Fellow Maximists,
About functions defined piecewise, these are sometimes
defined using a function denoted U(x) := 1 if x > 0 and
0 otherwise (i.e., a unit step function). Then
U(x-a) - U(x-b) is a "boxcar" from a to b,
(U(x-a) - U(x-b))*f(x) is a restriction of f to [a,b],
and so on. Sometimes these constructions are used in
engineering.
If some such functions appear in an integrand, it
seems plausible that one could reformulate the integral
as a collection of integrals in which U doesn't appear,
but the limits of integration are modified.
Maybe if a derivative and antiderivative for U are
added to what Maxima knows, expressions involving U
could be handled.
A problem which I've attempted to solve before,
without success -- let V(x) := U(x) - U(x-1).
The convolution V*V*V*...*V is a piecewise polynomial
approximation to something proportional to e^{-x^2}.
What is the polynomial in each piece?
I don't know if defining piecewise functions via U
is more fruitful than via IF or COND, but it could
be worth investigating.
For what it's worth,
Robert Dodier
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