Function:
math[pole] - find poles of a real-valued function
math[removable] - find removables of a real-valued function
math[jump] - find jumps of a real-valued function
Calling Sequence:
pole(f, x);
pole(f, x=a .. b);
removable(f, x);
removable(f, x=a .. b);
jump(f, x);
jump(f, x=a .. b);
Parameters:
f
- an algebraic expression
x
- the indeterminate in f
a, b
- interval boundaries (realcons)
Description:
pole determines the poles of a function f in one real x. A pole p is defined as:
= +/-
and
= +/-
; p may or may not belong to the domain of f.
removable returns all discontinuities r that are removable:
exists, but
. r may or may not belong to the domain of f.
jump returns jump discontinuities j:
. The left-hand and right-hand limits must exist, i.e. are finite. j may or may not belong to the domain of f.
In the respective first forms, be passing a name as the second argument, all points of the entire domain are returned. In the second forms, by specifying an interval a .. b, all points that may be inside this interval (including the boundaries a, b) are evaluated.
The return is a set of all the special points found.
In case of transcendental functions, no general solutions are computed. If no interval is given, the functions do not evaluate over the entire real domain. Instead the range a .. b is taken which is determined by the value of _MathDomain (-10 .. 10 by default).
Internally math/pole, math/removable and math/jump are interfaces to math/distinctpoints, which uses discont to determine possible discontinuities and passes each candidate to math/cont for further evaluation.
This function is part of the math package, and so can be used only after performing the command with(math) or with(math, poles).
Examples:
> with(math, pole, removable, jump):
> pole(1/x, x);
> pole(1/x, x=0 .. 1);
> f := x -> 0.5/(x+3)^2-0.5/(x-1)+0.5/(x-3):
> pole(f(x), x);
> removable(sin(x)/x, x);
> jump(floor(x), x);
See Also:
math/singularity , math/cont , discont , math/nondiff .
Version History:
Version 1.0 - December 22, 1998