Constant of integration (Was Re: sqrt(x)*sqrt(x))

Well, you are right.  I am the same way.  I don?t know Lisp so I would have 
a very hard time fixing anything that I see as wrong with Maxima.  I can 
extend it with Maxima code, but that is as good as I can do.  I would like 
to be taught Lisp.  You can?t read minds, programming languages are 
invented, so you need someone already trained by the original writers of 
Lisp or one of their disciples to translate for you until you can understand 
on your own. Then you become a disciple too and can train others and so on . 
. .

As far as the + C is concerned.  Actually I was not really criticizing the + 
C but the thread that has been going on forever it seems about sqrt(x^2) = 
abs(x).  I think I should say I like the absolute value function, some 
people don't.  They are not right, they just don't like it.  Maybe because 
it's not invented by them I guess.

I think abs_integrate and pw are cool.  I like being able to use abs(), 
signum(), iif(), %if(), unit_spike(), between() and unit_pulse() to 
represent piecewise functions.  They are like building blocks, you can make 
any piecewise continuous function from these basic building blocks.  You 
don't even need all of them. Just one or two suffices in most cases.  pw.mac 
allows you to use any of the above.  So what?  It is just a truth.  I don't 
like Maxima's prejudice against using these functions even when the answer 
is clearly an unexpected or expected piecewise continuous function.  Why is 
the following not just equal to %pi*exp(-abs(2*%pi*t))?  I can make it so 
but not with Lisp.  By the way, who taught me Maxima.  I don't really know. 
I watched coding in Maxima being presented to the list and I caught on. 
Total immersion maybe, I guess :)

(%i2) integrate(1/(x^2+1)*exp(-2*%i*%pi*x*t),x,minf,inf);
Is  t  positive, negative, or zero?p;
                                                                             
                            - 2 %pi t
(out2) 
%pi %e
(%i3) integrate(1/(x^2+1)*exp(-2*%i*%pi*x*t),x,minf,inf);
Is  t  positive, negative, or zero?

n;
                                                                             
                             2 %pi t
(out3) 
%pi %e

Rich


From: Raymond Toy
Sent: Friday, February 11, 2011 11:30 PM
To: maxima at math.utexas.edu
Subject: Constant of integration (Was Re: sqrt(x)*sqrt(x))

On 2/11/11 5:48 PM, Rich Hennessy wrote:
?There is no convenient way of telling Maxima that it should consider only 
real numbers . . .?

Inconvenience is not an excuse.  On a related issue.  It is complete 
inexcusable that Maxima does
Sure it is.  It's inconvenient for you to fix the things you don't like 
because it's inconvenient for you to learn the necessary stuff to do it.

Well, that's the excuse I use, anyway.  Works for me. :-)


not know that integrate(x,x) = x^2/2+C.  Maxima always forgets to add the C.

Why is this important?  Does any other CAS do that?  No table of integrals I 
know of does this.  I vaguely remember it being mentioned in high school 
calculus, but I don't think we were expected to answer every integration 
question with a + C term added.

Ray



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