[80] in mathematical software users group
multiple integral & pari
daemon@ATHENA.MIT.EDU (siman@BOURBAKI.MIT.EDU)
Fri Apr 23 17:28:10 1993
Date: Fri, 23 Apr 93 17:27:20 EDT
From: siman@BOURBAKI.MIT.EDU
To: msug@Athena.MIT.EDU
Hi Everybody,
I'm new to this mailing list, and I have a couple of questions about math
softwares.
First, is anybody here familar with a public domain software called "pari-gp"?
It's similar to maple etc, does not do a lot of symbolic manipulation, but is
*very* fast, primarily aimed at number theorists but good for others too. In
addition to using it as a calculator, one can use PARI routines in C programs;
it's the latter feature that I'd like to get some help.
Second, about numerical integration. I'd like to numerically integrate a
function with 4 variables:
\int_{ abs(x1), ... , abs(x4) <=1 } f(x1, ..., x4)
But maple's "int" function seems to accept functions of one variable only,
and I couldn't break my 4-fold integral into an iterated one. Any suggestion
as to what I can do?
(my integral is concentrated near the origin, so if I were to break the
region of integration into grid, it would have to be a *very* fine one, and
hence a real pain...)
Incidentally, suppose the integral does break up into an iterated integral:
/a /a(x1) /a(x1,x2) /a(x1,x2,x3)
| | | |
| | | | f(x1, ..., x4) dx4...dx1
| | | |
/b /b(x1) /b(x1,x2) /b(x1,x2,x3)
then what should I do? --- the point is that, even in this case, the three
inner integral's limit of integration are *functions*, not just numbers.
I'm happy to use mathematica to do the calculation, but it doesn't seem to
like multiple integral either...
Thanks!
Siman
