When does 1/2=0 ? (python's integer division Vs Sage's exact fractions)

Question

Hi all !

I know that python evaluates 1/2 to zero because it is making an integer division. Well. I was expecting Sage not to do so.

It does more or less ...

------ sagess.py ----------

#! /usr/bin/sage -python
# -*- coding: utf8 -*-

from sage.all import *

def MyFunction(x,y):
    print x/y

MyFunction(1,2)

------ end of sagess.py ----------

When I launche that script from the command line, I got what Python would give :

18:08:03 ~/script >$ ./sagess.py
0

But when I launch it from the sage'terminal it is less clear how it works :

18:16:04 ~/script >$ sage
----------------------------------------------------------------------
| Sage Version 4.5.3, Release Date: 2010-09-04                       |
| Type notebook() for the GUI, and license() for information.        |
----------------------------------------------------------------------
sage: import sagess
0
sage: sagess.MyFunction(1,2)
1/2

At the import, it returns zero, but when I reask the same computation, it gives the correct 1/2

I know that writing float(x)/y "fixes" the problem. But it looks weird and I want to keep exact values.

What do I have to write in my scripts in order to make understand to Sage that I always want 1/2 to be 1/2 ?

Thanks Have a good night ! Laurent

Answer 1

sage: import sagess
0
sage: sagess.MyFunction(1,2)
1/2

The reason for the above behavior is that in the second call, the arguments 1 and 2 are Sage Integers, not Python ints: when run interactively, Sage preparses the input, turning all integers into the type Integer. You could reproduce the effect of your original call of MyFunction(1,2) in sagess.py by this:

sage: sagess.MyFunction(int(1), int(2))

On the other hand, to get 1/2, use Sage integers: rewrite your file as

#! /usr/bin/sage -python
# -*- coding: utf8 -*-

def MyFunction(x,y):
    from sage.rings.all import Integer
    print Integer(x)/Integer(y)

MyFunction(1,2)

This will give the right answer with integer arguments, but it will raise an error if you pass non-integer arguments.

Answer 2

Ok, so the point is that when making an "interactive" import, the imported module is not preparsed ?

def MyFunction(x,y):
    from sage.rings.all import Integer
    print Integer(x)/Integer(y)

I cannot do that in my real live idea. My purpose was to write a function that convert a point (x,y) into polar coordinates (radius,angle) using atan(y/x). (the aim was to show the algorithm to some students)

Instead, you gave me the idea to write this one :

def MyFunction(x,y):
    x=SR(x)
    print x/y

This works fine.

Have a good night Laurent

When does 1/2=0 ? (python's integer division Vs Sage's exact fractions)

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