I tried to "prove" the general case by using changevar(). I was afraid changevar would not work and I do lose the "abs(a)" and get
"a" instead so now I am not sure what went wrong or if my original answer was wrong. I can't find the error.
(%i1) display2d:false;
(out1) false
(%i2) integrate(f(x)*pwdelta(a*x-b),x);
(out2) 'integrate(f(x)*pwdelta(a*x-b),x)
(%i3) changevar(%,a*x-y,y,x);
(out3) ('integrate(f(y/a)*pwdelta(y-b),y))/a
(%i4) pwint(f(y/a)*pwdelta(y-b),y)/a; /* maybe this is where I went wrong */
(out4) f(b/a)*(signum(y-b)+1)/(2*a)
(%i5) subst(a*x,y,%);
(out5) f(b/a)*(signum(a*x-b)+1)/(2*a)
(%i6)
Rich
----- Original Message -----
From: "Richard Hennessy" <rich.hennessy at verizon.net>
To: "reyssat" <eric.reyssat at math.unicaen.fr>
Cc: "Maxima List" <maxima at math.utexas.edu>
Sent: Tuesday, March 31, 2009 11:58 AM
Subject: Re: [Maxima] Endless loop during definte integral
Basically I was trying to verify an identity for diracdelta using thin spiking functions (let sigma approach 0).
(%i4) integrate(x*pwdelta(a*x-b),x);
(out4) b*(signum(x-b/a)+1)/(2*a*abs(a))
I can use a gaussian instead, so it's no big deal.
Rich
----- Original Message -----
From: "reyssat" <eric.reyssat at math.unicaen.fr>
To: "Richard Hennessy" <rich.hennessy at verizon.net>
Cc: "Maxima List" <maxima at math.utexas.edu>
Sent: Tuesday, March 31, 2009 3:38 AM
Subject: Re: [Maxima] Endless loop during definte integral
Richard Hennessy a ?crit :
> I also noticed that it is not caused by the limits being inf and minf.
>
> assume(a>0,b>0,sigma>0,c<d)$
> f2(x):=(2*sigma^(3/2))/(%pi*x^4+2*%pi*sigma*x^2+%pi*sigma^2)$
> integrate(f2(a*x-b)*x^3,x,c,d); /* loops long time */
>
> I am trying it and will let it run for a hour or two and see if I get an answer.
>
> Rich
>
>
>
This is enough to get stuck :
integrate(1/(x^4+x^2+1),x,c,c+1);
However,
integrate(1/(x^4+x^2+1),x,10,11);
and
integrate(1/(x^4+x^2+1),x);
are ok.
Maxima version: 5.17.1
Maxima build date: 19:10 12/18/2008
host type: i686-pc-mingw32
lisp-implementation-type: GNU Common Lisp (GCL)
lisp-implementation-version: GCL 2.6.8
Eric
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