Parallel algorithms for algebraic problems
SIAM Journal on Computing
Factoring Polynomials Over Algebraic Number Fields
ACM Transactions on Mathematical Software (TOMS)
Factoring Polynomials over Algebraic Number Fields
SIAM Journal on Computing
On determining the solvability of polynomials
ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
On Hensel construction of eigenvalues and eigenvectors of matrices with polynomial entries
ISSAC '93 Proceedings of the 1993 international symposium on Symbolic and algebraic computation
Resolvent systems of difference polynomial ideals
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Root isolation for bivariate polynomial systems with local generic position method
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Root isolation of zero-dimensional polynomial systems with linear univariate representation
Journal of Symbolic Computation
| Hi-index | 0.00 |
Several mathematical results and new computational methods are presented for primitive elements and their minimal polynomials of algebraic extension fields. For a field Q(@a"1,...,@a"t) obtained by adjoining algebraic numbers @a"1,...@a"t to the rational number field Q, it is shown that there exists at least one vector =(s"1,...,s"t) of integers in a specially selected set of (-1)N vectors such that s"1@a"1+s"2@a"2+...+s"t@a"t is a primitive element, where N is the degree of Q(@a"1,...,@a"t) over Q. Furthermore, a method is presented for directly calculating such a vector, that gives a primitive element. Finally, for a given polynomial f over Q, a new method is presented for computing a primitive element of the splitting field of f and its minimal polynomial over Q.