"quotient is not exact" with Taylor series expansion?

You should not use %o7 in a batch file, but I figured out that the
first line is %o2..
  If you can check that the series are the same, perhaps by substituting
numbers for letters, it would boost confidence (if they agreed, anyway),
and that simplification format was the issue.
  If they come out differently, I suggest you start by making the
substitutions (numbers for letters) earlier, and see if you
can convince yourself that one or the other is correct.
Good luck.
RJF


wheigl@mines.edu wrote:

>Found a workaround: setting gcd:spmod allowed taylor(expr,x,0,6).
>However, even after simplification the taylor series is significantly longer
>than the result obtained through Mathematica.
>
>Thanks,
>Werner
>
>Quoting wheigl@Mines.EDU:
>
>  
>
>>Thanks, that worked for that square root function. However, a little further
>>in
>>my derivation I need the taylor series of a longer expression which gave a
>>different error:
>>
>>Maxima encountered a Lisp error:
>>
>> Type-error in KERNEL::OBJECT-NOT-TYPE-ERROR-HANDLER:
>>    (LAMBDA (X Y)
>>      (GREATERP (CAR X) (CAR Y))) is not of type (OR FUNCTION SYMBOL)
>>
>>Automatically continuing.
>>To reenable the Lisp debugger set *debugger-hook* to nil.
>>
>>Here is the batch file I used:
>>
>>--------------------------------------------------------------------------
>>/* Maxima batch file to derive series expansion of group velocity */
>>
>>vp2:(a+b*(sin(x))^2+sqrt(c+d*(sin(x))^2+e*(sin(x))^4))/2;
>>ratsimp(diff(sqrt(vp2),x,1));
>>subst(x,sin(x),%);
>>subst(sqrt(1-x^2),cos(x),%);
>>ratsimp(%);
>>subst(x,sin(x),vp2);
>>Vphi2:%o7+%o6^2;
>>gcd:ez;
>>taylor(%o8,x,0,6);
>>--------------------------------------------------------------------------
>>
>>Quoting Richard Fateman :
>>
>>    
>>
>>>try typing gcd:ez;
>>>and then run it again.
>>>it's a bug that has yet to be fixed involving interactions
>>>with polynomial gcd and (I think) non-rational objects like sqrt.
>>>
>>>RJF
>>>
>>>
>>>wheigl@mines.edu wrote:
>>>
>>>      
>>>
>>>>Dear colleagues,
>>>>
>>>>I'm facing the following problem in Maxima 5.9.1:
>>>>
>>>>I need to find the 6-term Taylor expansion of
>>>>
>>>>sqrt((a+b*x^2+sqrt(c+d*x^2+e*x^4))/2);
>>>>
>>>>but Maxima responds with error message "quotient is not exact". However,
>>>>        
>>>>
>>a
>>    
>>
>>>>4-term Taylor expansion works fine. See below. Any ideas?
>>>>
>>>>        
>>>>
>>>--------------------------------------------------------------------------
>>>      
>>>
>>>>(%i1) sqrt((a+b*x^2+sqrt(c+d*x^2+e*x^4))/2);
>>>>
>>>>                                4      2           2
>>>>                   SQRT(SQRT(e x  + d x  + c) + b x  + a)
>>>>(%o1)               --------------------------------------
>>>>                                  SQRT(2)
>>>>(%i2) taylor(%,x,0,6);
>>>>
>>>>quotient is not exact
>>>>-- an error.  Quitting.  To debug this try DEBUGMODE(TRUE);
>>>>(%i3) taylor(%o1,x,0,4);
>>>>
>>>>        SQRT(SQRT(c) + a)
>>>>(%o3)/T/ -----------------
>>>>             SQRT(2)
>>>>
>>>>                                                           2
>>>>  (SQRT(SQRT(c) + a) SQRT(c) d + 2 SQRT(SQRT(c) + a) b c) x
>>>>+ ----------------------------------------------------------
>>>>             (4 SQRT(2) a + 4 SQRT(c) SQRT(2)) c
>>>>
>>>>                         2
>>>>+ ((8 SQRT(SQRT(c) + a) c  + 8 SQRT(SQRT(c) + a) SQRT(c) a c) e
>>>>
>>>>                                                             2
>>>>+ (- 3 SQRT(SQRT(c) + a) c - 2 SQRT(SQRT(c) + a) SQRT(c) a) d
>>>>
>>>>                                                           2  2   4
>>>>- 4 SQRT(SQRT(c) + a) SQRT(c) b c d - 4 SQRT(SQRT(c) + a) b  c ) x
>>>>
>>>>             3                2                          2
>>>>/(32 SQRT(2) c  + (32 SQRT(2) a  + 64 SQRT(c) SQRT(2) a) c ) + . . .
>>>>
>>>>_______________________________________________
>>>>Maxima mailing list
>>>>Maxima@www.math.utexas.edu
>>>>http://www.math.utexas.edu/mailman/listinfo/maxima
>>>> 
>>>>
>>>>        
>>>>
>>>      
>>>
>>
>>_______________________________________________
>>Maxima mailing list
>>Maxima@www.math.utexas.edu
>>http://www.math.utexas.edu/mailman/listinfo/maxima
>>
>>    
>>
>
>
>
>  
>