I have a list contains the triagles with in each triangle has mesure of the angle AOB equal to 45 degrees. Now I want to select four points in list so that they lie on the graph of the funtion y = (ax + b)/(cx + d), where c <> 0. This is the code which I make the list.

> restart:

ListTools[Categorize]:

N:=10:

L:=[]:

for x1 from -5 to N do

This is my question that I posted at http://mathematica.stackexchange.com/questions/32338/is-there-a-triangle-like-this "I want to find the numbers $a$, $b$, $c$, $d$ of the function $y = \dfrac{a x + b}{c x + d}$ so that the triangle $ABC$ with three points  $A$, $B$, $C$  have integer coordinates and lies on the graph of the given function, then the centroid of the triangle $ABC$ (have also integer coordinates) is also lies on the graph". The ansewr at that site...

I want to find the parameters m to the  equation x^4 -(3*m+2)*x^2 + 3*m+3 = 0 has four distinct solutions and all of them were less than 2. I tried

eq:= x^4 -(3*m+2)*x^2 + 3*m+3:

sol:=[solve(eq=0,x)]:

d:=discrim(eq,x):

solve([d>0,sol[1]<2,sol[2]<2,sol[3]<2,sol[4]<2],m):

allvalues(%);

How to reduce my code?

I want to find all values of m such that the equation (x-m)*(x-2*m-1)*(x+3*m-2)*(x+m+3)=0 has two positive solutions and two negative solutions. How to solve this problem with Maple?

I want to choose four points A, B, C, D on the sphere  (x-2)^2 + (y-4)^2 +(z-6)^2 -81=0 from the list L so that there are not any the right triangle are formed from the points A, B, C, D. How to get it? I tried

> restart:

with(geom3d):

eqS:=Equation(sphere(S,(x-2)^2 + (y-4)^2 +(z-6)^2 -81=0,[x,y,z],'centername'=T)):

L:=[]: