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Re: A strange bug in Solve

In a message dated 7/9/2000 5:36:52 AM, andrzej at 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:
>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
>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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