Thanks for your help! that was a complete answer :)
Best regards.
On Aug 2, 12:14 am, smichr <smi...@gmail.com> wrote:
> On Jul 31, 7:08 pm, New2Sympy <anartz.li...@gmail.com> wrote:
>
> > Hi All,
>
> > I am trying to get the Real root as shown below and keep getting a
> > NameError. Any suggestions?
>
> [cut]
> > NameError: global name 'conjugate' is not defined
>
> When you ask for a numerical solution, the first thing that nsolve
> does is evaluate your function and then create a "lambdified" version
> of it to pass to the solver. When you evaluate your function it looks
> like this:
>
> >>> 1/(.001+a)**3-6/(.9-a)**3
>
> (0.001 + a)**(-3) - 6/(0.9 - a)**3>>> _.evalf()
>
> 3.0e-6*conjugate(a)/(1.0e-6 + 0.001*a + 0.001*conjugate(a) +
> a*conjugate(a))**3 + 14.58*conjugate(a)/(0.81 - 0.9*a - 0.9*conjugate
> (a) + a*conjugate(a))**3 + 1.0e-9/(1.0e-6 + 0.001*a + 0.001*conjugate
> (a) + a*conjugate(a))**3 - 4.374/(0.81 - 0.9*a - 0.9*conjugate(a) +
> a*conjugate(a))**3 + 0.003*conjugate(a)**2/(1.0e-6 + 0.001*a +
> 0.001*conjugate(a) + a*conjugate(a))**3 - 16.2*conjugate(a)**2/(0.81 -
> 0.9*a - 0.9*conjugate(a) + a*conjugate(a))**3 + conjugate(a)**3/
> (1.0e-6 + 0.001*a + 0.001*conjugate(a) + a*conjugate(a))**3 +
> 6.0*conjugate(a)**3/(0.81 - 0.9*a - 0.9*conjugate(a) + a*conjugate(a))
> **3
>
> All those conjugates are there because sympy (I imagine) doesn't know
> whether a will be real or imaginary, so it's covering all bases. The
> problem is, in order to evaluate this, you need sympy but the only
> thing that nsolve passes along to the solver is mpmath's module. The
> solution is to pass sympy, too. I also like to watch the iteration
> process so I set the verbose flag to true:
>
> >>> nsolve(1/(.001+a)**3-6/(.9-a)**3,a,.3,modules="sympy",verbose=True)
>
> x: 0.315560066156274077187
> error: 0.25
> x: 0.318099998922522143874
> error: 0.234439933843725911711
> x: 0.31882324267983762464
> error: 0.00253993276624806668673
> x: 0.318830099704768381578
> error: 0.000723243757315480766644
> x: 0.318830113872912139068
> error: 0.00000685702493075693761643
> x: 0.318830113873185857794
> error: 1.4168143757489826177e-8
> x: 0.318830113873185911755
> error: 2.7371872575728692042e-13
> x: 0.318830113873185898265
> error: 5.39615044542560845509e-17
> x: 0.318830113873185905365
> error: 1.34903761135640211377e-17
> x: 0.31883011387318590714
> error: 7.10020074079996919847e-18
> x: 0.318830113873185905587
> error: 1.77506342008979314806e-18
> mpf('0.31883011387318591')
>
> And there you go!
>
> Notes:
>
> 1) If you want to use the sure-fire bisect method, don't forget to
> send in two values for the starting point:
>
> >>> nsolve(1/(.001+a)**3-6/(.9-a)**3,a,(.1,.5),modules="sympy",method="bisect")
>
> mpf('0.3188301138731859')
>
> 2) For nasty functions like this an alternative approach would be to
> find zeros of the numerator instead of the whole expression, or solve
> the problem symbolically and substitute in the values when you are
> done:
>
> >>> num,den = (1/(.001+a)**3-6/(.9-a)**3).as_numer_denom()
> >>> nsolve(num,a,.3) # no need for sympy now
>
> mpf('0.31883011387318584')
>
>
>
> or
>
> >>> var('c1 c2');solve(1/(c1+a)**3-6/(c2-a)**3,a)
>
> Hmmm...it hangs. (I filed this as issue 1571). But we can use the
> numerator tric to make things easier for the solver:
>
> >>> num = (1/(c1+a)**3-6/(c2-a)**3).as_numer_denom()[0]
> >>> ans=solv(num,a)
> >>> [t.subs({c1:.001,c2:.9}).evalf(n=4) for t in ans]
>
> [3.188e-1, 3.216e-2 - 5.706e-1*I, 3.216e-2 + 5.706e-1*I]
>
> Best regards, and welcome to sympy!
> /c
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