Something that FullSimplify knows but Reduce does not ?
- To: mathgroup at smc.vnet.net
- Subject: [mg118014] Something that FullSimplify knows but Reduce does not ?
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Fri, 8 Apr 2011 04:16:00 -0400 (EDT)
Consider the following (parametric) function of t:
g[t_] := (1/2)*Sin[2*t]*(((a - b)*(a + b))/
Sqrt[a^2*Sin[t]^2 + b^2*Cos[t]^2] +
(b^2 - a^2)/Sqrt[a^2*Cos[t]^2 + b^2*Sin[t]^2])
We try to find the roots of this for 0<=t<=Pi/4 using Reduce:
Reduce[
g[t] == 0 && a > 0 && b > a && 0 <= t <= Pi/4, t, Reals]
Reduce[
g[t] == 0 && a > 0 && b > a && 0 <= t <= Pi/4, t, Reals]
During evaluation of In[474]:= Reduce::ztest:Unable to decide whether numeric quantities HoldForm[{Pi - 8*ArcTan[Sqrt[3 - 2*Sqrt[2]]], -Pi + 8*ArcTan[Sqrt[3 - 2*Sqrt[2]]]}] are equal to zero. Assuming they are. >>
a > 0 && b > a && (t == 2*ArcTan[Sqrt[3 - 2*Sqrt[2]]] || t == 0)
So, Reduce claims that it was unable to decide if Pi - 8*ArcTan[Sqrt[3 - 2*Sqrt[2]]] is zero or not. But
FullSimplify[Pi - 8*ArcTan[Sqrt[3 - 2*Sqrt[2]]]]
0
Is everything here really as it should be?
Andrzej Kozlowski