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MathGroup Archive 2004

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Re: When/why is Denominator[p/q] != q?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg46037] Re: When/why is Denominator[p/q] != q?
  • From: Bill Rowe <readnewsciv at earthlink.net>
  • Date: Tue, 3 Feb 2004 03:21:19 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

On 2/2/04 at 5:21 AM, relishguy at pluggedin.org (Relishguy) wrote:

>I ran this code (from the "Tour of Mathematica" in the Book ):

> g6 = Flatten[Table[Point[{p/ q, Denominator[p/q]}], {q, 100}, {p, q - 1}]]; 

> (* same code with q instead of Denominator[p/q] *)
> g5 = Flatten[Table[Point[{p / q, q}], {q, 100}, {p, q - 1}]];

>Show[Graphics[g5, Frame -> True]]

>Show[Graphics[g6, Frame -> True]] (*

>For some reason the graphs are not identical. Can anyone point me
>to the reason for this?

Consider the case where p = 5 and q = 10. Then doing Denominator[p/q] results in an output of 2. That is Denominator first factors out all common factors of p and q then outputs the denominator of the result.
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