integrate rational function over a polyhedral domain
Hi,
I would like to integrate (symbolically or numerically) a rational function on some polyhedral domain. As an example, my function would be:
sage: f(a,b,c) = 1/((a+b)^2 * c)
and my domain would be the unbounded polyhedron:
sage: I = [
....: [0,1,0,0], # a > 0
....: [0,0,1,0], # b > 0
....: [0,0,0,1], # c > 0
....: [-1,1,1,1], # a + b + c > 1
....: [1,-1,-1,0], # a + b < 1
....: [0,0,-1,1] # b < c
....: ]
sage: P = Polyhedron(ieqs=I)
Is it possible to do it in Sage? With some optional package? With some other software?
(Note for suspicious minds: the integral is finite.)
Sage has something for polynomial functions (via the
latte_intoptional package), seebut I'm not aware of something for more general rational functions.
The distinction between polynomial and rational function matters a lot: the integration of a polynomial over a polytope is a rational number (that can be computed exactly by
latte_int). With rational function, the result is very often transcendental and could also be infinite.