Thanks kcrisman!!!
Maybe the choice of the function sin(x)/x was not a good one...i would
to extend the derivation for generally integral function (F(x)=int_a^x
g(t)dt) where does't exist a primitive of g. I try with some function
and my procedure seems to work.
Thanks!
On 27 Gen, 14:41, kcrisman <kcris...@gmail.com> wrote:
> On Jan 27, 7:51 am, Andrea Gobbi <andreamat...@gmail.com> wrote:
>
> > Hi!
> > Maybe I resolve it...:
>
> > def deriv(self, *args,**kwds): print args, kwds; return w(x)
> > f(x)=-x*x*x+1
> > w(x)=sin(x)/x
> > tc=3
> > def ef(self,x,parent=None):
> > return numerical_integral(w,tc,x)[0]
> > g=function('g',nargs=1,evalf_func=ef,derivative_func=deriv)
>
> Believe it or not, it wouldn't be too much harder to implement the
> sine integral Si(x) for Sage in general - as long as we had a reliable
> evaluation function in Pari, Scipy, mpmath, or somewhere. mpmath at
> least has
> it:http://mpmath.googlecode.com/svn/trunk/doc/build/functions/expintegra...
>
> I can't believe we don't have this already. Am I missing something -
> can someone else confirm this (though search_src and a Google search
> revealed nothing, and none of the usual suspects in sage/functions
> have it)?
>
> - kcrisman> In this way i can correctly compute for example the derivative of
> > f(integral(w)) as:
> > (diff(f(g(x)),x,1)
> > And the value assumed for example in 4
> > (diff(f(g(x)),x,1)(4).n())
>
> > and this works also for n-th-derivative.
>
> > I apologize if you waste time :-)
> > Thanks!
> > Andrea Gobbi
>
> > ---------- Forwarded message ----------
> > From: Andrea Gobbi <andreamat...@gmail.com>
> > Date: 2011/1/26
> > Subject: Integral functions
> > To: sage-support <sage-support@googlegroups.com>
>
> > Hi!
> > I have a question...I'm working with integral functions:
>
> > var('t,x')
> > f(t)=t^2
> > F(x)=integral(f,t,0,x)
>
> > and obviously:
>
> > F(x).derivative() give x^2 as result.
>
> > Now the question is: can i have the same result if f doesn't admit a
> > primitive? I think that when sage "sees" integral(f,t,0,x), tries to
> > compute a primitive G and then assigns to F the difference between
> > G(x) and G(0). In this way when i try to calculate the derivative of
> > F, the result is f.
> > For example:
>
> > var('t,x')
> > f(t)=t^2
> > F(x)=integral(sin(t)/t,t,1,x,assume(x>1))
>
> > I look at the reference manual and I find a section in which we can
> > force a funcion to have a rule for the derivation (pag. 252) but I
> > don't understand how to do this. Sorry for my awful english!
> > Thank you!
> > Best regards!
> > Andrea Gobbi
>
> > --
> > Andrea Gobbi
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