Hi
I want to numerically evaluate the integral of a function f(x,y) over a
region defined by linear inequalities, for example
1/8<=y<=x<=1/3
x+y<=1/3.
I can do this with a repeated call to numerical_integral because I can
re-write the constraints as y<=min(x,1/3-x). However, this solution
isn't very satisfying in general. If I have more constraints and/or
more variables then working out the limits on the repeated integrals by
hand is going to be rather unpleasant.
Is there any way I can get sage to compute the integral directly from
the inequalities. For example, if I use a Polyhedron object to store
the region of interest is there any way of getting functions from it
which describe the limits of integration? Ideally, if P is a Polyhedron
it would be nice to have something like P.integral(f) which computes the
integral of f over P.
Many thanks
Alastair Irving
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