Circuits for computing the GCD of two polynomials over an algebraic number field

We present algorithms that compute all irreducible factors of degree ≤ d of supersparse (lacunary) multivariate polynomials in n variables over an algebraic number field in deterministic polynomial-time in (l+d)ⁿ, where l is the size of the input ...

For a positive Borel measure dµ, we prove that the constant γ_n(dv;dµ) = sup_π∈Jn\{0} ∫_-x^x π²(x)dv(x)/∫_-x^x π²(x)dµ(x)' can be represented by the zeros of orthogonal polynomials corresponding to dµ in case (i) dv(x)=(A+Bx)dµ(x), where A+Bx is nonnegative ...

The algorithm for factoring polynomials over the integers by Wang and Rothschild is generalized to an algorithm for the irreducible factorization of multivariate polynomials over any given algebraic number field. The extended method makes use of recent ...