Date: Mar 24, 2013 4:35 AM
Author: Nasser Abbasi
Subject: Handling branch cuts in trig functions

I tried to simplify sqrt( sec(x)^2 ) but Mathematica willonly do this by assuming x is inside one branch, sayx>-Pi/2 && x<Pi/2  but Maple and maxima simplified itbut they gave the answer is terms of |sec(x)| to takecare of the sign which depends on the branch.Here is plot of sec(x)http://mathworld.wolfram.com/Secant.html-----------------------------In[37]:= Assuming[x>-Pi/2&&x<Pi/2,Simplify[Sqrt[Sec[x]^2]]]Out[37]= Sec[x]In[39]:= Assuming[x > Pi/2 && x < Pi, Simplify[Sqrt[Sec[x]^2]]]Out[39]= -Sec[x]------------------------------If I just tell M that x>0, it will not simplify it.------------------------------In[38]:= Assuming[x>0,Simplify[Sqrt[Sec[x]^2]]]Out[38]= Sqrt[Sec[x]^2]-------------------------------but Maple did it only with the x>0 assumption:----------------------restart;simplify(sqrt(sec(x)^2)) assuming  x::positive;                                1                             --------                             |cos(x)|restart;simplify(sqrt(sec(x)^2));                               /  1   \                           csgn|------|                               \cos(x)/                           ------------                              cos(x)---------------------------------On maxima 12.04.0   sqrt(sec(x)^2);    |sec(x)|I think now that answer to sqrt(sec(x)^2) should be|sec(x)| without need to give the branch. Since the onlydifferent is the sign. Or is there something else here?--Nasser