You can do this in Maxima. There is an external add-on package that can
integrate piecewise functions call pw.mac that
I wrote. I don't know how to port it to Sage though.
You would do it this way in Maxima.
load(pw)$
assume(a>0,b<0,c>0)$
define(p(x), piecewise([-a,(3*b*x^2+3*c)/(6*a*c+2*a^3*b),a],x))$ /* a typical
piecewise function */
define(pdf(x), pwdefint(p(p)*p(x-p), p, minf, inf))$ /* this is the
convolution */
for i : 1 thru 10 do define(pdf(x), pwdefint(pdf(p)*p(x-p), p, minf, inf))$ /*
you can repeat it */
I suppressed the output because it is very messy.
Rich
--------------------------------------------------
From: "Nasser Abbasi" <n...@12000.org>
Sent: Friday, December 25, 2009 11:10 PM
To: "sage-support" <sage-support@googlegroups.com>
Subject: [sage-support] Re: Symbolic convolution usage Sage
>
>
> On Dec 22, 5:08 pm, Maxim <maxim.courno...@gmail.com> wrote:
>> Hi all!
>>
>> I'm trying to do something which I haven't seen any examples so far :
>> symbolic convolution. I know I can use lists or Piecewise defined
>> functions to do a convolution, but here my interest is the symbolic
>> solution.
>>
>> To illustrate an example, I would like to make a function that would
>> do something like that :
>>
>> def conv(func1,func2):
>> # variable change
>> var('t')
>> h(tau)=func1(tau)
>> x(tau)=func2(-tau+t)
>> # proper convolution returns y(t)
>> y(t) = integrate(h(tau)*x(tau),tau,-infinity,+infinity)
>> return y(t)
>>
> <SNIP>
>
> I do not know sage well enough, but can't one in Sage just pass the
> independent variable, say "t", as an additional argument to the conv()
> function and inside the conv() function, simply write the definition
> of the convolution integral?
>
> This is the convolution of your 2 given functions
>
> unit_step(t), exp(-0.5*t)*unit_step(t)
>
> So, in Mathematica, I write the following 4 lines of code:
>
> f1[t_] := UnitStep[t]
> f2[t_] := Exp[-0.5*t]*UnitStep[t]
> conv[f1_, f_, t_] := Integrate[ f1[tao]* f2[t - tao], {tao, -
> Infinity, Infinity} ]
>
> (*now do the convolution*)
> conv[f1, f2, t]
>
> Out[11]= (2. - 2./E^(0.5*t))*UnitStep[t]
>
> The above is y(t).
>
> Can't the above be translated to Sage?
>
> --Nasser
>
>
> --
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