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 will

only do this by assuming x is inside one branch, say

x>-Pi/2 && x<Pi/2 but Maple and maxima simplified it

but they gave the answer is terms of |sec(x)| to take

care 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 only

different is the sign. Or is there something else here?

--Nasser