>
>
> I am in the process of learning Sage, coming from Maxima (and Mathematica,
> which I do not like much...).
> Cut'n'pastes from a notebook running on sagenb.org
> version()
>
> version()
>
> ==>
>
> 'Sage Version 5.4, Release Date: 2012-11-09'
>
> var('t,a,b,d')
> ## beta density
> dbeta(t,a,b)=t^(a-1)*(1-t)^(b-1)/beta(a,b)
> ## density of the *difference* of two independent beta(1,1)-distributed RVs
> ## (yes, I mean uniforms(0 1)...)
> integrate(dbeta(t,1,1)*dbeta(t+d,1,1),t,max(0, -d), min(1,1-d))
>
> ==>
>
> 1
>
> Huh ?? This is seriously whacky :
>
>
>
You might want to see what "max(0,-d)" does. The function "max_symbolic"
should do what you want, though I don't know whether your integration will
work. Hopefully it would.
> dbeta(t,a,b):=t^(a-1)*(1-t)^(b-1)/beta(a,b)
> integrate(dbeta(t,1,1)*dbeta(t+d,1,1),t,max(0,-d),min(1,1-d))
>
> ==>
>
> dbeta(t,a,b):=t^(a-1)*(1-t)^(b-1)/beta(a,b)
> min(1,1-d)-max(0,-d)
>
>
>
I'm also not sure what the := notation would mean here in Sage; that's
Maxima style, right?
> But another one : i tried to give dbeta a proper definition, i. e. with a
> domain of definition, therefore allowing convolutions :
>
>
> db2(t,a,b)=Piecewise([[(0,1),t^(a-1)*(1-t)^(b-1)/beta(a,b)]])
> db2
>
>
You would get this even with
db2(x) = Piecewise([[(0,1),x^2]])
because piecewise functions do not accept this construction.
db2 = Piecewise([[(0,1),x^2]])
works. Unfortunately, I'm not so sure the three-variable equivalent is
much better here, as this (now very old) class was designed for
single-variable constructs (though it does support convolution in that
context). You may want to use pw.mac inside Maxima for this, I'm not sure.
Or there might be a way to trick a lambda function to make this work.
I'm sorry that our piecewise support is not the greatest. It's a
longstanding annoyance.
- kcrisman
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