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Mathematica the Simplify[] command

  1. Dec 25, 2009 #1

    Mentallic

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    1. The problem statement, all variables and given/known data
    Simplify to a certain extent, as much as possible (factorized form would be best):

    [tex]\frac{\sqrt{3}}{2}\left(\frac{md}{m-\sqrt{3}}\right)^2+\frac{\sqrt{3}}{2}\left(\frac{m(s+d)}{m+\sqrt{3}}\right)^2+\frac{1}{2}\left(s+\frac{md}{m-\sqrt{3}}-\frac{m(s+d)}{m+\sqrt{3}}\right)\left(\frac{\sqrt{3}md}{\sqrt{3}-m}+\frac{\sqrt{3}m(s+d)}{m+\sqrt{3}}\right)[/tex]


    3. The attempt at a solution
    This isn't an actual question but rather a part of a bigger picture. I need this simplified as much as possible before I can even think of manipulating it further.

    I've tried quite a bit, but after expanding the last factored expression, it became pretty ugly. This route seems most promising:

    [tex]\frac{\sqrt{3}}{2}\left(\left(\frac{md}{m-\sqrt{3}}\right)^2+\left(\frac{m(s+d)}{m+\sqrt{3}}\right)^2+\left(s+\frac{md}{m-\sqrt{3}}-\frac{m(s+d)}{m+\sqrt{3}}\right)\left(\frac{m(s+d)}{m+\sqrt{3}}-\frac{md}{m-\sqrt{3}}\right)\right)[/tex]

    [tex]\frac{\sqrt{3}}{2}\left(\left(\frac{md}{m-\sqrt{3}}\right)^2+\left(\frac{m(s+d)}{m+\sqrt{3}}\right)^2+s\left(\frac{m(s+d)}{m+\sqrt{3}}-\frac{md}{m-\sqrt{3}}\right)-\left(\frac{2\sqrt{3}md+\sqrt{3}ms-m^2s}{m^2-3}\right)^2\right)[/tex]

    [tex]\frac{\sqrt{3}}{2}\left(\left(\frac{md}{m-\sqrt{3}}\right)^2+\left(\frac{m(s+d)}{m+\sqrt{3}}\right)^2-s\left(\frac{2\sqrt{3}d+\sqrt{3}s-ms}{m^2-3}\right)-m^2\left(\frac{2\sqrt{3}d+\sqrt{3}s-ms}{m^2-3}\right)^2\right)[/tex]

    I'm unsure of what else to do without making a big mess. And this still isn't simple enough for what I need this for, so if you have the stomach to tackle this, please do so :smile:
     
  2. jcsd
  3. Dec 25, 2009 #2
    Re: Simplifying

    attachment.php?attachmentid=22689&stc=1&d=1261729547.jpg
     

    Attached Files:

  4. Dec 25, 2009 #3

    Mentallic

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    Re: Simplifying

    Thanks for the response.

    I don't quite understand what your final solution is. When it gets to the : and then it has just one entire fraction. That one fraction can't possibly be equal? It only has a second degree for m, while if you look at this part which is located on the last line in the last factor of my OP:

    [tex]m^2\left(\frac{2\sqrt{3}d+\sqrt{3}s-ms}{m^2-3}\right)^2[/tex]

    it clearly suggests the denominator should be of a 4th degree in m, no?
     
  5. Dec 26, 2009 #4
    Re: Simplifying

    I hope this answers your question.(=
    attachment.php?attachmentid=22702&stc=1&d=1261818750.jpg
     

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    • sol.jpg
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  6. Dec 26, 2009 #5

    Mentallic

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    Re: Simplifying

    Oh wow thanks a lot for that!

    It still took me a while to understand what was happening, but it all sunk in :smile: and when I tested it for some values of s,d and m and they turned out equal, I was even more ecstatic!
     
  7. Dec 26, 2009 #6
    Re: Simplifying

    you are most welcome(=
     
  8. Dec 26, 2009 #7

    Mentallic

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    Re: Simplifying

    Did you simplify this yourself, or did you use a program of some sort?
    Reason being because I'm going to need more simplifying of this type to be done.
     
  9. Dec 26, 2009 #8
    Re: Simplifying

    I've checked with a program and indeed it is the simplest form.
     
  10. Dec 26, 2009 #9
    Re: Simplifying

    If you have access to Mathematica the Simplify[] command would come in handy.

    Come to think of it there might also be something similar you can use on Wolfram Alpha to simplify expressions.
     
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