Cantor–Zassenhaus algorithm: Difference between revisions

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In [[Computational mathematics|computational]] [[Abstract algebra|algebra]], the '''Cantor–Zassenhaus algorithm''' is a well known method for factorising [[polynomial]]s over [[finite field]]s (also called Galois fields).

The algorithm consists mainly of exponentiation and polynomial [[greatest common divisor|GCD]] computations. It was invented by D[[David G. Cantor]] and [[Hans Zassenhaus]] in 1981.

It is arguably the dominant algorithm for solving the problem, having replaced the earlier [[Berlekamp's algorithm]] of 1967. It is currently implemented in many well-known [[computer algebra system]]s.

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==References==

*{{citation

* {{cite journal|title=A New Algorithm for Factoring Polynomials Over Finite Fields

| last1 = Cantor | first1 = David G. | author1-link = David G. Cantor

|author=David G. Cantor, Hans Zassenhaus

| last2 = Zassenhaus | first2 = Hans | author2-link = Hans Zassenhaus

|journal=Mathematics of Computation

| date = April 1981

|volume=36

| doi = 10.1090/S0025-5718-1981-0606517-5 }}

| issue = 154

|date=April 1981

| journal = [[Mathematics of Computation]]

|pages=587–592

| jstor = 2007663

| mr = 606517

| pages = 587–592

|ref=harv

| title = A new algorithm for factoring polynomials over finite fields

|doi=10.1090/S0025-5718-1981-0606517-5 }}

| volume = 36}}

{{DEFAULTSORT:Cantor-Zassenhaus algorithm}}