Hi,

I think that the distinction between

def f(x):
    return x^2

and

f(x) = x^2

is a common source of confusion, and everyone will run into it when trying
to define piecewise functions. It would be possible to introduce a
decorator, say @symbolic_function, that makes sure that

@symbolic_function(x)
def f(x):
    return x^2

makes f a symbolic function. I've done just that in this published
worksheet:
http://www.sagenb.org/home/pub/4919

As you can see, it works with piecewise functions, too. Of course, it
should probably do something sane with multiple variables, class methods,
etc, but it seems possible.

I can probably produce a patch for this, but I would like some feedback
first.

Best regards,
Timo Kluck

2012/8/5 Timo Kluck <tkl...@gmail.com>

Unfortunately... "Public worksheets are currently disabled."

:(

--
*Andrea Lazzarotto* - http://andrealazzarotto.com*
*

Sorry, I didn't realize that. Here's the code.

---
def symbolic_function(variables, *args, **kwds):
    def result(f):
        def evalf_func(self,x,parent=None):
            if parent == None:
                return f(x)
            else:
                return parent(f(x))
        return function(f.__name__, variables, evalf_func=evalf_func,
*args, **kwds).operator()

    return result

@symbolic_function(x)
def steps(x):
    if x < 0:
        return -x
    elif x < 3:
        return x
    else:
        return 3

steps(5)

n(steps(5))

plot(steps(x),(x,-3,6))

On Aug 5, 10:28 am, Timo Kluck <tkl...@gmail.com> wrote:

Hi!

On 2012-08-05, Timo Kluck <tkl...@gmail.com> wrote:

Please excuse a stupid question of someone who doesn't use symbolic
functions or symbolic variables (I rather work with polynomials).

Why should one want to turn a Python function (or method) into a
symbolic function? I guess one couldn't do calculus (differentiate,
integrate) the resulting symbolic function, or can one? So, beyond
calculus, what can one do with a symbolic function that can't be done
with a Python function?

Best regards,
Simon

You can differentiate and integrate, but the result will be formal:

diff(steps(x),x)
D[0](steps)(x)

That's already more than you can do with Python functions. Additionally,
you can specify a derivative_func to the decorator that returns the exact
derivative.

Also, this allows you to use the function in an expression and have it
simplify. For example,

2*steps(x) - steps(x) - steps(x)

will be zero.

Hi Timo,

On Sun, 5 Aug 2012 10:12:41 -0700 (PDT)

This looks great. Can you upload your code to #7636 on trac.

http://trac.sagemath.org/sage_trac/ticket/7636

On Sun, 5 Aug 2012 10:28:43 -0700 (PDT)

It might be better to use the function_factory method from
sage.symbolic.function_factory instead of the top level function()
method. This would remove the need to specify the names of the
variables, then get the symbolic function using .operator().

You can get the number of arguments with f.__code__.co_argcount.

Cheers,
Burcin