Re[2]: kubische Gleichung führt zu komplexem Unsinn

[Udo und Susanne Krause <su.krause@XXXXXXX.ch>]

Guten Morgen allerseits,

die sehr schöne Erklärung wird von Mma. 5.2 punktuell unterlaufen:

Es heisst dort:
--- ZitatBeginn ---
(6) Sometimes conversion from trigs to exponentials, or expansion of 
trigs, can be of help. For example, the following was posed in the news 
group comp.soft-sys.math.mathematica.
In[5]:=
eqns = {-L+C*x+(2*R)/Tan[y/2],-x+2*((V-R-R/Cos[y])*Tan[y])};
In[6]:=
Timing[sol1=Solve[Together[TrigToExp/@eqns]\[Equal]0, {x,y}];]
From In[6]:= Solve::ifun: Inverse functions are being used by Solve, so 
some solutions may not be found; use Reduce \
for complete solution information. Mehr ...
Out[6]= {0.266 Second,Null}

An alternative that works better is to expand the trigs, first changing 
y to 2*z to get rid of the denominator inside one of the trigs. We get a 
result with small LeafCount quite fast.

In[7]:=
eqs=TrigExpand/@{-L+C*x+(2*R)/Tan[z],-x+2*((V-R-R/Cos[2*z])*Tan[2*z])};
Timing[sol=Solve[eqs\[Equal]0,{x,z}]/.(z\[Rule]a_)\[RuleDelayed]y\[Rule]2*a;]
From In[7]:= Solve::ifun: Inverse functions are being used by Solve, so 
some solutions may not be found; use Reduce \
for complete solution information. Mehr ...
Out[8]= {17.312 Second,Null}
--- ZitatEnde ---

Der Text meint, dass die Methode mit TrigExpand schneller sein sollte, 
unter XP mit Mma 5.2 ist dies nicht (mehr) so.

Gruss
Udo.