Re: [Maxima-discuss] Integrating piecewise defined functions

[Barton W. <wi...@un...>]

(%i1) load(abs_integrate)$

(%i2) f(x) := (signum(x) - signum(x-1))/2$

(%i3) g(x) :=  x*f(x)$

(%i4) integrate(f(t) * g(x-t),t,0,x);
"Is "x" positive, negative or zero?"p;

(%o4) (signum(x-2)*signum(x-1)*x^2-2*signum(x-1)*x^2+signum(x-2)*x^2-2*signum(x-2)*signum(x-1)*x+2*signum(x-1)*x-2*signum(x-2)*x+2*x
-(signum(x-2)*signum(x-1)*(x-1)^2)/2+(signum(x-1)*(x-1)^2)/2-(signum(x-2)*(x-1)^2)/2+(x-1)^2/2+(signum(x-2)*signum(x-1))/2-signum(x-1)/2+
signum(x-2)/2-1/2)/4

(%i5) integrate(f(t) * g(x-t),t,0,x);
"Is "x" positive, negative or zero?"n;
(%o5) 0

Also, see https://sourceforge.net/projects/piecewisefunc/

--Barton

________________________________
From: El Observatorio De Matemática <obs...@gm...>
Sent: Thursday, November 28, 2024 12:57
To: Andrei Zorine <zoa...@gm...>; Eduardo Ochs <edu...@gm...>; <max...@li...> <max...@li...>
Subject: Re: [Maxima-discuss] Integrating piecewise defined functions

Caution: Non-NU Email

Here is a version of the pw package:
https://github.com/jlapeyre/mext/tree/master/packages/pw<https://urldefense.com/v3/__https://github.com/jlapeyre/mext/tree/master/packages/pw__;!!PvXuogZ4sRB2p-tU!A3qyT2ZYs3LXl7V6DWM7fes6dX9tDelXhnHbSCpqgYycc9ctTml9y8Z_rUtMvQz9YvH54PLfyQOy2URadUIVaO1PDQ$>

El jue, 28 nov 2024 a las 13:30, Andrei Zorine (<zoa...@gm...<mailto:zoa...@gm...>>) escribió:
Hi, Eduardo!
There was a PW package by Richard Hennessy. It's still available online if you search, but it's unmaintained and abandoned. The latest version is 6.5.
When I tried to use it, it reported a syntax error which I had to fix manually; I removed "_funcs" symbol from the list of block variables inside of 'pwint' function definition. Now it works fine.

As to your example, try
load(pw)$
 f(x) := ''(piecewise( [minf, 0, 0, 1, 1,0, inf], x))$
g(x) := ''(piecewise( [minf, 0, 0, x, 1,0, inf], x))$
pwint(f(t)*g(x-t), t, -2, 2);

Best wishes,
Andrei Zorine

чт, 28 нояб. 2024 г. в 00:59, Eduardo Ochs <edu...@gm...<mailto:edu...@gm...>>:
Hi list,

what is the recommended way to integrate piecewise defined
functions? I tried this,

  f(x) := if     x<0 then 0
          elseif x<1 then 1
          else            0;
  g(x) := if     x<0 then 0
          elseif x<1 then x
          else            0;
  h(x) := integrate(f(t)*g(x-t), t, -2, +2);

and I couldn't find a way to make Maxima calculate this
integral...

        integrate(f(x), x, -2, 4);
  float(integrate(f(x), x, -2, 4));

The convolution left Maxima even more confused, obviously...
Thanks in advance!
  Eduardo Ochs
  http://anggtwu.net/eev-maxima.html<https://urldefense.com/v3/__http://anggtwu.net/eev-maxima.html__;!!PvXuogZ4sRB2p-tU!A3qyT2ZYs3LXl7V6DWM7fes6dX9tDelXhnHbSCpqgYycc9ctTml9y8Z_rUtMvQz9YvH54PLfyQOy2URadUKVpdPbyg$>
  http://anggtwu.net/eev-qdraw.html<https://urldefense.com/v3/__http://anggtwu.net/eev-qdraw.html__;!!PvXuogZ4sRB2p-tU!A3qyT2ZYs3LXl7V6DWM7fes6dX9tDelXhnHbSCpqgYycc9ctTml9y8Z_rUtMvQz9YvH54PLfyQOy2URadUIEonogqg$>
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