Groups > comp.soft-sys.math.mathematica > #16681

Problems with Solve

From	Samuel Mark Young <sy81@sussex.ac.uk>
Newsgroups	comp.soft-sys.math.mathematica
Subject	Problems with Solve
Date	2014-03-22 04:09 +0000
Message-ID	<lgj2cs$lcg$1@smc.vnet.net> (permalink)
Organization	Time-Warner Telecom

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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@sussex.ac.uk with advice. Thank you in advance for any help!

Regards,
Sam

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Problems with Solve Samuel Mark Young <sy81@sussex.ac.uk> - 2014-03-22 04:09 +0000
  Re: Problems with Solve totarefugium <mtaktikos@t-online.de> - 2014-03-23 09:01 +0000
  Re: Problems with Solve totarefugium <mtaktikos@t-online.de> - 2014-03-23 08:59 +0000
  Re: Problems with Solve danl@wolfram.com - 2014-04-01 07:03 +0000

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