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

1
t == 0 && u == -2 ArcCos[-------] ||
Sqrt

-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:=
>> 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)], t -> 0},
> {u -> -2*ArcCos[1/Sqrt], t -> 0}}
>
> eqns /. %
>
> {{True, True}, {True, True}}
>
>
> Bob Hanlon

```

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