I was not very fond for defining sympy Add, Mul, Pow or Function
application for equation object because I don't think that the algebra of
equation looks well unifiable with other mathematical objects like Expr at
the first glance,
And I think that it's important to introduce Add, Mul, Pow, or function
application for Expr or at least the mathematical objects that are
conceptually unifiable with Expr.
We automatically arrive to a conclusion that we need to define unevaluated
sympy functions like `Add(eq1, eq2, evaluate=False)`, `sin(eq,
evaluate=False)`, once we define how to define function application for
them.
And we would also arrive in questions like: If equation brings its own
algebra system, there should be an equation of equations? How should we
solve them?
On Sunday, February 7, 2021 at 8:29:58 PM UTC+9 Oscar wrote:
> On Sun, 7 Feb 2021 at 00:07, David Bailey <da...@dbailey.co.uk> wrote:
> >
> > Dear Group,
> >
> > While thinking about Jonathon's question, I came across this oddity:
> >
> > x=symbols('x')
> >
> > f=symbols('f',cls=Function)
> >
> > diff(f,x)
> >
> > 1
> >
> > Why 1? I think I would have expected it to generate a TypeError, just
> like f+x does.
>
> The problem is that an undefined function like f is actually a class.
> An object like f(x) is an instance of that class. When you do diff(f,
> x) that calls through to f.diff(x). The f class has a diff method but
> it is supposed to be called with an instance. Instead if you just call
> f.diff(x) then the diff method is called with x as the instance so
> what you get is equivalent to x.diff() which is treated as x.diff(x)
> which gives 1.
>
> It's like this:
>
> In [10]: class MyExpr(Expr):
> ...: def diff(self, *symbols):
> ...: print('self =', self)
> ...: print('symbols =', symbols)
> ...:
>
> In [11]: diff(MyExpr, x)
> self = x
> symbols = ()
>
> In [12]: diff(MyExpr(y), x)
> self = MyExpr(y)
> symbols = (x,)
>
> Ideally we should change it so that an undefined function like f is a
> Basic instance rather than a Basic subclass.
>
>
> Oscar
>
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