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MathGroup Archive 2000

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solving third order equation: bad result

  • To: mathgroup at smc.vnet.net
  • Subject: [mg22152] solving third order equation: bad result
  • From: "Wolter Kaper" <kaper at chem.uva.nl>
  • Date: Wed, 16 Feb 2000 02:35:18 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Dear Mathgroup members,

When I solve the following equation for V, in terms of symbolic P and then
substitute a value for P, I get a result that is wrong. (The right result is
returned when I solve the equation with P substituted beforehand.)

P == RT /(V - b) - a/V^2 /. {a -> 0.142666, b -> 3.913*10^(-5), RT -> 2494})

The following notebook demonstrates the problem and compares results after
the equation has been rewritten in standard (third order polynomial ==0)
form. In that case the right result is returned.
My questions are: does anybody know why this behaviour occurs, has anybody
seen it before, should I report a bug to Wolfram research?

Thanks beforehand,
Wolter Kaper
Univ. Of Amsterdam, dept. of Chemistry

Notebook follows.

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  " When I solve the following equation for V, in terms of symbolic P and \
then substitute a value for P, I get a result that is wrong. The right
result \
is returned when I solve the equation with P substituted beforehand."
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                      1.9565`*^9\ P)\)\)\/P\)\)}, {V \[Rule] \
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These solutions are OK. None of them is equal to the faulty 0.0000151217.\
\>", "Text"],

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As a comparison, I can also rewrite eq1 in standard \"third order \
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afterwards.\n",
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  ": why does the deviating solution \"0.0000151217\" appear? Is it a matter
\
of limited numerical accuracy? \nAnd why does \"Solve\" come up with three \
solutions that are identical? I know that a cubic equation has three \
(complex) roots, but apparently \"Solve\" has not used the general routine \
for solving a cubic equation, because then it should have arrived at the \
result presented last."
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