TOPICS
Search

Squarefree Factorization


Squarefree factorization is a first step in many factoring algorithms. It factors nonsquarefree polynomials in terms of squarefree factors that are relatively prime. It can separate factors of different multiplicities, but not factors with the same multiplicity. One way to find a squarefree factorization is to compute polynomial greatest common denominators iteratively.

The squarefree part (i.e., product of all distinct monic irreducible factors) of a monic nonconstant polynomial p in a field of characteristic zero is p/GCD(p,p^'), where p^' is the derivative of p.


See also

Factorization, Prime Factorization

This entry contributed by Bhuvanesh Bhatt

Explore with Wolfram|Alpha

References

Gathen, J. von zur and Gerhard, J. Modern Computer Algebra. Cambridge, England: Cambridge University Press, pp. 601-606, 1999.Geddes, K. O.; Czapor, S. R.; and Labahn, G. §8.2 in Algorithms for Computer Algebra. Amsterdam, Netherlands: Kluwer, 1992.

Referenced on Wolfram|Alpha

Squarefree Factorization

Cite this as:

Bhatt, Bhuvanesh. "Squarefree Factorization." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/SquarefreeFactorization.html

Subject classifications