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MathGroup Archive 2005

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Re: Solve Limitations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg62980] Re: [mg62963] Solve Limitations
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Sat, 10 Dec 2005 06:02:49 -0500 (EST)
  • References: <200512091010.FAA05489@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

On 9 Dec 2005, at 19:10, Marcelo Mayall wrote:

>
> Let's suppose that we are interested in the roots analytic  
> expression of
> the following function:
> In[1] :=  f = a x + b x^(3/2) + c;
> The function Solve could be used:
> In[2] :=  sol = Solve[f==0, x];
> Defining the values of the constants a, b, c would return the  
> following numeric values:
> In[3] :=  froots = Solve[f==0, x]/. {a->1, b->1, c->1} //N
> Out[3] =  {{x-> 2.1479}, {x-> -0.57395 + 0.368989 I}, {x-> -0.57395  
> - 0.368989 I}}
> However, f is not null for those values and therefore, these are  
> not the roots of f:
> In[4] :=  f/. froots/. {a-> 1, b-> 1, c-> 1} //Chop
> Out[4] =  {6.2958, 0, 0}
> At first, it seems that the function Solve doesn't take  
> appropriately in
> consideration the term in square root.
> Some idea to obtain the correct analytic solution of f ??? Or, in  
> fact, this a limitation of the function Solve???
>
> Thanks,	
> Marcelo Mayall
>
>

There is no way, in general, to avoid getting so called "parasite"  
solutions in parametric equations with radicals. This is not a  
limitation of Solve but of known mathematics.

If your equation has numerical coefficients then the option  
VerifySolutions->True will usually (but not always) insure that the  
parasite solutions are eliminated.

Andrzej Kozlowski 


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