<ruby id="d9npn"></ruby>

      <sub id="d9npn"><progress id="d9npn"></progress></sub>

      <nobr id="d9npn"></nobr>

      <rp id="d9npn"><big id="d9npn"><th id="d9npn"></th></big></rp>

      <th id="d9npn"><meter id="d9npn"></meter></th>

      Questions tagged [polynomials]

      Questions in which polynomials (single or several variables) play a key role. It is typically important that this tag is combined with other tags; polynomials appear in very different contexts. Please, use at least one of the top-level tags, such as nt.number-theory, co.combinatorics, ac.commutative-algebra, in addition to it. Also, note the more specific tags for some special types of polynomials, e.g., orthogonal-polynomials, symmetric-polynomials.

      Filter by
      Sorted by
      Tagged with
      0
      votes
      0answers
      70 views

      If the coefficient of the polynomial positive

      I want to know what is following sum coefficient looks like. We sum over all integers $p$, $q$ also we put the condition that $q$ is even. Also, it should depend on the parity of $k$ $$\bar{S}(k)=\...
      2
      votes
      0answers
      46 views

      The graph polynomial of the Total Graph of a Graph

      Consider the Total Graph ($T(G)$) of a graph $G$ with vertex set $V$ edge set $E=\{(u,v)\}$ with Line graph $L(G)$ and subdivision graph $S(G)$ (formed by putting a vertex in each edge of the original ...
      4
      votes
      0answers
      78 views

      Divisibility of the derivatives of a polynomial

      (Related to MO Problem 9924.) Suppose that $f$ is a polynomial of degree $d>0$ over a field of zero characteristic. It is not difficult to see that if $Q$ is yet another, non-constant polynomial, ...
      -3
      votes
      0answers
      49 views

      roots after modulus [closed]

      If I know some (not all) roots of a polynomial $P$, what can I say about the roots of the polynomial $P$ $mod$ $q$? Is there a way to find a root of $P$ $mod$ $q$ given a root of $P$?
      2
      votes
      0answers
      32 views

      Concerning $(x,y) \mapsto (x^{\frac{n}{r}+1}y + A,\mu x^{-\frac{n}{r}}+B)$

      Let $r \in \mathbb{N}-\{0\}$. Commutative case: Let $f : (x,y) \mapsto (p,q)$ be a map from $\mathbb{C}[x,y]$ to $\mathbb{C}[x^{1/r},x^{-1/r},y]$ satisfying the following two conditions: (i) $\...
      -1
      votes
      0answers
      100 views

      Integral zeros of the Newton polynomial

      I'm trying to understand the following result; Statement: A newton polynomial of the form $$a_1 {x\choose c_1}+a_2{x\choose c_2}+a_3{x\choose c_3}+?+a_s{x\choose c_s},$$ where $0 ≤c_1<c_2<c_3&...
      3
      votes
      1answer
      126 views

      complement of the set of numbers of the form $ 4mn - m - n$?

      Numbers of the form $4mn-m-n$ where $m,n\in\mathbb{Z}^+$ are $$ A=\{2, 5, 8, 11, 12, 14, 17, 19, 20, 23, 26, 29, 30, 32, 33, 35, \ldots\} $$ The set complement of the above set is $$ B=\{1, 3, 4, 6, ...
      9
      votes
      2answers
      687 views

      Polynomials that share at least one root

      This is a generalization of an MSE question, Polynomials that share at least one root. Let $P(x)$ be a specific polynomial of degree $d$, with given real coefficients $A_i$ ($A_d=1$), and real roots: ...
      5
      votes
      0answers
      166 views

      A non-commutative analog of a result concerning a Jacobian pair

      Let $k$ be a field of characteristic zero and let $E=E(x,y) \in k[x,y]$. Define $t_x(E)$ to be the maximum among $0$ and the $x$-degree of $E(x,0)$. Similarly, define $t_y(E)$ to be the maximum among $...
      3
      votes
      0answers
      202 views

      Interlacing sequences by polynomials?

      Given $t=2^\ell$ where $\ell\in\mathbb N_{>0}$ and $M\in\mathbb Z$ and two sets of integers $\{a_1,\dots,a_t\}$ and $\{b_1,\dots,b_t\}$ with $0<a_1\leq \dots\leq a_t<M$ and $0<b_1\leq \...
      7
      votes
      0answers
      153 views

      Differentiating $(x-1)(x-g)\dotsb(x-g^{d-1})Q(x)$

      Suppose that $g$ is a nonzero, infinite-order element of a field of characteristic $0$, and $d$ is a positive integer. Let $$ f(x):=(x-1)(x-g)\dotsb(x-g^{d-1}). $$ Suppose, furthermore, that $1<...
      13
      votes
      1answer
      361 views

      Are the logarithms of the integer polynomials discrete in $L^1$ of the unit circle?

      Tautologically, the integer polynomials form a discrete set in $L^1$ of the unit circle. On the other hand, a set of logarithms ordered by norm becomes generally rather denser than the original set. ...
      8
      votes
      0answers
      158 views

      Computing coefficients of polynomials from roots in $O(n\log{n})$ time

      Suppose I have a univariate polynomial $p$ over a prime-order finite field $\mathbb{F}_q$ whose roots I know. Suppose that the roots of $p$ are always an $n$-sized subset of $R=\{1,2,\dots,N\}, N <...
      2
      votes
      0answers
      55 views

      Density of integral values of a rational function

      Let $\mathbf{x} = (x_1, \cdots, x_n)$, and consider a rational function $F : \mathbb{R}^n \rightarrow \mathbb{R}$ be given by $$\displaystyle F(\mathbf{x}) = \sum_{i = 1}^m \frac{Q_i(x_1, \cdots, x_{...
      2
      votes
      0answers
      80 views

      Can entropy of a network be written as a polynomial?

      In my research, I met a problem here. Consider a weighted graph Laplacian matrix $$\mathcal{L}_w(\mathcal{G}) = DWD^T,$$ where $D$ is a incidence matrix and $W$ is diagonal with each diagonal ...

      15 30 50 per page
      特码生肖图
      <ruby id="d9npn"></ruby>

          <sub id="d9npn"><progress id="d9npn"></progress></sub>

          <nobr id="d9npn"></nobr>

          <rp id="d9npn"><big id="d9npn"><th id="d9npn"></th></big></rp>

          <th id="d9npn"><meter id="d9npn"></meter></th>

          <ruby id="d9npn"></ruby>

              <sub id="d9npn"><progress id="d9npn"></progress></sub>

              <nobr id="d9npn"></nobr>

              <rp id="d9npn"><big id="d9npn"><th id="d9npn"></th></big></rp>

              <th id="d9npn"><meter id="d9npn"></meter></th>

              四驱英雄怎么玩 海底总动员整体简笔画 奇才vs小牛视频直播 千斤顶或更好彩金 摩雷伦斯费伦斯现场042 gpk电子宝石糖果派对 宙斯古代财富免费试玩 英雄联盟佐伊 东方珍兽卡图爆大象 K歌乐韵登陆