How to compose multi-variate polynomials?

Dear Barton Willis

    From: Barton Willis <willisb at unk.edu>
    Date: Sun, 7 May 2006 06:10:04 -0500

    > Q2: How can I define a poly f, so that f is
    > viewed as a 1-variable function, but the variable comes from,
    > say, 3-dim'al space and the output is a point in
    > 3-dim'al space? So, for instance, I can write
    >
    >  f(f(f([1,2,3])))  ?
    >
    > (...except that the input-point [1,2,3] might be
    > some other kind of Maxima object other than a list.)

    Maybe you want to do something like:

    (%i1) f(x) := block([x1 : part(x,1), x2 : part(x,2)], [-x2, -x1]);
    (%o1) f(x):=block([x1:part(x,1),x2:part(x,2)],[-x2,-x1])
    (%i2) f([1,4]);
    (%o2) [-4,-1]
    (%i3) f(f([1,4]));
    (%o3) [1,4]
    (%i4) f(f(f([1,4])));
    (%o4) [-4,-1]

I will look up the "part" operator.

    The function 'part' can be applied to (I think) any
    non-atomic object, so maybe something like this would
    work if the input to f was not a list. Does this help,
    or did I misunderstand?

    Good luck with your project.

Thank you.  At the moment, the students are away  are summer
break.  They are a lot more computer-savvy than I am...
                           --Jonathan 

-- 
Prof. Jonathan LF King   Mathematics dept, Univ. of Florida
<squash at math.ufl.edu>,   <http://www.math.ufl.edu/~squash/>;