Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.symbolic.independent

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Axel Vogt

Posts: 1,042
Registered: 5/5/07
Re: Handling branch cuts in trig functions
Posted: Mar 24, 2013 11:06 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Using Maple 17 for sqrt(sec(x)^2); simplify(%); gives csgn(1/cos(x))/cos(x).

Better use t instead of sec(x) = 1/cos(x) to see what is meant, cf the help:

1) sqrt(x) represents the "principal square root", defined by the formula
sqrt(x) = exp(1/2 * ln(x)) [they mean: using the pricipal branch of log]

2) Without the symbolic option, Maple computes simplify((x^2)^(1/2)) as csgn(x)*x.

3) The csgn function is used to determine in which half-plane ("left" or "right")
the complex-valued expression or number x lies. It is defined by

csgn(x) = piecewise(`or`(0 < Re(x), `and`(Re(x) = 0, 0 < Im(x))), 1,
`or`(Re(x) < 0, `and`(Re(x) = 0, Im(x) < 0)), -1)

4) The value of csgn(0) is controlled by the environment variable _Envsignum0.

Note that Maple extends *into* the (usual) branch cut counterclockwise,
i.e. as limit from the upper left halfplane into the negative axis.





Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.