@rlopez If there is three points are collinear, how can I get the annount "three points are collinear"? For example, if list of points contains three points [[1, 2, 3], [3, 4, 5], [4, 5, 6]].

@Kitonum If there is three points are collinear, how can I get the annount "three points are collinear"? For example, if list of points contains three points [[1, 2, 3], [3, 4, 5], [4, 5, 6]].

@rlopez  Thank you very much.

I added 
print(L[k], Temp*signum(lcoeff(Temp)) = 0)
in your code. It works.

@vv  Thank you very much.

@Kitonum Thank you very much.

I want the equation has the form a x + by + cz + d = 0 and gcd(a,b,c,d)=1 and a >0, If a = 0, then b>0, if b=0, then c>0...

@Christian Wolinski It doesn't work. I tried.

@vv How about?
lnrel(log[10](2), log[10](3), log[10](5), log[10](150))

@vv Thank you very much.

@Kitonum Thank you very muc, It works.

@Christian Wolinski My version is  2016. 

@Christian Wolinski I can't the result of your proc(S, T). I got                
 [log[36](24)], [log[36](24)]
 [log[140](63)], [log[140](63)]

@Kitonum I got Error, invalid input: eval expects its 2nd argument, eqns, to be of type {integer, equation, set(equation)}, but received {[ln(3) = a*ln(2), ln(5) = b*a*ln(2), ln(7) = ln(2)/c]*[]}

@Kitonum Thank you very much. 
How can I improve your code with the problem: Let log[2](3)=a, log[3](5)=b and log[7](2)=c. Express log[140](63) in term a, b, c?

@Christian Wolinski Nice solution. Thank you very much.