ratinterpol does not reproduce rational function

On 12/27/2012 04:56 PM, Stavros Macrakis wrote:
> ratinterpol(float(h),2) gives the correct result (within 1e-8 or so) after
> you eliminate small coefficients and rationalize the result.

My obviously wrong belief was, that ratinterpol can reproduce
a rational function, if the degree of the numerator is known,
and one does have enough interpolation points.

I normally use factor(ratinterpol(h,deg))
for discovering mathematical relations
if lagrange doesn't work.

So the usage of float(h) wouldn't have helped me here either.

Regards
Andre

P.S.
-2*(k+1)*(2*k+1)/(k*(k+2)) was indeed the correct function.
Factoring the denominator of the interpolation values did the job.


>
> On Thu, Dec 27, 2012 at 5:53 AM, Mario Rodriguez <biomates at telefonica.net>wrote:
>
>> El jue, 27-12-2012 a las 02:23 +0100, andre maute escribi?:
>>> Hi list,
>>>
>>> I have the following test case
>>>
>>> --- ratinterpol.mac ------------
>>> display2d : false;
>>> load(interpol);
>>> h : makelist( [k,-2*(k+1)*(2*k+1)/(k*(k+2))], k,1,12);
>>> ratinterpol(h,2);
>>> --- ratinterpol.mac ------------
>>>
>>> I get this unexpected behavior
>>>
>>> --- output -------------
>>> $ maxima -b ratinterpol.mac
>>> Maxima 5.27.0 http://maxima.sourceforge.net
>>> using Lisp SBCL 1.0.57-1.fc17
>>> Distributed under the GNU Public License. See the file COPYING.
>>> Dedicated to the memory of William Schelter.
>>> The function bug_report() provides bug reporting information.
>>> STYLE-WARNING: redefining MAXIMA::$FILE_TYPE in DEFUN
>>> (%i1) batch(ratinterpol.mac)
>>>
>>> read and interpret file: /home/user/ratinterpol.mac
>>> (%i2) display2d : false
>>> (%o2) false
>>> (%i3) load(interpol)
>>> (%o3)
>> "/home/user/opt/maxima/share/maxima/5.27.0/share/numeric/interpol.mac"
>>> (%i4) h:makelist([k,(-2*(1+k)*(1+2*k))/(k*(2+k))],k,1,12)
>>> (%o4)
>>>
>> [[1,-4],[2,-15/4],[3,-56/15],[4,-15/4],[5,-132/35],[6,-91/24],[7,-80/21],[8,-153/40],[9,-380/99],[10,-77/20],[11,-552/143],[12,-325/84]]
>>> (%i5) ratinterpol(h,2)
>>> Unable to compute the LU factorization
>>> #0:
>>>
>> ratinterpol(tab=[[1,-4],[2,-15/4],[3,-56/15],[4,-15/4],[5,-132/35],[6,-91/24],[7,-80/21],[8,-153/40],[9,-380/99],[10...,r=2,select=[])(linearalgebra.mac
>>> line 310)
>>>    -- an error. To debug this try: debugmode(true);
>>> (%o5) "/home/user/ratinterpol.mac"
>>> --- output -------------
>>
>> Hello,
>>
>> ratinterpol calls linsolve_by_lu to solve a linear system that gives the
>> values of the coefficients of the two polynomials in the rational
>> function.
>>
>> In your example, the linear system built by ratinterpol is not
>> compatible. Maybe there is not any rational function with degree 2 in
>> the numerator such that it passes thru all the sample points. The degree
>> of the denominator is automatically calculated so that the there are as
>> many unknowns as equations.
>>
>> Perhaps you can change the second argument to ratinterpol and try other
>> degrees for the numerator.
>>
>> --
>> Mario
>>
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>>