[Maxima] How to compose multi-variate polynomials?
Jonathan LF King
squash at math.ufl.edu
Sat May 6 23:56:45 CDT 2006
[repost: I have now subscribed to the Maxima list.]
I am working with 6 undergraduates on a Number Theory
project that involves exploring (integer coefficient)
polynomials. I am a complete beginner in Maxima.
The project involves looking for patterns in polynomials of
f(xvec) = f(x1,x2,...,xN)
where N is a value known at run-time. The polys
("polynomials") are typically the determinant of an NxN
matrix whose entries have been populated by polys.
Among the operations we'll want to do on polys is to factor
them: To see if f is a power of a simpler poly g. For
this, it it may be best to leave f as an *expression*, e.g
f_xvec : 3*x1*x7^4 + ...
We'll also need to *compose* polys, e.g suppose we have
H maps 2N-dimensional space to N-dim'al space, and
f,g1,g2 each map N-dim'al space to N-dim'al space.
We'll want to test if
equals f(xvec) .
Q1: How can I set-up my polys so that this type of
composition is easy to do?
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
(...except that the input-point [1,2,3] might be some other
kind of Maxima object other than a list.)
Sincerely, -Prof. Jonathan King
PS: I have figured out that maxima notation
define(funmake(f, makelist(concat( 'x,j) , j , 1,N)) , ''expression_in_xvec)
makes a fnc f(x1, ..., xN). But I haven't figured out how
to treat tuple (x1, ..., xN) as a single object, in terms
of polynomial composition.
Prof. Jonathan LF King Mathematics dept, Univ. of Florida
<squash at math.ufl.edu>, <http://www.math.ufl.edu/~squash/>
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