On Wed, Sep 12, 2018 at 7:47 AM, Oscar Benjamin
<oscar.j.benja...@gmail.com> wrote:
> Hi,
>
> I was just looking at a way to solve ODEs algebraically and came up with the
> code below which almost works (just needs integration constants). I have a
> few questions though.
>
> 1. What is the right way to define an arbitrary invertible function and its
> inverse?
I believe so. There was an issue about being able to make undefined
functions invertible (I can't find it right now), but it isn't
implemented.
>
> 2. Is the code below abusing doit() or is that a reasonable way to use it?
It's fine. The only potential issue is that it will also evaluate any
other unevaluated subexpression.
>
> 3. Should I check for the inverses in __new__ or is there a better way to do
> that?
You shouldn't define __new__ on Function subclasses. Rather, define
the classmethod eval, which returns what the function should evaluate
to, or None if it shouldn't evaluate.
>
> 4. Does this represent a reasonable approach for something that could be
> implemented in dsolve?
As far as I know it should work. It might even solve weird ODEs like
>
> 5. How can I make a different integration constant each time I call
> intx.doit()?
I think there is a iterator in the dsolve module that gives new constants.
Aaron Meurer
>
> class diffx(Function):
> def __new__(cls, expr):
> if isinstance(expr, intx):
> return expr.args[0]
> else:
> return super().__new__(cls, expr)
> def inverse(self):
> return intx
>
> class intx(Function):
> def __new__(cls, expr):
> if isinstance(expr, diffx):
> return expr.args[0]
> else:
> return super().__new__(cls, expr)
> def inverse(self):
> return intx
> def doit(self):
> return Integral(self.args[0].doit(), x).doit() # + Symbol('C')
>
> eqn = diffx(x*diffx(f(x)))/x - exp(x)
> soln,= solve(eqn, f(x))
> print(soln.doit())
>
> --
> Oscar
>
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