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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
Jean-Pierre Merlet