I think that simplify or evaluation should rather be decomposed in many components such that 'simplify' is not a silver bullet solution, but users can mix in some components of 'simplify' to solve math problems in the very precise way what they want to. I still need some time to write out full proposal about this because I'm studying some part of it to fill in the gaps.
On Sunday, January 1, 2023 at 7:30:20 PM UTC+2 gu...@uwosh.edu wrote: > I agree that we should avoid arguments unrelated to the question at hand. > > For the part of this proposal that I think I understand (avoiding > evaluation/simplification unless requested), does this imply you want the > user to deal with collapsing expressions to avoid them becoming too large? > > Jonathan > > On Saturday, December 31, 2022 at 8:05:11 AM UTC-6 syle...@gmail.com > wrote: > >> > 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/b186b084-5146-40d5-93db-b2a51ea98254n%40googlegroups.com.
