Hi.
I'm trying to evaluate a definite volume integral in a tetrahedral domain.
load("vect")
/* the integrand */
(%i42) tmpp: (x2/2+x1/2)*sin((%pi*(-x3/2-(-x3-x2-x1+1)/2+x2/2+x1/2))/2);
(%o42) (x2/2+x1/2)*sin((%pi*(-x3/2-(-x3-x2-x1+1)/2+x2/2+x1/2))/2)
/* The full triple integral */
(%i43) integrate(integrate(integrate(tmpp, x3, 0, 1-x1-x2), x2, 0, 1-x1), x1, 0
,1);
Is x2+x1-1 positive, negative, or zero?
....
It then continues to ask a number of (irrelevant?) sign questions. It
seems to give me the same result irrespective of what combination of
positive or negative I answer, which is:
(%o43) -(sqrt(2)*%pi^2+12*sqrt(2)*%pi-48*sqrt(2))/%pi^4
If I succesively take indefinite integrals and manually substitute the bounds I
get the same answer, without any asksign questions (I omitted some of the
intermediate results to save space):
(%i34) integrate(tmpp, x3);
(%o34) (x2/2+x1/2)*sin((%pi*x2)/2+(%pi*x1)/2-%pi/4)*x3(%i35) ev(%, x3:1-x2-x1)
- ev(%,x3:0);
(%o35) (-x2-x1+1)*(x2/2+x1/2)*sin((%pi*x2)/2+(%pi*x1)/2-%pi/4)(%i36)
integrate(%, x2);
(%o36) .....
(%i36) ev(%, x2:1-x1) - ev(%,x2:0);
(%o37) .....
(%i38) integrate(%, x1);
(%o38) ...
(%i39) ev(%, x1:1) - ev(%,x1:0);
(%o39) .....
(%i40) fullratsimp(%);
(%o40) -(sqrt(2)*%pi^2+12*sqrt(2)*%pi-48*sqrt(2))/%pi^4
Is there a good reason for the ask-signs when I ask integrate() to evaluate the
definite integrals that I am missing or is it a limitation of Maxima?
I also tried adding various assume() and declare() facts with no change in the
outcome:
(%i44) facts();
(%o44) [kind(.,commutative),kind(order,commutative),kind(x1,real),kind(x2,real),
kind(x3,real),kind(x4,real),-x3-x2-x1+1>=0,1>=x1,1>=x2,1>=x3,
x3+x2+x1>=0,x1>=0,x2>=0,x3>=0]
Thanks
Neilen
--
you know its kind of tragic
we live in the new world
but we've lost the magic
-- Battery 9 (www.battery9.co.za)