I just wanted to let you know that now that I can diff with respect to y I can now use a variation of either Heun's method or Runge Kutta to find the eigenvalues of the x^4 potential to any degree of accuracy I choose.
I guess I can work on that now. This needs some more thinking and it will take time. But the basic idea is obvious now.
Thanks you all for your patience with my bothersome posts.
Rich
------------Original Message------------
From: "Stavros Macrakis" <macrakis at alum.mit.edu>
To: "Richard Hennessy" <rvh2007 at comcast.net>
Cc: "Maxima List" <maxima at math.utexas.edu>
Date: Mon, Apr-21-2008 2:42 PM
Subject: Re: [Maxima] Feature request
On Mon, Apr 21, 2008 at 1:28 PM, Richard Hennessy <rvh2007 at comcast.net> wrote:
I just want to be able to diff it with respect to y. Is this too much to ask?
Why the exasperated tone? Maxima easily does this, though the result and the coefficients are large. Just use rat form for reasonable runtime.
f(rat(x),rat(y))$
Evaluation took 2.17 seconds (2.17 elapsed)
diff(%,y)$
Evaluation took 2.61 seconds (2.61 elapsed)
Displaying the results in a reasonable way might be trickier, since this is an expanded polynomial of 15000+ terms, with many of the coefficients > 1000 digits (e.g. 326 digit numerator, 738 digit denominator).
ratcoef(ratcoef(sr,x,250),y,49);
Evaluation took 1.54 seconds (1.54 elapsed)
=> 4316..(166 more digits)..1583 / 9660..(403 more digits)..0000
i.e. the term is
4316..(166 more digits)..1583 / 9660..(403 more digits)..0000 * x^250 * y^49
display2d:false might be your best bet for simple printout.
What exactly is the next step in your processing of terms like this?
Instead of printing them out, perhaps you should continue processing with Maxima somehow? Of course, if it's good enough to truncate to N decimal digits, you can also use fpprec:N and convert to bfloats.
-s
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