On 5/July/2017, Kitonum responded to the 3/July/2017 MaplePrimes question "How to perform double integration over subdomain" by providing code for a procedure IntOverDomain that implements Green's theorem applied to a planar region whose boundary is a simple, closed, rectifiable, oriented curve (SCROC by some authors).
I was intrigued. First, this is a significant extension of existing Maple functionalities. Second, the implementation admits boundaries defined piecewise with sections defined parametrically; or sections that are polygonal lines defined by a list of nodes.
But how was the line integral around such boundaries coded? In the worksheet "IntOverDomain_Deconstructed," I summarize the existing Maple functionality for implementing iterated double integrals over specified domains, then analyze how Kitonum coded Green's theorem as an extension of Maple's capabilities. After recognizing the great coding skills of Kitonum, I conclude with a short wishlist of related extensions that I would like to see added to Maple in the future.
Download the worksheet: IntOverDomain_Deconstructed.mw