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MathGroup Archive 2000

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Re: A strange bug in Solve

  • To: mathgroup at smc.vnet.net
  • Subject: [mg24376] Re: [mg24354] A strange bug in Solve
  • From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
  • Date: Wed, 12 Jul 2000 23:13:16 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

This is true and I should have noticed it. But still, note that Solve finds
fewer solutions than Reduce, and in fact it misses most of them (so to
speak: there are of course infinitely many, but I mean most of the
"geometric" solutions)

In[1]:=
eqns = {2*Cos[2*t]*Cos[u/2] + Cos[t]*Sin[u/2] ==
        0, (Cos[u/2]*Sin[t])/2 - (Sin[2*t]*Sin[u/2])/2 == 0};

In[2]:=
Reduce[eqns, {t, u}]
Reduce::ifun: 
   Inverse functions are being used by Reduce, so some
     solutions may not be found.
Out[2]=
                             1
t == 0 && u == 2 ArcCos[-(-------)] ||
                          Sqrt[5]
 
                              1
  t == 0 && u == -2 ArcCos[-------] ||
                           Sqrt[5]
 
       -Pi                     Pi
  t == --- && u == -Pi || t == -- && u == Pi ||
        2                      2
 
                    3
              -Sqrt[-]
                    2                          3
  t == ArcCos[--------] && u == 2 ArcCos[-Sqrt[-]] ||
                 2                             5
 
                   3
              Sqrt[-]
                   2                         3
  t == ArcCos[-------] && u == 2 ArcCos[Sqrt[-]]
                 2                           5

Andrzej

on 7/9/00 11:23 PM, BobHanlon at aol.com at BobHanlon at aol.com wrote:

> 
> In a message dated 7/9/2000 5:36:52 AM, andrzej at tuins.ac.jp writes:
> 
>> I have long ago learned to be careful when making claims about kernel bugs
>> in Mathematica, but this time I am pretty sure I have found a fairly serious
>> one, even though it looks rather strange.
>> 
>> I asked Mathematica to solve a system of two trigonometric equations:
>> 
>> In[1]:=
>> eqns = {2*Cos[2*t]*Cos[u/2] + Cos[t]*Sin[u/2] == 0,
>> (Cos[u/2]*Sin[t])/2 - (Sin[2*t]*Sin[u/2])/2 == 0};
>> 
>> To my surprise Solve returned the empty list (I knew these equations do
>> have
>> solutions for geometric reasons):
>> 
> 
> Solve doesn't get confused if you simplify the expression:
> 
> eqns = {2*Cos[2*t]*Cos[u/2] + Cos[t]*Sin[u/2] ==
> 0, (Cos[u/2]*Sin[t])/2 - (Sin[2*t]*Sin[u/2])/2 == 0};
> 
> Solve[eqns // Simplify, {t, u}]
> 
> "Solve::ifun : Inverse functions are being used by Solve, so some solutions
> may not be found."
> 
> {{u -> 2*ArcCos[-(1/Sqrt[5])], t -> 0},
> {u -> -2*ArcCos[1/Sqrt[5]], t -> 0}}
> 
> eqns /. %
> 
> {{True, True}, {True, True}}
> 
> 
> Bob Hanlon



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