       Re: Problems with Solve

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• Subject: [mg132494] Re: Problems with Solve
• From: danl at wolfram.com
• Date: Tue, 1 Apr 2014 03:03:17 -0400 (EDT)
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```On Friday, March 21, 2014 11:09:00 PM UTC-5, Samuel Mark Young wrote:
> Hello everyone,
>
> I'm trying to use the solutions of Solve from solving a cubic equation - however, it keeps returning complex answers when there are real solutions. For example:
>
>
>
> Solve[z + 5 (z^2 - 1) + 1 z^3 == 1, z]
>
>
>
> This equation has 3 real solutions. However, the answers returned when I ask mathematica for a decimal answer are complex (which I need to do later on when an integration needs solving numerically):
>
> {{z -> 0.925423 + 0. I}, {z -> -4.47735 +
>
>     2.22045*10^-16 I}, {z -> -1.44807 - 4.44089*10^-16 I}}
>
>
>
> I'm guessing this is to do with the finite precision that is used in the calculations as the imaginary components are very small, but am unsure how to deal with them and they shouldn't be there. Any suggestions?
>
>
>
>
>
> The second problem I am having is that I need to solve for s in a function B[s] == 10^-5, where B is some (complicated) function of s.
>
>
>
> The form of the function depends on s - and this is handled by If[] commands in the function B. For example, the s dependance might be:
>
>
>
> B[s]:=If[s<0.5,Erfc[-x],Erfc[-x]+Erfc[y]-Erfc[z]]
>
>
>
> B[s] is a smooth function of s.
>
>
>
> The problem seems to arise because, before it has found a solution for s, it can't decide which form of the function to use - and so just returns an error message (I've tried using Solve, NSolve, and FindRoot with different methods). However, since I'm only looking for a numerical solution it is easily possible to solve this manually using trial and improvement - which seems to be something that Mathematica should be able to do? But I can't figure out how.
>
>
>
> Please feel free to contact me directly at sy81 at sussex.ac.uk with advice.  Thank you in advance for any help!
>
>
>
> Regards,
>
> Sam

For item (1) you might wish to do it via Solve[..., Cubics->False]. The result you are getting is correct but it will indeed numericize with those small phantom imaginary parts; that's a result of what's called truncation error.

For item (2) I would have recommended exactly what Ray Koopman already posted.

Daniel Lichtblau
Wolfram Research

```

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