On 7 Feb 2003, Wolfgang Jenkner wrote:
> Martin RUBEY <rubey@labri.fr> writes:
>
> > I think that it is a bad idea that (rat)coeff returns zero, if it can't
> > make the coefficient explicit, it should rather return 'ratcoeff...:
> >
> > (C1) ratcoeff((1+x)^k,x,2);
> >
> > (D1) 0
> > (C2) ratcoeff(x^k,x,2);
> >
> > (D2) 0
>
> But it does make the coefficient explicit (in the CRE representation
> (1+x)^k is just a polynomial in the indeterminate (1+x)^k, but you
> know that). IMHO the behaviour is perfectly consistent.
well, consistent to what? I think the behaviour is odd.
> You could use POWERSERIES and dig out the coefficients with PART or
> something.
Great idea, thanks (taylor doesn't work for (poly)^k for symbolic k,
powerseries does)
Some bugs (with questionmark):
1. Powerseries doesn't seem to remove its facts:
(I think this is well discussed that we need to think about keeping /
removing facts generated by programs. However, in this instance, there is
no user interaction...)
GCL (GNU Common Lisp) Version(2.5.0) Sun Nov 17 15:58:09 CET 2002
Licensed under GNU Library General Public License
Contains Enhancements by W. Schelter
Maxima 5.9.0rc3 http://maxima.sourceforge.net
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
This is a development version of Maxima. The function bug_report()
provides bug reporting information.
(C1) powerseries((1+x)^k,x,0);
INF
==== I1
\ x
> ------------------------
/ BETA(k - I1 + 1, I1 + 1)
====
I1 = 0
(D1) -------------------------------
k + 1
(C2) facts();
(D2) [KIND(I1, INTEGER)]
2.
(C3) prederror:false;
(D3) FALSE
(C4) if (a>0) then c else d;
(D4) IF UNKNOWN THEN C ELSE d
while it would be a LOT more useful if it returned
if (a>0) then c else d
3.
declare(f,linear) does not work if f is a function:
(C1) declare(f,linear);
(D1) DONE
(C2) f(x+y,x);
(D2) f(1, x) y + f(x, x)
(C3) f(e,x):=g(e,x);
(D3) f(e, x) := g(e, x)
(C4) f(x+y,x);
(D4) g(y + x, x)
(C5) declare(f,linear);
(D5) DONE
(C6) f(x+y,x);
(D6) g(y + x, x)
4. Question:
Why doesn't linearity extend to f(sum(e,i,a,b)) ?
Martin