Re: [Maxima-discuss] fourie.mac package fails for simple square wave

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

Here is a way to the simplification unit_step(X) + unit_step(-X) --> 1 without using matchdeclare. This simplification is OK for X real and nonzero.  Maybe the freeof(x,ax) check isn't wanted.

(%i1) load("opsubst")$

(%i2) unit_step_reduce(e,x) := block([a : gatherargs(e,'unit_step)],
           for ax in a do (
              ax : first(ax),
              if equal(imagpart(ax),0) and not freeof(x,ax) then (
                  e : ratsubst(1, unit_step(ax)+unit_step(-ax),e))),
          e)$

OK:

(%i13)      unit_step_reduce(x+unit_step(x) + unit_step(-x),x);
(%o13)      x+1

OK:

(%i14)      unit_step_reduce(x + unit_step(x) + unit_step(-x),z);
(%o14)      unit_step(x)+x+unit_step(-x)


Not wrong, but maybe not what you all want:

(%i15)      unit_step_reduce(x + 5*unit_step(x) - unit_step(-x),x);
(%o15)      6*unit_step(x)+x-1

--Barton
________________________________
From: Majzoub, Eric <eri...@um...>
Sent: Friday, March 15, 2024 15:57
To: rob...@gm... <rob...@gm...>
Cc: max...@li... <max...@li...>
Subject: Re: [Maxima-discuss] fourie.mac package fails for simple square wave

Caution: Non-NU Email


Hi Robert: Thanks for the reply.

I tried using tellsimpafter by itself and your suggestion with
matchdeclare as well. But the code in fourie.mac still returns the
wrong answer -- the coefficients are returned as functions of x, which
should integrated out.

In any case, the pdefourier package works and there is code
infrastructure for piecewise continuous functions there.

-Eric


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