Is Mathematica Reliable for Complex Calculations?

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Discussion Overview

The discussion revolves around the reliability of Mathematica for complex calculations, particularly in the context of electrical engineering. Participants share their experiences and opinions regarding the accuracy of Mathematica compared to manual calculations and other computational tools.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Exploratory

Main Points Raised

  • Niko expresses concern about discrepancies between results obtained from Mathematica and manual calculations, questioning the reliability of Mathematica for complex equations.
  • One participant asserts that Mathematica is correct 100% of the time, emphasizing its reliability as a computational tool.
  • Another participant acknowledges the reliability of Mathematica but warns that user error can lead to incorrect results, stressing the importance of accurately inputting problems.
  • A participant notes that Mathematica and similar systems may sometimes yield different results in intensive tensor calculations involving ordinary differential equations (ODEs), although they believe the solvers are generally reliable.
  • Some participants suggest that discrepancies may stem from errors in manual calculations rather than issues with Mathematica itself.
  • Niko mentions that Mathematica's output was not simplified as expected, raising a question about the use of the FullSimplify command and its effectiveness.
  • A participant recommends using ExpandAll followed by FullSimplify to potentially resolve the simplification issue.
  • Niko reports that the suggested method did not yield the desired simplification.

Areas of Agreement / Disagreement

Participants exhibit a mix of confidence in Mathematica's reliability while acknowledging the potential for user error. There is no consensus on the specific issue of simplification, as Niko's attempts to simplify the output have not been successful.

Contextual Notes

Participants highlight the importance of ensuring accurate problem input and the potential for discrepancies in results due to the complexity of the calculations involved. The discussion reflects varying levels of experience with Mathematica and other computational tools.

niko2000
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Hi,
Recently I was doing some calculations with Mathematica then I did it on paper and the results weren't the same. I am almost sure I didn't make any mistake. I study electrical engineering and we have to do a lot of calculations. I have used Matlab and Mathematica for calculations with symbols. Until now I haven't done much complex calculations with Mathematica. Does anyone know if Mathematica is 100% reliable for every equation or is it only a tool for simple equations?
Regards,
Niko
 
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In short, yes, it is correct 100% of the time I would say. If it wasn't there would be no use for it. I use it all the time and it can out-math pretty much anything out there, it is a computer program after all, its job is to do math calculations.
 
I haven't used Mathematica very much but I've never had Maple screw up and I'd wager Mathematica is quite reliable.

There is a disclaimer though, these programs will be able to reliably perform any computation that you tell them to perform. Make sure you're actually telling it to do what you think you're telling it to do. They aren't free of user error.
 
Mathematica, MATLAB, and other CA systems will sometimes disagree when doing really, really intensive tensor-calc problems with lots of ODEs. The ODE solvers are not always perfect, but are, well, virtually always right.

If you're doing some simple EE work, and your pencil-and-paper solution doesn't match Mathematica's solution, it's almost surely your error. Check your pencil-and-paper work, then check to make sure you accurately supplied the problem to Mathematica.

- Warren
 
They wouldn't release it if they knew that it wasn't 100% reliable. Even if it was 99%, I doubt they would.

I think you may have done something wrong when you did it on paper. Double check it.
 
Thank you.
Maybe the result isn't different but it isn't simplified. I am sure I haven't done any error with my calculations.
Something that also seems strange is that Mathematica gave the result in note like this:
Sqrt[a^2...] I have put FullSimplify command but it hasn't changed. Anyone knows why?
 
You might want to use an ExpandAll followed by a FullSimplify.

- Warren
 
It still doesn't work.
I get this result:
Sqrt[a^2*Cosh[x]^2*Sin[y]^2]
 

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