On Fri, Jun 6, 2008 at 7:50 PM, Rickard Armiento <[EMAIL PROTECTED]> wrote:
>
> Hi,
>
> I recently discovered sympy and really like the idea of a symbolic
> math engine in python. I'm trying to learn how to use it, but I am
> confusing myself with how to work with generic functions. Any help is
> much appreciated.
>
> Sorry for being so verbose, but I thought that it might be helpful to
> see the process that got me into my current state of confusion...
>
> Just as a first test, this of course worked nicely:
>
> In [1]: sin(5*x).diff(x)
> Out[1]: 5*cos(5*x)
>
> So I was surprised that I couldn't do the same with a generic
> function:
>
> In [2]: f = Function("f")
> In [3]: f(5*x).diff(x)
> ** backtrace ending in core/function.py in __new__(cls, expr,
> *symbols, **assumptions)
> <type 'exceptions.TypeError'>: __new__() argument after * must be a
> sequence
This is a serious bug, thanks a lot for discovering it. This should
just work. I created a new issue for it:
http://code.google.com/p/sympy/issues/detail?id=877
>
> After digging into the framework I think I understood that the
> 'problem' is that the generic function I get out of Function("f") is
> not 'prepared' to be derived. Or, if you will, not assumed to be
> analytical.
Well, it's just a bug that needs to be fixed.
>
> So, based on the tutorial I instead created my own function like this:
> =======
> class myfunction(Function):
> nargs = 1
> def fdiff(self, argindex=1):
> return Function("myfunctionPrime")(self.args[0])
> =======
>
> This works fine:
> In [6]: myfunction(5*x).diff(x)
> Out[6]: 5*myfunction_prime(5*x)
>
> But, of course I want my function to be indefinitely derivable so that
> I can, for example, work with series expansions. So I fiddled around
> trying to create a clever fdiff implementation that adds a 'Prime' to
> the previous name. But, when trying to solve my problems with that
> approach I realized that it seems stupid to go for a specific function
> definition like this, and what I *really* would want is to subclass
> Function to an AnalyticalFunction and use as a generic function
> factory for functions with the relevant property. That is, I would
> like it to work like this:
>
> In [1]: f = AnalyticalFunction("f")
> In [2]: f(5*x).diff(x)
> Out[2]: 5*fPrime(5*x)
>
> And:
>
> In [3]: f(x).series(x,0,3)
> Out[3]: f(0) + x*fPrime(0) + x**2/2*fPrimePrime(0)+O(x**3)
>
> A first simple attempt was something along the lines of:
> =======
> class AnalyticFunction(Function):
>
> def fdiff(self, argindex=1):
> return AnalyticFunction(self.__class__.__name__+"Prime")
> (self.args[0])
> =======
>
> However, I just cannot get any subclass of Function to work as a
> general function factory! I always get something like this:
>
> In [1]: f = AnalyticalFunction("f")
> In [2]: f(1)
> ** backtrace ending in core/basic.py in __call__(self, *args,
> **removeme)
> <type 'exceptions.NameError'>: global name 'Function' is not defined
SymPy can what you need and I think you are doing things right -- I
need to go now, but I'll look into it in the afternoon (couple hours
from now) why it isn't working and how to fix it.
>
> So, given the complexity I have run into, I have clearly barked off in
> the wrong direction, right? All I wanted to do at this point was to
> work with general, derivable, functions. Where did I go wrong? Or is
> this part of sympy still very much work in progress?
Well, some things work already, e.g.:
In [1]: f(x).diff(x)
Out[1]:
d
──(f(x))
dx
In [2]: (f(x)**2).diff(x)
Out[2]:
d
2*f(x)*──(f(x))
dx
In [3]: f(f(x)).diff(x)
Out[3]:
d d
─────(f(f(x)))*──(f(x))
df(x) dx
>
> Thank you for your great work with sympy,
Thanks a lot for your feedback and I hope you weren't disappointed too
much -- SymPy is a young project, but we try to fix all such problems
that people find quickly and we always write tests for them, so that
they never happen again. I'll look into this in the afternoon and I
would appreciate very much if you could provide us feedback how *you*
would like things to work, so that things are easy to use and easy to
understand for new people coming to SymPy.
See you for now and I'll write soon after I figure out what's wrong,
now I need to go,
Ondrej
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