Question (signum function in maple)

[alejandrito29]

in maple signum(x) is |x|/x

the derivate is d/dx {|x|/x} =signum(1,x)

what is:

signum(1,x,0)
signum(0,x,0)
?

 

[g_edgar]

in maple signum(x) is |x|/x

That is incorrect for complex values x. Better is x/|x| which holds for all complex x except zero.

the derivate is d/dx {|x|/x} =signum(1,x)

what is:

signum(1,x,0)
signum(0,x,0)
?

In Maple, type ?signum to see the help page.

signum(1,x) is the derivative of signum, so it is zero for nonzero real x and undefined otherwise. The optional third argument tells Maple what you want to do with signum(0), some conventions say it should be 0, others that it should be 1, so you could say signum(0,x,0) and signum(0,x,1) for those two signum functions.

 

[oswaler]

In maple, the signum function returns the sign of a given number. The derivative of the signum function is equal to the signum function itself. Therefore, when evaluating the signum function at a specific value, such as 1, the result will always be 1.

signum(1,x,0) would return 1, as 1 is a positive number, and the signum function returns the sign of the number, which in this case is positive.

signum(0,x,0) would return 0, as 0 is neither positive nor negative, and the signum function returns 0 for any non-zero value.