I've found this letter in smc newsgroup... Please CC: the responces to
the author.
--
Good luck
-Boris
http://www.plmsc.psu.edu/~boris/
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From: David Ronis <ronis at gibbs>
Subject: Problem/Bug in Maxima?
Newsgroups: sci.math.symbolic
Message-ID: <2p715.78$_r3.43895@carnaval.risq.qc.ca>
Date: Mon, 12 Jun 2000 15:33:18 GMT
I've encountered what I think are two bugs in maxima. I need to do
iterated integrals of the form:
f[n](x):=p[n](x)+ W(x) + integrate(f[n-1](s[n-1]),s[n-1],0,x);
f[0](x):=0;
where p[n](x) is a low-order polynomial (defined explicitly) and W(x)
is an unknown function. I've decleared integrate linear.
Here's what happens (say for p[n](x):=x):
(C1) f[n](x):=p[n](x)+ W(x) + integrate(f[n-1](s[n-1]),s[n-1],0,x);
(D1) f (x) := p (x) + W(x) + INTEGRATE(f (s ), s , 0, x)
n n n - 1 n - 1 n - 1
(C2) f[0](x):=0;
(D2) f (x) := 0
0
(C3) declare(integrate,linear);
(D3) DONE
(C4) p[n](x):=x;
(D4) p (x) := x
n
(C5) f[1](x);
(D5) W(x) + x
(C6) f[2](x);
(D6) W(x) + (W(s ) + s ) x + x
1 1
If instead I try:
(C1) declare(integrate,linear);
(D1) DONE
(C2) p[n](x):=x;
(D2) p (x) := x
n
(C3) f[n](x):=p[n](x)+ W(x) + integrate(f[n-1](s),s,0,x);
(D3) f (x) := p (x) + W(x) + INTEGRATE(f (s), s, 0, x)
n n n - 1
(C4) f[0](x):=0;
(D4) f (x) := 0
0
(C5) f[1](x);
(D5) W(x) + x
(C6) f[2](x);
Is x positive, negative, or zero?
pos;
x x
/ /
[ [
(D6) W(x) + x + I W(s) ds + I s ds
] ]
/ /
0 0
(C7) f[3](x);
Is x positive, negative, or zero?
pos;
x s x s x x
/ / / / / /
[ [ [ [ [ [
(D7) W(x) + x + I I W(s) ds ds + I I s ds ds + I W(s) ds + I s ds
] ] ] ] ] ]
/ / / / / /
0 0 0 0 0 0
(C8) f[4](x);
Is x positive, negative, or zero?
pos;
x s s x s s x s
/ / / / / / / /
[ [ [ [ [ [ [ [
(D8) W(x) + x + I I I W(s) ds ds ds + I I I s ds ds ds + I I W(s) ds ds
] ] ] ] ] ] ] ]
/ / / / / / / /
0 0 0 0 0 0 0 0
x s x x
/ / / /
[ [ [ [
+ I I s ds ds + I W(s) ds + I s ds
] ] ] ]
/ / / /
Which is slightly better but still wrong. My questions are:
1. Why doesn't maxima do the trivial integral of x?
2. How do I get it to properly change the symbol used for the
integration variable and limits in multiple integrals?
David
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