proving two formula are same each other!

[Steven D'Aprano]

On Tue, 01 Nov 2011 05:03:17 -0700, pyman wrote:

> hello, I need some idea to prove two formula is same.

Impossible. As you explained further on, they are different formula. If 
they are different, they aren't the same. This has nothing to do with 
Python.

In another message, you tell us:

"these formula are completely different each other"

and give the formula:

A formula : f(x,y,z)=3x+4y+2z+3
B formula : f(k,j,t)=2k+3j+2t+1

Perhaps what you mean is that you want to solve for when the two formula 
give equal results? Here's a simpler example:

f(x) = 2x + 1
g(x) = 3x - 2

Solving for x:

f(x) = g(x)
2x + 1 = 3x - 2
1 = 3x - 2 - 2x
1 + 2 = 3x - 2x
3 = x

so the solution is x = 3, f(3) = 7 = g(3).

This is also not easy, since you have SIX variables (x, y, z, k, j, t) 
and only two equations. This is known as an under-determined system, and 
means that there is no exact solution. Perhaps something like Mathematica 
could do something useful with it?

Is there some way you can use the same variables in each formula? For 
example, if x=t, y=j, z=k (or some other combination), then you have a 
simpler three-dimensional problem:

f(x,y,z) = 3x + 4y + 2z + 3
g(x,y,z) = 2z + 3y + 2x + 1

which is still under-determined, but not as badly (now you have three 
variables and only two equations).

In any case, you *might* be able to solve this using numpy. 

http://numpy.scipy.org/


-- 
Steven