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MathGroup Archive 2007

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Re: Re: rationalize numerator of quotient

  • To: mathgroup at smc.vnet.net
  • Subject: [mg81227] Re: [mg81208] Re: rationalize numerator of quotient
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Sun, 16 Sep 2007 04:09:02 -0400 (EDT)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <29319569.1189724898261.JavaMail.root@eastrmwml14.mgt.cox.net> <fcdf9p$plc$1@smc.vnet.net> <200709150818.EAA28315@smc.vnet.net> <7EB64796-3E91-4153-8BFB-6717780343BE@mimuw.edu.pl>
  • Reply-to: murray at math.umass.edu

There appears to be a little syntax error in RationalizeDenominator as 
defined in the quoted message below.  Namely, there a missing third 
argument to PolynomialExtendedGCD, which should be t here.


Andrzej Kozlowski wrote:


> ... The factthat a fraction like:
> 
> (2 + Sqrt[2])/(3 - 5*Sqrt[2])
> 
> 
> can be uniquely expressed in the form
> 
> RationalizeDenominator[(2 + Sqrt[2])/(3 - 5*Sqrt[2]), Sqrt[2]]
> 
> -(16/41) - (13*Sqrt[2])/41
> 
> (where the function RationalizeDenominator is defined by
> 
> RationalizeDenominator[f_, a_] := Block[{t},
>   Numerator[f]*
>      PolynomialExtendedGCD[Denominator[f] /. {a -> t},
>        MinimalPolynomial[a, t]][[2, 1]] /. t -> a // Expand]
> 
> )
> ....
-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305


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