Function domain problems



Hello guys, I'm from the same team as Andrey Yeltsin - we're using
Maxima in our project.

We have encountered some problems in the process of development:
Maxima doesn't work correctly with function domains and critical
points, which is very unconvenient in some cases.

e.g.

(%i3)  solve (log(x)*((x+1)^2)/(x+1) = 0, [x]);
(%o3)                          [x = 1, x = - 1]

and

(%i3) solve (sqrt(x)*(x+5)/(x-5) = 0,[x]);
(%o3)                          [x = - 5, x = 0]

In fact, we need 2 functions:

1) critical_points - returns points that turns function into infinity.
e.g.
(%i5) critical_points(log(x)/(x+5), [x])
[x=0, x=-5]

2) the second funtion would give us the domain of a function or at
least the domain boundaries.
e.g.
(%i5) domain (sqrt(x)*(x+5)/(x-5), [x]);
[0<=x<5] union [5<x<inf]
or
(%i5) domain_boundary(sqrt(x)*(x+5)/(x-5), [x]);
[x=0,x=-5]

I'm wondering if any of you have already developed these functions or
is/are willing to develop it.
We're ready to give you some compensations for your work.
Thank you in advance

Nguyen Duc Ngoc