"quotient is not exact" with Taylor series expansion?
Subject: "quotient is not exact" with Taylor series expansion?
From: Richard Fateman
Date: Thu, 04 Aug 2005 13:21:25 -0700
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 ) + . . .
>
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