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Topic: Handling branch cuts in trig functions
Replies: 9   Last Post: Mar 26, 2013 4:54 PM

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Nasser Abbasi

Posts: 5,694
Registered: 2/7/05
Re: Handling branch cuts in trig functions
Posted: Mar 24, 2013 7:39 AM
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On 3/24/2013 5:26 AM, G. A. Edgar wrote:
> In article <kimdsn$lj3$1@speranza.aioe.org>, Nasser M. Abbasi
> <nma@12000.org> wrote:
>
>

>>
>> I think now that answer to sqrt(sec(x)^2) should be
>> |sec(x)| without need to give the branch.

>
> That answer is incorrect for complex x ... so to get that answer in
> Maple, you must assume x is real.
>
> simplify(%) assuming x::real;
>


But I am using Maple 17?

-----------------------------------
ans:=simplify(sqrt(sec(x)^2)) assuming x::positive;

1
--------
|cos(x)|

simplify(abs(sec(x))- ans);
0

-------------------------------------

Unless x::positive implies x::real (since positive does
not apply to complex numbers). Is this what you meant?
I get same result using x::positive or x::real.

So Maxima was wrong then:

sqrt(sec(x)^2);
|sec(x)|

No assumptions!

thanks,
--Nasser



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