Algorithms for computer algebra
Algorithms for computer algebra
Modern computer algebra
A Course in Computational Algebraic Number Theory
A Course in Computational Algebraic Number Theory
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In this paper, we give an efficient algorithm to find symbolically correct zeros of a polynomial f ∈ R[X] which can be represented by square roots R can be any domain if a factorization algorithm over R[X] is given, including finite rings or fields, integers, rational numbers, and finite algebraic or transcendental extensions of those Asymptotically, the algorithm needs $O(T_{f}(d^{2}))$ operations in R, where Tf(d) are the operations for the factorization algorithm over R[X] for a polynomial of degree d Thus, the algorithm has polynomial running time for instance for polynomials over finite fields or the rationals.