quadratic polynomialspower series ringsunique factorizationintegral power seriesp-adic numbersWe establish necessary and sufficient conditions for a quadratic polynomial to be irreducible in the ring Z[[ x]] of formal power series over the integers. In particular, for polynomials of the form p(n) ...
Furthermore, \bar h has no quadratic factor in Z_2[x] (For if so, the factor would have to be either x^2 +x + 1 or x^2 + 1 . Long division shows that x^2 +x + 1 is not a factor, and x^2 + 1 cannot be a factor because it has a zero, whereas \bar h does not...
This is the only way to get a primitive quadratic polynomial. From 3.4 and 4.2 we get another corollary: Corollary 5.3. Suppose K : GF(2)] is even. Only two types of odd- degree trinomials have an even number 1. g(x) = xn + axk + b, 2jkj2n, if t2 of + tfa+ctao2rknsb,...
Consider f(x) = ax^2+bx+c , there are (p-1)p^2 distinct polynomials of degree 2 . We know from p23 that the number of reducible quadratic polynomials over Z_p is p(p^2-1)/2 So we can always find a irreducible polynomial of degree 2 Done p24 Let p be a prime. (a) Sho...
Theorem.Let E be a finite set, and letdenote the set of real E × E matrices with non-negative off-diagonal elements and with non-positive row sums. Let A be a symmetric element of,and let V be a diagonal real E × E matrix. Then there exists a unique pair (H+, H−) of ...
英汉-汉英词典 n.因数分解 近义、反义、联想词 近义词 n. resolution,resolving 联想词 polynomial多项式;matrices基质;algebraic代数的;quadratic二次的;theorem定理;matrix矩阵;integers整数;algebra代数学;primes一级品;tensor张量;Euler欧拉; 英语例句库 1.Abstract: In this paper, the method and theory of coprim...
Factorization mode, specified as the comma-separated pair consisting of'FactorMode'and one of these character vectors. 'rational'Factorization over rational numbers. 'real'Factorization over real numbers. A real numeric factorization is a factorization into linear and quadratic irreducible polynomials with...
Factorization mode, specified as the comma-separated pair consisting of'FactorMode'and one of these character vectors. 'rational'Factorization over rational numbers. 'real'Factorization over real numbers. A real numeric factorization is a factorization into linear and quadratic irreducible polynomials with...
In fact, the factorization Algorithm 2.2 also works under slightly more general assumptions: We can allow that the primal part of P has real factors as long as these real factors are not norm polynomials of linear motion polynomials. The norm polynomial of a rotation polynomial is quadratic ...
The following sections are included:A General AlgorithmDetermining the Period of a PolynomialTrinomials Over GF(2)Factoringxn1ExplicitlyDetermining the Degrees of the Irreducible Factors of the Cyclotomic PolynomialsIs the Number of Irreducible Factors off(x)Over GF(q)Odd or Even?Quadratic Reciprocity...