PolyFactors

PolyFactors factors univariate polynomials over the integers.

PolyFactors uses the ZZX polynomial type and the ZZXFactoring routines from Victor Shoup's NTL (http://www.shoup.net/ntl/). He deserves most of the credit. PolyFactors just provides a GUI for input and output.

Input Polynomial:

x^2-3x+2

and click on the "Factor" button. Under "Factors" you should see:

x - 2

x - 1

The number of factors with degree 1 is 2.

So we now know (x - 2)(x - 1) = x^2 - 3x + 2. That last form is also acceptable to PolyFactors, as is any permutation of the terms. Now copy and paste:

x^4-x^3-x+1

You should see:

x^2 + x + 1

multiplicity = 2
x - 1

The number of factors with degree 1 is 2.
The number of factors with degree 2 is 1.

So (x^2 + x + 1)(x - 1)^2 = x^4-x^3-x+1

(x^2 + x + 1) is irreducible. It cannot be factored into smaller degree polynomials with integer coefficients.

The web site:

http://www.loria.fr/~zimmerma/mupad/

has some big polynomials with which you can test PolyFactors. Not all of them are suitably formatted for PolyFactors. The ones which work as they stand are: P1(x), P2(x), P3(x), P4(x), P5(x), and P7(x). Except for P7(x) they are compressed files. Double click them to uncompress. Open them with TextEdit. Copy and Paste the polynomial into PolyFactors. Don't worry about extra characters, PolyFactors will filter them out.

Dr. Robert M. Delaney
Emeritus Professor of Physics
Saint Louis University
delaneyrm@earthlink.net
delaneyrm@mac.com