# [Maxima] powerseries

Barton Willis willisb at unk.edu
Wed Jul 11 08:44:28 CDT 2007

I think the function %piargs (in trigi.lisp) is buggy (it's
possible that the bug is in %piargs-sin/cos).

Before 5.13, we need to fix this bug and append regressions tests
for them. Until then, do %piargs : false.

Barton

-----maxima-bounces at math.utexas.edu wrote: -----

To: Barton Willis <willisb at unk.edu>
From: Dan Gildea <gildea at pobox.com>
Sent by: maxima-bounces at math.utexas.edu
Date: 07/10/2007 08:10PM
cc: maxima at math.utexas.edu, Robert Dodier <robert.dodier at gmail.com>
Subject: Re: [Maxima] powerseries

On Mon, July  9, 2007 at 11:13AM, Barton Willis wrote:
> Question: Is this a rectform bug?
>
> (%i13) powerseries(1/(1+x+x^2),x,0)\$
> (%i14) rectform(%)\$
> Is  x   positive or negative? pos;
> (%i15) subst(inf=5,%);
> (%o15)
>
%i*((3*x^4)/(2*sqrt(3))+(3*x^3)/(2*sqrt(3))+(3*x)/(2*sqrt(3))+3/(2*sqrt(3)))-x^4+x^3-x+1

>
>
> (%i16) taylor(1/(1+x+x^2),x,0,5);
> (%o16) 1-x+x^3-x^4+...

rectform calls cos, which returns -1 to a fractional power:

(%i2) declare(x, integer);
(%o2) done

(%i3) cos( 2*%pi*x/3 );
(%o3) (-1)^(2*x/3)

(%i4) cos( 2*%pi*x/5 );
(%o4) cos(2*%pi*x/5)

(%i5) cos ( 7777777*%pi*x/7777778 );
(%o5) (-1)^(7777777*x/7777778)
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