Unable to integrate this user-defined function

[aheight]

I am working with a polynomial and wish to integrate over one of it's branch surfaces with high precision. The function is:

$-z^2 + z^3 + w (-4 z + 3 z^2) + w^3 (-2 + 8 z + 4 z^2 - 4 z^3) + w^2 (-z^3 - 9 z^4) + w^4 (6 - 8 z^2 + 7 z^3 + 8 z^4)=0$

So I first solve the associated differential equation to obtain a trace over $w(z)$ . This is theCentralTrace[t]. Next, in order to obtain precise values of the function over this trace, I solve for the roots over the trace. Then I can compare the trace values to the list of roots and get a more precise value of the function over the trace. As written, I can plot myFunction[t]. However, when I attempt to integrate myFunction[t] via:

NIntegrate[myFunction[t],{t,tStart,tEnd}]

the conditional in the code returns an unevaluated 't' so the Position fails. The function getDigits in the code simply converts the floating point numbers to integer sequences so I can make an exact comparison to a particular precision (5 in the code). I was wondering if someone could help me with this.

Thanks.

myFunction[t_] := Module[{cDigits, fVal,fDigits, pos, cVal},
  cVal = theCentralTrace[t];
  cDigits = getDigits[cVal, 5];
  fVal = w /. NSolve[theFunction == 0 /. z -> rnorm Exp[I t], w];
  fDigits = getDigits[fVal, 5];
  pos = Position[fDigits, cDigits[[1]]];
  If[Length[pos] == 0,
     Print[t];
     Abort[];
  ];
  Re[fVal[[pos[[1, 1]]]]]
  ];

 

[mmwave]

Hello,

Thank you for sharing your code and explaining your problem. I am a scientist with experience in numerical integration and differential equations, and I would be happy to help you with this issue.

After reviewing your code, I believe the problem lies in your use of the Re[] function in the last line of the myFunction[t_]. The Re[] function takes the real part of a complex number, but in this case, you are using it on a list of complex numbers. This is causing the conditional in your code to return an unevaluated 't', as you mentioned.

To fix this issue, you can use the Part (or [[ ]]) function to extract the real part of the complex number at the desired position. So the last line of your code would become:

Re[fVal[[pos[[1, 1]]]][[1]]]

This will extract the real part of the complex number at the first position in the list of fVal, which is what I believe you are trying to achieve.

I hope this helps and please let me know if you have any further questions or if you need any more clarification. Good luck with your project!