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Rounding problems in sagetex. Sometimes

asked 2012-06-24 16:24:50 -0500

dazedANDconfused gravatar image

I was getting wrong answers with Sage. It came down to this:

\documentclass[12pt]{article}%
\usepackage{sagetex}
\begin{document}
\begin{sagesilent}
c = randint(14,20)
d = randint(5,10)
\end{sagesilent}
$\frac{\sage{c}}{\sage{d}}-\frac{\sage{c-3}}{\sage{d+1}}=$ \\
%$\sage{c/d-((c-3)/(d+1))}$\\
$\sage{c/d}$\\
$\sage{((c-3)/(d+1))}$\\
$\sage{c/d-((c-3)/(d+1))}$
\end{document}

When I compiled with the commented out line I got the wrong answer, so I commented it out and broke it down into the 3 calculations below it. Output is below: for 20/7 - 17/8, Sage calculates 20/7 as 2 (rounding down) but 17/8 as 17/8 (not rounding down) to get a final answer of 2-17/8=-1/8. Image of output below. Why does it round (down) in one case and not in the others? What is the proper way to get the correct fractional answer?

image description

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answered 2012-06-24 17:35:38 -0500

DSM gravatar image

updated 2012-06-24 17:36:11 -0500

This isn't a sagetex-related issue: it's because randint returns a Python int:

sage: c = randint(14, 20)
sage: d = randint(5, 10)
sage: c
17
sage: d
7
sage: type(c), type(d)
(<type 'int'>, <type 'int'>)

and division of Python ints is truncating:

sage: c / d
2

The reason that the second one behaves is because the 3 and 1 in c-3 and d+1 are Sage Integers, and operations involving them and Python ints produce Sage objects (Integers, Rationals, etc), so things work the way they should:

sage: (c-3)/(d+1)
7/4
sage: type(_)
<type 'sage.rings.rational.Rational'>

If you wrap the randint call in Integer, it should behave, although I can't do a sagetex test at the moment:

sage: c = Integer(randint(14, 20))
sage: c
15
sage: type(c), parent(c)
(<type 'sage.rings.integer.Integer'>, Integer Ring)
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I tested it in sagetex and it works, Thanks! +1.

dazedANDconfused gravatar imagedazedANDconfused ( 2012-06-24 17:52:34 -0500 )edit

Hmm. At first I thought this should be fixed. But now I'm not so sure, since it calls the Python random stuff more or less directly. Worth raising on sage-devel?

kcrisman gravatar imagekcrisman ( 2012-06-25 05:44:47 -0500 )edit

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Asked: 2012-06-24 16:24:50 -0500

Seen: 109 times

Last updated: Jun 24 '12