< -----Original Message-----
< From: maxima-bounces at math.utexas.edu [mailto:maxima-bounces at math.utexas.edu]
<
< Subject: Suspicious behaviour of "residue"
However I've come across the following problem, involving residues :
<
< (%i1) set_display('ascii) $
< domain : complex $
< declare(N, integer) $
< H : 1 / (x*(x - x0)*(1 - x^N/y)) $
<
< (%i5) residue(H, x, 0);
< y
< (%o5) - ------------
< N
< x0 y - x x0
<
You can compute the residue from first principles and maxima
does it correctly in 2/3 cases:
(%i4) domain:complex$ declare(N,integer)$ H : 1/(x*(x-x0)*(1-x^N/y));
(%o6) 1/(x*(x-x0)*(1-x^N/y))
(%i7) limit(x*H,x,0);
Is N+1 positive, negative, or zero?
p;
Is N positive, negative, or zero?
p;
(%o7) -1/x0
(%i8) limit(x*H,x,0);
Is N+1 positive, negative, or zero?
p;
Is N positive, negative, or zero?
z;
(%o8) -y/(x0*y-x0)
(%i9) is(x^0=1);
(%o9) true
-----------------------------------------------------
Bug: (I have filed a report),
(%i1) domain:complex$ declare(N,integer)$ H:1/((x-x0)*(1-x^N));
(%o3) 1/((1-x^N)*(x-x0))
(%i4) limit(H,x,0);
Is N+1 positive, negative, or zero?
n;
Is N an even number?
y;
(%o4) -1/x0 <-----incorrect answer
(%i5) H:subst(N=-N,H);
(%o5) 1/((1-1/x^N)*(x-x0))
(%i6) limit(H,x,0);
Is N-1 positive, negative, or zero?
p;
Is N an even number?
y;
(%o6) 0
(%i7) build_info();
Maxima version: 5.18.1
Maxima build date: 14:8 4/20/2009
host type: i686-pc-linux-gnu
lisp-implementation-type: CLISP
lisp-implementation-version: 2.47 (2008-10-23) (built 3448862542)
(memory 3449221717)
Leo.
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