I think that the basic problem is just this (which is a bug): In [86]: expr = f(y(t)).diff(y(t))
In [87]: print(expr) Derivative(f(y(t)), y(t)) In [88]: print(expr.subs(t, 0)) Derivative(f(y(0)), y(0)) There is code to detect this in some cases but it doesn't work for your example. If y(t) was just t then you'd get: In [89]: expr2 = f(t).diff(t) In [90]: print(expr2) Derivative(f(t), t) In [91]: print(expr2.subs(t, 0)) Subs(Derivative(f(t), t), t, 0) The two cases diverge at this line: https://github.com/sympy/sympy/blob/6dd5c539952c2e8a6a611a421af373689709e726/sympy/core/function.py#L1693 Also yes you are right that this would be a lot easier if sympy had functions as first class objects and could represent abstract derivatives. -- Oscar On Tue, 5 Oct 2021 at 18:44, gu...@uwosh.edu <gu...@uwosh.edu> wrote: > Marcel, > > I believe you are correct that sympy has a problem with this. I ran into > issues when trying to define the behavior of integration and > differentiation for the equation class I have defined. Unfortunately, I am > completely swamped with committee and large class administration duties > right now, so cannot really spend time on this. My basic thoughts are that > to make this work well, SymPy would need to be expanded to include the > concept of a partial differential. I believe some of that has been > discussed on this list. I will write again, if I find time to dig up the > discussions. > > Jonathan > > On Tuesday, October 5, 2021 at 12:34:08 PM UTC-5 > m.ol...@jacobs-university.de wrote: > >> >> Hello, >> >> I am currently converting, for teaching purposes, a number of code >> examples from Mathematica to sympy in order to have a purely Python-based >> teaching environment (the numerical part has long been done in >> Numpy/Scipy). >> >> I have now run into a situation where I can get some code to work in a >> mathematically correct way, but produce output that makes me think I am not >> doing things quite right. >> >> The task is to use sympy to verify the order of a finite difference time >> integrator for an ODE (for the sake of simplicity, autonomous), which >> involves Taylor expanding the error with respect to the stepsize parameter, >> the substituting the differential equation and its derivatives. >> >> The attached code does just that, here with the implicit midpoint rule as >> a simple example. The issue I have is that sympy does not seem to have >> the notion of an abstract derivative, so the series expansion produces >> terms where Subs is used to represent derivatives with an argument that is >> not simply a symbol. In the end, however, I have to force evaluation with >> doit((), so that terms cancel properly, which has the side effect that all >> Subs are resolved and I get nonsense terms like >> >> Derivative(f(y(0)), y(0)) >> >> Of course, I could just ignore this as I have already achieved my goal, >> but I am trying to teach "good" sympy and this result strikes me as not >> being formulated the way it should. >> >> Any comments highly appreciated! >> >> Marcel >> > -- > 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/3a35d4c8-c439-4259-bf03-5ba8a27e4cf3n%40googlegroups.com > <https://groups.google.com/d/msgid/sympy/3a35d4c8-c439-4259-bf03-5ba8a27e4cf3n%40googlegroups.com?utm_medium=email&utm_source=footer> > . > -- 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/CAHVvXxTW0Dj1BDJBPM9W36L%2BXr-tv7dG9BDEMk6WGkUN-Es88g%40mail.gmail.com.
