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