3 Factorisation into irreducibles
... Lemma 3.5. The ring Z of integers is a unique factorisation domain. If K is a field then K[X] is a unique factorisation domain. We have seen already (2.2, 2.7) that these are PIDs, so this will follow from 3.14. We will show that if K is a field then K[X1 , . . . , Xt ] is also a unique factorisati ...
... Lemma 3.5. The ring Z of integers is a unique factorisation domain. If K is a field then K[X] is a unique factorisation domain. We have seen already (2.2, 2.7) that these are PIDs, so this will follow from 3.14. We will show that if K is a field then K[X1 , . . . , Xt ] is also a unique factorisati ...
Factorization of multivariate polynomials
... Multivariate polynomial factorization is a cornerstone of many applications in computer algebra. It is used in computing primary decompositions of ideals, Gröbner basis, and many other applications. On the other hand, it can serve as a benchmark for many basic operations such as univariate polynomi ...
... Multivariate polynomial factorization is a cornerstone of many applications in computer algebra. It is used in computing primary decompositions of ideals, Gröbner basis, and many other applications. On the other hand, it can serve as a benchmark for many basic operations such as univariate polynomi ...