I think that software engineers should be satisfied for solving 'easy' and 'decidable' problems for derivative, like formal deriviative <https://en.wikipedia.org/wiki/Formal_derivative>, which is sometimes a sound reasoning for the actual physical/analytical derivative, however, not always. and even if you attempt to relate more physical implementation just by 'software engineering', I'd only warn that it would not be merely more than some 'heuristics', and such 'heuristics' are just going to define less uniform and awkward formal grammar <https://en.wikipedia.org/wiki/Formal_grammar> about the inputs the software it accepts, rather than making it more deeply connected with the physics.
Similar as how you'd usually perceive that numeric analysis need hypothesis about approximating the physical world problem by numeric errors, I also believe that any symbolic computation need hypothesis that it just approximates the the physical/business world problem as syntactical way. And to develop the useful and stable library, the only thing to concern is that we get at least the syntactical part correctly. On Thursday, December 29, 2022 at 12:13:19 AM UTC+2 gu...@uwosh.edu wrote: > S.Y., > > The only part of what you are proposing that I believe I understand is > that you suggest sympy should avoid automatic > evaluation/simplification/collapse of expressions. The specific example I > can think of where this would often be useful is with differentiation (the > default behavior of Derivative() does this, but not the convenience > implementation diff()). I have certainly had to be careful while trying to > define a partial derivative operation that works the way we usually use it > in the physical sciences (for thermodynamics in particular). Can you > illustrate how your proposal would provide a clean and mathematically sound > way of defining things such as a total differential (e.g. df = (df/dx)_y dx > + (df/dy)_x dy) and the derivative relationships they imply? Would this > ease the handling of the circularity of functional dependence implied by > the Euler circular chain rule used to figure out what combinations of > measurable quantities (partial derivatives) will provide values for partial > derivatives that cannot be measured directly? > > I appreciate your interest in helping to improve the open source > mathematical offerings. Can you provide a baby implementation that does not > impinge on the intellectual property of your employer (Qanda) for us to > consider? > > A word to the wise: I know you are not a native English speaker. However, > I think you need to be more careful about broad statements such as the one > below. > > On Wednesday, December 28, 2022 at 1:35:17 PM UTC-6 syle...@gmail.com > wrote: > >> >> I believe that my prompt can already address and solve the problem below, >> and beyond the fact that the calculus is merely Turing-complete >> (such that we can develop a library to be closed against anti-pattern >> <https://en.wikipedia.org/wiki/Anti-pattern> practices by developers for >> stability), >> it also provides pretty much well-studied and uniform representation for >> the application, without introducing some deviated object by some nerds and >> having poorly defined calculus over it. >> >> - Abstract algebra <https://github.com/sympy/sympy/pull/19750> >> - Decimal object <https://github.com/sympy/sympy/issues/17648> >> - Algebra with SymPy <https://github.com/gutow/Algebra_with_Sympy> >> - ... >> > > I, like you, am not a mathematician by training. Your training is in > engineering mine is in physics/chemistry. I do not claim to be cognizant of > all details necessary to generate completely general representations of > many mathematical operations. Thus, I am always happy to get issues with my > understanding corrected. However, I have been working with and teaching > about the multidimensional partial differential equations of quantum > mechanics and thermodynamics for longer than you've been alive. They are > very specific applications of calculus over a well specified domain. Please > do not belittle things that allow physical scientists such as myself to > work effectively in that domain. I suggest in the future you provide > specific examples of where these tools do not work and then we can address > those specific issues. It may be that a more general implementation that > can then be used to easily provide the same behavior is possible, but we > need specific examples. > > Regards, > Jonathan > -- 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/8462c206-e687-4a8e-b960-5578736358e4n%40googlegroups.com.
