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Mathematica Real Part of Solve output

  1. Jan 18, 2012 #1
    I am trying to solve 0.125 + 0.5 (1-x)^3 - (12.5/y)==0 for x, when y is real and y>0. I thus want to find x= 1- 0.63 ((100-y)/y)^(1/3), so that if y=100, x=1. Mathematica's Solve yields 3 roots:

    sol=Solve[0.125 + 0.5 (1 - x)^3 - (12.5/y) == 0, x]

    Root 1:
    1.+((0.+0. I) y^(1/3))/(-100.+1. y)^(1/3)-((0.31498+0.545562 I) (-100.+1. y)^(1/3))/y^(1/3),

    Root 2:
    1.+((0.+0. I) y^(1/3))/(-100.+1. y)^(1/3)-((0.31498-0.545562 I) (-100.+1. y)^(1/3))/y^(1/3),

    Root 3:
    1.+(0. y^(1/3))/(-100.+1. y)^(1/3)+(0.629961 (-100.+1. y)^(1/3))/y^(1/3)



    If I now evaluate root 1 at y=100, I get an Infy error because of division by zero. How can I drop the imaginary part of this function? I have tried (without succes) a bunch of things such as:

    xroot1=x/.sol[[1]]

    *ComplexExpand[xroot1]

    *Assuming[p > 0, {Simplify[xroot1]}]
     
  2. jcsd
  3. Jan 18, 2012 #2

    phyzguy

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    Science Advisor

    Try:

    Limit[xroot1,y->100]
     
  4. Jan 18, 2012 #3
    Marvelous, that indeed does the trick. However, if the polynomial is of a higher order (see below) I again run into trouble.

    For instance, if I want to find the real root of 0.1 + 0.5 (1-x)^4 - (1/y)=0, (which you can easily solve for x=1- [ 2 (1-0.1 y ) / y ]^(1/4) ), I again use

    sol = Solve[0.1 + 0.5 (1 - x)^4 - (1/y) == 0, x];

    If I now plot the real part of these roots, none of them look like the one found above.

    e.g. Plot[Re[(x /. sol[[1]])], {y, 0, 10}]

    Is the solve algorithm not suited for solving equations of this order or am I doing something very very wrong?

    EDIT1: It seems to be a Mathematica 7 problem. In Mathematica 8 the plots are just fine. Is this a known bug?
     
    Last edited: Jan 18, 2012
  5. Jan 18, 2012 #4

    phyzguy

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    Science Advisor

    Interesting. I think what you are looking at is numerical round-off error. When you use a number like 0.1 in Mathematica, it only keeps a certain number of digits, I think 6. However, if you use the number 1/10, then it treats it as an exact mathematical quantity and there is no round-off error. If I use:

    sol = Solve[1/10 + 1/2 (1 - x)^4 - (1/y) == 0, x]
    Plot[Re[(x /. sol[[1]])], {y, 0, 10}]

    Then everything looks fine. i am using Mathematica 7.0.1.
     
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