> 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.
If I have to apologize, I should be. I would not want to see this thread contaminated by arguments by university major, job experience, ... and which makes the conversation toxic and look like a fallacy overall. On Thursday, December 29, 2022 at 2:34:54 AM UTC+2 S.Y. Lee wrote: > And at least the term-algebraic definition of computing total derivative, > is not evaluating dy/dx -> 0. In that sense, > if the chain rule is implemented faithfully, dy/dx itself becomes normal > form, such that no further computation is done for it. > And the triple product rule for derivative is implemented as something > like viewing derivative as fraction, which may not be very mathematically > sound reasoning, > but for practices in term rewriting, we try to detach the semantics and > try to solve problems only by syntax, which also gives a plausible > reasoning how to combine problem solving skills, and even more abstract or > deeper view of it. > > On Thursday, December 29, 2022 at 2:23:07 AM UTC+2 S.Y. Lee wrote: > >> 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/3eb0d701-c12f-4e30-9aa3-42a595ea83ccn%40googlegroups.com.
