On 04/04/12 15:39, Nils Bruin wrote:
> On Apr 1, 2:34 pm, Michael Orlitzky <mich...@orlitzky.com> wrote:
>
>> Substitution doesn't even work pre-evaluation:
>>
>> sage: f = function('f', x)
>> sage: f_prime = f.diff(x)
>> sage: g = function('g', x)
>> sage: f_prime.substitute_function(f,g)
>> D[0](f)(x)
>
> That's because you're trying to substitute expressions, not functions:
>
> sage: f,g
> (f(x), g(x))
>
I sort of buy that, but if,
sage: f = function('f', x)
doesn't make `f` a function, that's a user-interface WTF =)
It wouldn't matter if I could substitute them as expressions, but that
doesn't work either:
sage: f = function('f', x)
sage: g = function('g', x)
sage: f.diff(x).substitute_expression(f==g)
D[0](f)(x)
sage: f.diff(x).subs(f=g)
D[0](f)(x)
sage: f.diff(x)(f=g)
D[0](f)(x)
I reported a lot of these at,
http://trac.sagemath.org/sage_trac/ticket/11842
and later duped it to,
http://trac.sagemath.org/sage_trac/ticket/6480
which seems to be the first report of the problem.
> For that, you would have to use a different substitution function and
> it wouldn't have any effect anyway because the expression f(x) does
> not occur in f_prime.
>
> If you fix this, the substitution does work:
>
> sage: f = f.operator()
> sage: g = g.operator()
> sage: f,g
> (f, g)
> sage: f_prime.substitute_function(f,g)
> D[0](g)(x)
>
> There is a different issue, which is fixed by
> http://trac.sagemath.org/sage_trac/ticket/12801
>
After #12801, I'm having trouble reconciling these two examples:
sage: f = function('f', x)
sage: g = function('g')
sage: f.diff(x).substitute_function(f,g)
D[0](f)(x)
versus,
sage: f = function('f')
sage: g = function('g')
sage: f(x).diff(x).substitute_function(f,g)
D[0](g)(x)
It would be slightly better I think if the first example worked, but I
can live with using the second (although I never would have discovered
it on my own).
What I would /really/ like to be able to do is,
midpoint = (1/2)*( f(a) + f(b) )
and then approximate multiple functions by swapping out the symbolic `f`
for a real function like sine.
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