How to pass a power series to find_root

Yes, thanks for your help.

Rich



From: Stavros Macrakis
Sent: Sunday, May 30, 2010 1:15 PM
To: Richard Hennessy
Cc: Maxima List ; Barton Willis
Subject: Re: [Maxima] How to pass a power series to find_root


Rich,

You should be able to modify bffind_root so that this works.

              -s


On Sun, May 30, 2010 at 13:14, Richard Hennessy <rich.hennessy at verizon.net> wrote:

  My find_root example I could not get to work before today.

  I think I can get the rest.

  (%i8) bffind_root('(f(5.9b-9,e)), [],  e, 4.047b-19,4.4947335b-19,30);
  Evaluation took 3.0700 seconds (3.0700 elapsed)
  (out8) 4.09507811775768571897060610354b-19

  Rich






  From: Richard Hennessy
  Sent: Sunday, May 30, 2010 1:03 PM
  To: Stavros Macrakis
  Cc: Maxima List ; Barton Willis
  Subject: Re: [Maxima] How to pass a power series to find_root


  I got it to work now.

  (%i5) bffind_root('f(5.9b-9,e), f,  e, 4.047b-19,4.4947335b-19,30);
  Evaluation took 3.1600 seconds (3.1600 elapsed)
  (out5) 4.09507811775768571897060610354b-19
  (%i6) find_root('(f(5.9b-9,x)),x,4.047e-19,4.49e-19 );
  Evaluation took 1.0300 seconds (1.0300 elapsed)
  (out6) 4.0950781177607183*10^-19
  (%i7) find_root('(f(5.9e-9,x)),x,4.047e-19,4.49e-19);
  find_root: function has same sign at endpoints: f(4.047*10^-19)=3.1839205475930013*10^23, 
f(4.4899999999999998*10^-19)=1.9111895122777875*10^24
   -- an error. To debug this try: debugmode(true);

  For some reason the third way does not work but I can live with that.

  Thanks,

  Rich



  From: Stavros Macrakis
  Sent: Sunday, May 30, 2010 8:26 AM
  To: Richard Hennessy
  Cc: Barton Willis ; Maxima List
  Subject: Re: [Maxima] How to pass a power series to find_root


  I have not studied your code in detail, but the basic problem appears to be your use of 'f(...) as an argument and 
then 'at' and apply/ev to evaluate it at given points.

  The syntactic form 'f(...) creates a noun-form of f, which there is no reason to have here.  The argument should be 
'( f(...) ).  You mention that you couldn't get that to work, but that is the form you need to make work.  The 
complicated workaround of at/apply/ev should not be necessary.  What problems did you have with the simple, ordinary 
approaches?

  If you can't figure that out, please send us a *minimal* reproducible example.  Surely most of the code in 'f' and 
'bffind_root' is not necessary to reproduce the problem, and is not the crux of the problem.


                   &a mp;n bsp; -s



  On Sat, May 29, 2010 at 19:38, Richard Hennessy <rich.hennessy at verizon.net> wrote:

    Okay I think I understand that nfloat() isn't helping but what about how to prevent evaluation of a function passed 
as a parameter to another function.  makelist(f(5.9b-9, e), e, 1, 100) does not take a long time.  In fact it is pretty 
fast. Something is different about makelist().  I think I remember reading that makelist was "designed for functions" in 
some of the documents on the Wiki.

    I have a bffind_root() function that I wrote and when I call it it takes so long that I have yet to see it complete. 
bffind_root() is defined in pw.mac.  It is just a simple binary search.  I have tried all kind of quoting of the f() 
like '(f(5.9,e)) but it does not work.  Typing in f(5.9b-9,e) also never completes which makes sense.

    I have changed bffind_root() to take the function name as an extra parameter and that works but I would prefer a 
better way.

    This is my power series.

    f(x,e):=sum(
      block([hbar : bfloat(6.6260693b-34/(2*%pi)), mu : 1b15, m : 9.109389754b-31],
          if  equal(_i ,0) then
          (
              a : 1,
              acc : 1,
              am2 : 0,
              am4 : 0,
              am6 : 0
          )
          elseif mod( _i , 2)=0 then
          (
              a : 2 * m / hbar^2 * (mu * am6 - am2 * e)/(_i * (_i - 1))
          ),
          if mod(_i , 2)=1 then
          (
              _num : 0
          )
          else
          (
              am6 : am4,
              am4 : am2,
              am2 : a,
              tmp : a*acc,
              acc : acc * x^2,
              _num : tmp
          ),
    _num
    ), _i, 0, 300)$

    bffind_root('f(5.9b-9, e), f, e, 4.047b-19,4.4947335b-19,30);  this works fine because I modified bffind_root() to 
pass the function name as the second parameter.

    bffind_root('f(5.9b-9, e), e, 4.047b-19,4.4947335b-19,30);  this takes forever.

    find_root('f(5.9e-9, e), e, 4.047e-19,4.4947335e-19);  this takes forever.

    Thanks for advance for any help.

    Rich

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