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Strange behaviour of Solve without VerifySolutions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg85146] Strange behaviour of Solve without VerifySolutions
  • From: "Jaccard Florian" <Florian.Jaccard at he-arc.ch>
  • Date: Wed, 30 Jan 2008 06:06:49 -0500 (EST)

Dear Mathematica-specialists,

One of my students needed to solve a simple system:

equations =
     {(2 + 1.6*a + 8*b)^2/
             (8*a*(3 + 8*c + 1.6*b)) -
           1.7 == 0,
       (3 + 8*c + 1.6*b)^2/
             ((8*b + 2 + 1.6*a)*
                (3 + 1.6*c)) - 1.7 == 0,
       (3 + 1.6*c)^2/(3 + 8*c +
                1.6*b) - 1.7 == 0};
res = Solve[equations, {a, b, c}]

My student saw that there is a problem because he compared with the 
answers he obtained using another system, which were completely different!

Just type :

Chop[equations /. (expr_) == (n_) ->
         expr /. res]

As you easily can see, all solutions are wrong!

Looking in the Solve options, I saw that you can add the option : 
VerifySolutions->True:

res2 = Solve[equations, {a, b, c},
     VerifySolutions -> True]
And here, you can see that the solutions are all OK:

Chop[equations /. (expr_) == (n_) ->
         expr /. res2]

My question: Why did Wolfram make such a, I believe, stupid thing? Is 
there a good reason?

I'm not sure students (ore engineers and so on) will take the time to 
verify all solutions (usually, Mathematica tells when there may be a 
problem!) ore to Rationalize all the numbers of the equations... and I'm 
afraid they won't think about VerifySolutions. And as Mathematica is 
used to make a good job, students usually believe in the 
Mathematica-responses...

I'm also afraid the other system does in this case a better job...

In a future release, I would appreciate more trustworthiness!

Best Regards


Florian Jaccard





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