Can you link me to any discussions related to first-class symbolic functions? I want to know what have been tried and why they have failed, but I couldn't find it.
'D(sin) -> cos' seems good. It will be worth implementing. 2019년 12월 8일 일요일 오전 1시 54분 44초 UTC+9, Oscar 님의 말: > > I would like to make it so that functions like `sin` are first-class > symbolic objects, subclassing from Basic. There has been an abandoned > attempt to do that in the past. If we had that then we could have a > symbolic differentiation operator. > > I don't think I'd want normal SymPy functions to support things like > `sin + cos` but composition, symbolic inverse, differentiation etc > should work. I think we need functions to be first class objects in > order to have a differentiation operator so we can represent things > like f'(0) without using Subs as D(f)(0). > > I'm not sure what sort of differential operators we would want though. > You've proposed something like d/dx which differentiates with respect > to x. Actually one of the most useful possibilities that we could get > from a differential operator would be the possibility to differentiate > functions directly without needing any reference to an unnecessary > symbol as in `D(sin) -> cos`. In the context of multivariable > functions and partial differentiation maybe that would be something > like `D[2](atan2)`... > > -- > Oscar > > On Fri, 6 Dec 2019 at 09:37, JS S <[email protected] <javascript:>> > wrote: > > > > In the top docstring of core/function, such behavior is proposed. > > I also found it mentioned in https://github.com/sympy/sympy/issues/5105, > which was open 10 years ago... > > I know that using `rcall` on `Lambda(x,sin(x))+Lambda(x,cos(x))` will do > it, but it seems a bit verbose. > > > > I am currently developing modules for fluid mechanics, which are purely > dependent on sympy. (Hopefully, I want to contribute it to sympy after I'm > finished) > > In this module, what I plan to is to make 'Operator' class, which is a > subclass of Expr. > > It will have callable sympy class (not instance) as argument. > > Also, classes such as 'OperAdd' and 'OperMul' will be introduced. > > > > For example, it will behave like this: > > > > ``` > > >>> Operator(sin)(x) > > sin(x) > > > > >>> Operator(sin)+Operator(cos) > > OperAdd(Operator(sin), Operator(cos)) > > > > >>> Operator(sin) + cos # This will convert cos to Operator(cos) > > OperAdd(Operator(sin), Operator(cos)) > > > > >>> OperAdd(Operator(sin), Operator(cos))(x) > > sin(x) + cos(x) > > > > >>> 2*Operator(sin) > > OperMul(2,Operator(sin)) > > > > >>> OperMul(2,Operator(sin))(x) > > 2*sin(x) > > > > >>> Operator(sin)(cos) > > OperComposite(sin, cos) > > > > >>> OperComposite(sin, cos)(x) > > sin(cos(x)) > > ``` > > > > Perhaps, it may also have not-callable Expr instance as argument. > > ``` > > >>> Operator(1+x)(y) > > y + x*y > > ``` > > > > > > Also, I am planning to make differential operator class, named DiffOp, > which is a subclass of Operator. > > Instead of sympy class, it will have variables which will differentiate > the expression. > > DiffOp(x) will represent d/dx. > > > > ``` > > >>> DiffOp(x)(sin(x)) > > cos(x) > > > > >>> DiffOp(x)(DiffOp(y)) > > DiffOp(x,y) > > > > >>> DiffOp(x) + Operator(sin) + x > > OperAdd(DiffOp(x), Operator(sin), Operator(x)) > > > > >>> (DiffOp(x) + Operator(sin) + x)(x) > > 1 + sin(x) + x**2 > > ``` > > > > How is it? Will it be OK? > > > > -- > > 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 [email protected] <javascript:>. > > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/b26e04b9-d137-48ca-b40a-a9b7fdec645d%40googlegroups.com. > > > -- 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 [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/f11e98e9-78eb-4289-9b8f-84efe23f3b01%40googlegroups.com.
