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The basic multiple integral procedure of `ALIAS` is

IntegrateMultiRectangle(Func,Vars,Init)

that may be used as in this example:
IntegrateMultiRectangle(x*sin(y),[x,y],[[0,1],[0,1]]);

This procedure requires that the function is at least twice
differentiable.
A more sophisticated procedure is based on Taylor expansion. Its
syntax is

IntegrateMultiTaylor(Func,Vars,Init,N,Type)

where `N` is the order used for the Taylor expansion. If `N`
is large (i.e. say larger than 6) the remainder of the Taylor
expansion may be a very large expression, that may be difficult to
compile. `Type`, which should either "explicit" or "autodiff", may
be used to deal with this problem. If it is set to "explicit" the
remainder will be calculated exactly and be compiled as it is. If `Type` is set to "autodiff" the procedure will try to use forward
automatic differentiation
and elementary components identification
(see the procedures `Decompose_Diff` and `Auto_Diff`) to
reduce the compilation time. Still you cannot expect to be able to use
very large value for `N` if the integrand is complicated.

** Next:** Continuation for one-dimensional system
** Up:** Integration
** Previous:** Integral in one variable
** Contents**
Jean-Pierre Merlet
2012-12-20