Common minimal multiples and divisors for rational matrix functions
نویسندگان
چکیده
منابع مشابه
Multiples and Divisors
Before discussing multiplication, let us speak about addition. The number A(k) of distinct sums i+ j ≤ k such that 1 ≤ i ≤ k/2, 1 ≤ j ≤ k/2 is clearly 2 bk/2c − 1. Hence the number A(2n) of distinct elements in the n × n addition table involving {1, 2, . . . , n} satisfies limn→∞A(2n)/n = 2, as expected. We turn to multiplication. Let M(k) be the number of distinct products ij ≤ k such that 1 ≤...
متن کاملComputing Divisors and Common Multiples of Quasi-linear Ordinary Differential Equations
If solutions of a non-linear differential equation are contained in solutions of another equation we say that the former equation is a generalized divisor of the latter one. We design an algorithm which finds first-order quasi-linear generalized divisors of a second-order quasi-linear ordinary differential equation. If solutions of an equation contain solutions of a pair of equations we say tha...
متن کاملRational Matrix Functions and Rank-1 Updates
Suppose f = p/q is a quotient of two polynomials and that p has degree rp and q has degree rq . Assume that f(A) and f(A+ uv ) are defined where A ∈ R, u ∈ R, and v ∈ R are given and set r = max{rp, rq}. We show how to compute f(A+uv ) in O(rn2) flops assuming that f(A) is available together with an appropriate factorization of the “denominator matrix” q(A). The central result can be interprete...
متن کاملRational Divisors in Rational Divisor Classes
We discuss the situation where a curve C, defined over a number field K, has a known K-rational divisor class of degree 1, and consider whether this class contains an actual K-rational divisor. When C has points everywhere locally, the local to global principle of the Brauer group gives the existence of such a divisor. In this situation, we give an alternative, more down to earth, approach, whi...
متن کاملMinimal Polynomials of Algebraic Cosine Values at Rational Multiples of π
Lehmer proved that the values of the cosine function evaluated at rational multiples of π are algebraic numbers. We show how to determine explicit, closed form expressions for the minimal polynomials of these algebraic numbers.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1990
ISSN: 0024-3795
DOI: 10.1016/0024-3795(90)90143-z