12.04.2011 02:20, Aaron S. Meurer пишет: > On Apr 11, 2011, at 4:12 PM, Alexey U. Gudchenko wrote: > >> 12.04.2011 01:56, Ronan Lamy пишет: >>> Le lundi 11 avril 2011 à 15:42 -0600, Aaron S. Meurer a écrit : >>>> On Apr 11, 2011, at 2:25 AM, smichr wrote: >>>> >>>>> Should `Integral(x, (x, 1, 2)) == Integral(y, (y, 1, 2))` be True? If >>>>> so, smichr branch 2068b has a commit that makes this testing possible. >>>>> >>>> This is a good question. For one thing, == is not mathematical >>>> equality but exact equality, so there is no reason why it should have >>>> to be True. So my initial response is that no, it should not. >>>> >>> I think it should. x and y are bound symbols that have no meaning >>> outside the integrals, so their identity should be completely >>> irrelevant. In fact, they should probably be replaced with dummies upon >>> instantiation of the Integral. >>> >>> >> >> Mathematically equal. (especially when assumptions for symbols are equal >> too). >> >> Another question what means "==" in SymPy: mathematical >> or not (pythonic?). >> >> Aaron, what do you mean by "exact equality"? >> E.g Does the "Max(1, 2, x)" exact equal to the "Max(2, x)" or not? >> >> >> -- >> Alexey U. > > "Exact" meaning it checks if the objects are equal. The usual example is > that we have > >>>> (x + 1)**2 == x**2 + 2*x + 1 > False > > I thought Max(1, 2, x) automatically reduced to Max(2, x). In that case, > then, obviously they would be equal with ==. Also you would have Max(2, x) > == Max(x, 2) because it internally uses a data structure that does not care > about order (set or frozenset).
> Whenever you see == in SymPy, it is specifically assuming this exact/object > equality. > > Another thing to consider is: > > In [190]: hash(Integral(x, (x, 0, 1))) > Out[190]: -9173880960074697984 > > In [191]: hash(Integral(y, (y, 0, 1))) > Out[191]: −299967655319032172 > > A == B should imply hash(A) == hash(B). > > Aaron Meurer > About Max, you are right exactly. But why not to use data structure in Integrals too (do not care about dummy variable) ? -- Alexey U. -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
