The second example given in the documentation for pade
doesn't work. With clisp, cmucl,and gcl, it produces
an error that 134217728 is not a list.
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The problem with the example in the documentation seems to
stem from this: the polynomial (1st argument) in taylor is
written in terms of X (majuscule), but the variable (2nd
argument) is said to be x (minuscule).
Here is a simpler example that shows the same behavior:
(%i1) t: taylor (1 + X, x, 0, 1);
(%o1)/T/ X + 1 + . . .
(%i2) pade (t, 1, 1);
Maxima encountered a Lisp error:
Type-error in KERNEL::OBJECT-NOT-LIST-ERROR-HANDLER: 1 is
not of type LIST
Now redo this example, but with the variable declared
appropriately in taylor:
(%i3) t: taylor (1 + X, X, 0, 1);
(%o3)/T/ 1 + X + . . .
(%i4) pade (t, 1, 1);
(%o4) [- -----, X + 1]
X - 1
Replacing "x" by "X" in the example so that it reads "ff:
taylor (<stuff>, X, 0, 10);" makes the calls to pade succeed.
This behavior is a bug of some kind, although I don't know
if it's a bug in pade or somewhere else.
I have fixed the example in doc/info/Series.texi so that it
Maxima version: 188.8.131.52cvs
Maxima build date: 11:16 2/26/2005
host type: i686-redhat-linux-gnu
lisp-implementation-version: 2.31 (released 2003-09-01)
Maxima version: 5.9.1
Maxima build date: 21:24 9/23/2004
host type: i686-pc-linux-gnu
lisp-implementation-type: CMU Common Lisp
Logged In: YES
Fixed in pade.lisp rev 1.7 - extend $pade to handle case where input
is constant w.r.t. taylor var.
(%i1) t: taylor(1+a, x, 0, 1);
(%o1)/T/ a + 1 + . . .
(%i2) pade(t, 1, 1);
(%o2) [a + 1]
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