2
t.round?

( 2016-05-21 19:02:08 +0200 )edit

Also, you may wish to use ceil or floor for your application.

( 2016-05-21 19:30:21 +0200 )edit

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I just tested int(-7/4) on sagecell.sagemath.org and it returns -1 as expected. This server is now running Sage 7.2, so perhaps there is an issue in 7.1.

The .round() option only applies to half integers, as indicated in the documentation. For example, (-3/2).round("toward") returns -1 while (-3/2).round("away") returns -2.

As suggested by @calc314, here is a function that rounds toward zero:

def f(x):
if x > 0:
return floor(x)
else:
return ceil(x)

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