Hello Oscar. Thank you very much for the reply. Yes, I am indeed looking at the source. I think Faisal identified the problem in his response and I look forward to being a part of the discussion to address it. The SymPy community seems very open, and I appreciate that.
Joe Heafner Sent from my iPad > On Jul 19, 2021, at 05:37, Oscar Benjamin <oscar.j.benja...@gmail.com> wrote: > > Hi Joe, > > The vector integration functionality is relatively new. It was added > last year I think in a GSOC project. It's possible that this is a bug > or a corner case that wasn't fully considered. > > Have you looked into the code at all? > > Oscar > >> On Sun, 18 Jul 2021 at 00:19, Joe Heafner <heafn...@gmail.com> wrote: >> >> Hello everyone. >> >> I teach undergraduate physics and have used Python, specifically VPython, >> for going on 20 years although I am by no means an expert. I am interested >> in incorporating computation (with Python using Jupyter Notebook) into >> introductory calculus-based mechanics and electromagnetic theory courses. I >> have an MS in physics and have taught for 30 years. I am a Python and LaTeX >> evangelist. >> >> I am relatively new to SymPy and am amazed at its power. I want to bring >> this power into the introductory undergraduate physics curriculum. >> >> Now that you know a bit about me, I have some questions about orienting >> surfaces defined with ParametricRegion. After a lot of online searching, I >> found this discussion >> >> https://github.com/sympy/sympy/issues/19320 >> >> which doesn't seem to address my questions so was directed here by the SymPy >> Twitter feed. >> >> Here is my specific situation. Consider the integral of a vector field over >> a surface to calculus flux. >> >> from sympy import * >> from sympy.vector import * >> C = CoordSys3D('C') >> a, b, c = symbols('a b c', positive=True) >> x, y, z, F = symbols('x y z F') >> F = 3*(-C.k) # F points in the -z direction >> >> Consider a square with vertices (0,0),(5,0),(5,5),(0,5). Treat the square as >> a Type 1 region, doing the y integral first. >> >> square = ParametricRegion((x,y),(,y,0,5),(x,0,5)) >> vector_integrate(F, square) >> >> I get 75 as the answer, which means that square must have an orientation in >> the -z direction. I can justify that by noting that the order in which I >> defined the parameters implies such an orientation ( yhat \times xhat = >> -zhat) >> >> Now if I treat the square as a Type 2 region, doing the x integral first, I >> get a different answer. >> >> square = ParametricRegion((x,y),(x,0,5),(y,0,5)) >> vector_integrate(F, square) >> >> I get -75 as the answer, which means that square must have an orientation in >> the +z direction. I can also justify this because note that I reversed the >> order of the parameter definitions (xhat \times yhat = +zhat). Reversing the >> definitions reverses the surface's orientation. No problem. >> >> Now here's where my trouble begins. Consider now a triangular region with >> vertices (0,0),(5,0),(0,5). Treat the triangle as a Type 1 region, doing the >> y integral first. >> >> triangle = ParametricRegion((x,y),(x,0,5),(y,0,5-x)) >> vector_integrate(F, triangle) >> >> I get 75/2, which means triangle must have an orientation in the -z >> direction. This does NOT seem to follow the convention from the previous >> example since I specified the parameter definitions in the order that I >> thought would give triangle an orientation in the +z direction but >> apparently that is wrong. Unlike with square, reversing the order of the >> parameter definitions doesn't change the orientation. >> >> Now if I treat the triangle as a Type 2 region, doing the x integral first I >> get a different answer. >> >> triangle = ParametricRegion((x,y),(x,0,5-y),(y,0,5)) >> vector_integrate(F, triangle) >> >> I get -75/2, which means triangle must have an orientation in the +z >> direction, which, again, doesn't match my intuition from the square example. >> Also once again, reversing the order of the parameter definitions doesn't >> change the orientation. >> >> With square, I can EITHER change the order of the parameters themselves >> (e.g. (x,y) vs. (y,x)) OR change the order of the parameter definitions >> (e.g. (x,0,5),(y,0,5) vs. (y,0,5),(x,0,5)). >> >> With triangle, it seems that changing the order of the parameters themselves >> (e.g. (x,y) vs. (y,x)) DOES change the surface's orientation but changing >> the order of the parameter definitions DOES NOT. If I keep the order of the >> parameters the same (e.g. always (x,y)) then the only way to change >> triangle's orientation is to treat it as either a Type 1 or Type 2 region. >> >> Here is my ultimate question. What rule(s) is/are used internally to orient >> a surface and why does the rule(s) appear to be different for different >> surfaces as I have presented here? How/why does a Type 1 region's >> orientation differ from a Type 2 region's orientation? They seem to collapse >> to behavior with square when the integral is the same regardless of whether >> it's written for a Type 1 or Type 2 region. I have never seen that addressed >> in calculus UNLESS different forms are used. Am I missing something obvious? >> Am I missing something subtle? I can't seem to find a consistent SymPy rule >> for surface orientation. Does one exist? >> >> I look forward to responses! >> Joe >> >> -- >> You received this message because you are subscribed to the Google Groups >> "sympy" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to sympy+unsubscr...@googlegroups.com. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/sympy/2a688b87-2616-49ab-b62e-42b417b48cb5n%40googlegroups.com. > > -- > You received this message because you are subscribed to a topic in the Google > Groups "sympy" group. > To unsubscribe from this topic, visit > https://groups.google.com/d/topic/sympy/zy9gQH9gMvQ/unsubscribe. > To unsubscribe from this group and all its topics, send an email to > sympy+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/CAHVvXxRcbYHAcncvcMtdURGQ134RD9XevcyvBDhGFumeaTP2wg%40mail.gmail.com. -- You received this message because you are subscribed to the Google Groups "sympy" group. 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