Showing papers on "Square-free polynomial published in 1971"
TL;DR: In this article, it was shown that the factorization in the number field k of the positive rational primes less than the degree of k can be checked to decide whether or not some integer θ of k has a minimal polynomial F ( X ) all of whose values at rational integer x possess a nontrivial common divisor.
10 citations
7 citations
01 Jan 1971
5 citations
TL;DR: This paper shows that in a certain model of symbolic manipulation of algebraic formulae, the simple method of computing a power of a symbolic polynomial by repeated multiplication by the originalPolynomial is, in essence, the optimal method.
Abstract: This paper shows that in a certain model of symbolic manipulation of algebraic formulae, the simple method of computing a power of a symbolic polynomial by repeated multiplication by the original polynomial is, in essence, the optimal method.
5 citations
TL;DR: An error bound is deduced depending only of the degree of the polynomial and the values of the reduced polynomials at the approximation being factored, in the case where round-off is involved.
Abstract: The errors of the approximations to the zeros of a polynomial are analyzed, supposing these approximations have been found successively using factorization of the polynomial. We deduce an error bound depending only of the degree of the polynomial and the values of the reduced polynomials at the approximation being factored. The same method may be used to calculate error bounds in the case where round-off is involved.
TL;DR: In this article, a polynomial approximation of the roots of the equation ΜtanΜ=b is presented, valid uniformly on the interval b e [0, ∞].
Abstract: A polynomial approximation of the roots of the equation ΜtanΜ=b are tabulated, valid uniformly on the interval b e [0, ∞].