> From: Lukasz Stafiniak [mailto:lukstafi at wp]
> My piecewise defined functions emerged from taking maximum of
> a number of
> polynomials (which in turn from taking a supremum of a
> polynomial in another
> variable), so they are continuous.
> I've started writing a tiny library for functions defined as e.g. [x =
> MINF, -x, x = -2, 2, x = 2, x, x = INF]. But then I've
> browsed the archive
> and found propositions to use 'boxcars' (U(x - a) - U(x -
> b)), U(x) = 0 for
> x < 0, 1 for x > 0. What do you think?
>
> Perhaps writing datatypes for mathematical objects from
> scratch, when they
> can be encoded in the existing machinery, is no good.
>
In case you want a simpler conceptual form; piecewise polynomial forms can
be represented directly by a series of Dirac delta functions of various
orders, stationed at the break points. This has some advantages doing
manipulation and spectral estimation.
Ray