proving two formula are same each other!

[pyman]

hello, I need some idea to prove two formula is same. if N = 3, these
formula are same each other. each formula has 3 input . To prove this,
drawing shape or anything would be possible. how can I do this? please
give me your idea!

for example:
N = 1 : formula1 has a, b, c input value, formula2 has d, e, f input
value and each formula's output are different.
N = 2 : formula1 has a, b, c input value, formula2 has d, e, f input
value and each formula's output are different.
N = 3 : formula1 has a, b, c input value, formula2 has d, e, f input
value and each formula's output are SAME.

Wonjun, Choi

 

[Dave Angel]

hello, I need some idea to prove two formula is same. if N = 3, these
formula are same each other. each formula has 3 input . To prove this,
drawing shape or anything would be possible. how can I do this? please
give me your idea!

for example:
N = 1 : formula1 has a, b, c input value, formula2 has d, e, f input
value and each formula's output are different.
N = 2 : formula1 has a, b, c input value, formula2 has d, e, f input
value and each formula's output are different.
N = 3 : formula1 has a, b, c input value, formula2 has d, e, f input
value and each formula's output are SAME.

Wonjun, Choi

Python doesn't have formulae, it has functions and methods. So you have
to describe more completely what kind of formula you have, math,
physics, chemistry? And how is one different than the next? And how
can a formula with 3 input use four values, N, a,. b, and c ?

Please be more specific, and maybe somebody can help.

 

[Dave Angel]

(You forgot to do a REPLY-ALL, so that your message didn't get sent to
the list)

what kind of formula you have, math, physics, chemistry?

the formula is related to math.




these formula are completely different each other and it is custom
formula.
for example, when I put 3 input into A formula, it outputs 1 result.
and when I put 3 input into B formula, it outputs 1 result
so each formula have 3 input for example

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

this formula is different each other which has 3 input.
and have only 1 result

and if I loop this formula from 0 to N(for example : N = 3)
if N=1, the result will be different each other. and N=2 too.
but when N=3, the result will be same each other.

Since N isn't a parameter to either function, the results can never change.

so I wanted to prove this. by drawing shape or something so that children
can be understand easily.

I'm still trying to help you clarify your problem, but you are getting
much closer. Those two formulae take three arguments (although you
should use the same name for the arguments if the comparison is to mean
anything). N doesn't come into it at all.

Perhaps by N you mean tuples like (2,1,1) and (4,2,1), and you want to
know for which tuples the result will be the same.

That could be represented by some 4 dimensional graph, but I don't know
any graphing package that could show it, in python or otherwise.

 

[pyman]

first of all, thank you for trying to understand my issue.

do you know sigma? I omitted sigma it means sum...

 

[Steven D'Aprano]

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/