       Re: A strange bug in Solve

• To: mathgroup at smc.vnet.net
• Subject: [mg24366] Re: [mg24354] A strange bug in Solve
• From: BobHanlon at aol.com
• Date: Wed, 12 Jul 2000 23:13:08 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```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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