"quotient is not exact" with Taylor series expansion?

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
> >  
> >
> 
>