proving two formula are same each other!

Discussion in 'Python' started by pyman, Nov 1, 2011.

  1. pyman

    pyman Guest

    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
     
    pyman, Nov 1, 2011
    #1
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  2. pyman

    Dave Angel Guest

    On 11/01/2011 08:03 AM, pyman wrote:
    > 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.

    --

    DaveA
     
    Dave Angel, Nov 1, 2011
    #2
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  3. pyman

    Dave Angel Guest

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

    >>
    >>> 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?
    >
    > the formula is related to math.
    >
    >
    >> And how is one different than the next?

    >
    >
    > 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.


    --

    DaveA
     
    Dave Angel, Nov 1, 2011
    #3
  4. pyman

    pyman Guest

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

    do you know sigma? I omitted sigma it means sum...
     
    pyman, Nov 1, 2011
    #4
  5. 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
     
    Steven D'Aprano, Nov 1, 2011
    #5
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