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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[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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