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
-----Original Message-----
From: Richard Hennessy
Sent: Sunday, November 14, 2010 9:25 PM
To: Richard Fateman
Cc: Richard Fateman ; Maxima - list
Subject: Re: [Maxima] caps complex tests
I just realized you defined PRI in a previous email on this thread. Since
it is not clear what x is in the case of radcan(sqrt(y^2-2*y+1)) then when
you apply the PRI you get y-1.
It is good to have flags like radexpand too. You have to have more than one
algorithm for simplification since different problems might require a
different answer. I don't think integrate(sqrt(1-2*y+y^2),x) can have just
one right answer.
I don't know if I should change pw.mac to handle this case. It's probably a
bad idea. I have to think about it.
pwint(sqrt(1-2*y+y^2),x)=?
Rich
-----Original Message-----
From: Richard Hennessy
Sent: Sunday, November 14, 2010 8:34 PM
To: Richard Fateman
Cc: Richard Fateman ; Maxima - list
Subject: Re: [Maxima] caps complex tests
I downloaded you paper yesterday. It does not define "positive real
interpretation" but it refers to it. Is there a precise definition of PRI
that will not cost me another chunk of change to download?
Rich
-----Original Message-----
From: Richard Fateman
Sent: Sunday, November 14, 2010 8:24 PM
To: Richard Hennessy
Cc: Richard Fateman ; Maxima - list
Subject: Re: [Maxima] caps complex tests
On 11/14/2010 4:59 PM, Richard Hennessy wrote:
> Speaking of interpretation. radcan(sqrt(y^2-2*y+1)) is using sqrt(x^2)=x
> so you get y-1. Well, why not 1-y instead as your example below points
> out?
>
> radcan(sqrt(y^2-2*y+1));
> -> y-1
>
There is one answer which corresponds to PRI (positive real
interpretation), which is y-1.
That is what radcan is supposed to return.
It does NOT return 1-y for sqrt((1-y)^2).
because that is not the PRI. y-1 is.
RJF
_______________________________________________
Maxima mailing list
Maxima at math.utexas.edu
http://www.math.utexas.edu/mailman/listinfo/maxima
_______________________________________________
Maxima mailing list
Maxima at math.utexas.edu
http://www.math.utexas.edu/mailman/listinfo/maxima