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/expintegrals.html#si
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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