I have updated pw.mac.
Now you get.
pwint(sqrt(x^2-2*a*x+a^2),x);
(x^2/2-a*x+a^2/2)*signum(x-a)
pwint(sqrt(x^2+2*x+1)*sqrt(x^2-4*x+4),x);
signum(x-2)*(((2*x^3-3*x^2-12*x)/6-7/6)*signum(x+1)+9/2)
pwint(1/(sqrt(x^2-2*x+1)+1),x);
signum(x-1)*log(x)/2+log(x)/2+log(2-x)*signum(x-1)/2-log(2-x)/2
I have added these cases to the rtest_pw.mac file.
The link to the files are here, http://mysite.verizon.net/res11w2yb/id2.html
Rich
-----Original Message-----
From: Richard Hennessy
Sent: Friday, November 19, 2010 12:44 AM
To: Richard Fateman
Cc: Richard Fateman ; Maxima - list
Subject: Re: [Maxima] caps complex tests
Rich,
I think it is not a bad idea. I have decided to add this case to pw.mac.
That way integrate() can give the answer for the integration with the
assumption that sqrt(x^2)=x and pwint() and pwdefint() can use the other
interpretation, sqrt(x^2) = abs(x). Then users can use whichever integrate
command they think is right for their situation. It makes more sense to me
than any other idea. pwint() is designed for piecewise functions so if you
use it you should expect a piecewise function interpretation of radicals
like sqrt(x^2), if you use integrate then I would not expect that but I have
no say over what the group will decide to do for that case.
It may take a while to do this but I will get around to it soon. I have my
other studies right now.
Rich