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MathGroup Archive 1994

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Transformation of Expressions

  • To: mathgroup at yoda.physics.unc.edu
  • Subject: Transformation of Expressions
  • From: rickli at aut.ee.ethz.ch (Martin Rickli)
  • Date: Tue, 28 Jun 1994 17:28:03 +0200

My professor asked me the following:

If we have an expression built with rational numbers and a irrational
number, it is nown that there exists a ("linear") representation of the
form

      f[irrational] = rational +  rational*irrational

e.g.  Sqrt[ (3 + Sqrt[5])/2 ] = 1/2 + 1/2 Sqrt[5]

(here Sqrt[5] is the irrational number).

How can we find these rational numbers (of course using Mma)?

To my regret I couldn't help him.
Is it possible to set up transformation rules doing this (hopefully yes)?

Thanks for any hint.

With kind regards

______________________________________________________________________
Martin Rickli                           E-mail: Rickli at aut.ee.ethz.ch
Automatic Control Laboratory
ETH Zurich                              Physikstr. 3, ETL K12
CH-8092 Zurich,  Switzerland







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