"quotient is not exact" with Taylor series expansion?
Subject: "quotient is not exact" with Taylor series expansion?
From: wheigl at mines
Date: Thu, 4 Aug 2005 13:42:55 -0600
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 ) + . . .