...$x,y,\dots,w$ are variables and $A,B,\dots,D$ (the ''coefficients'' of the polynomial) and $k,l,\dots,t$ (the ''exponents of the powers'', which are non-negative
...with zero coefficients and, in each individual term, zero powers. When the polynomial has one, two or three terms it is called a monomial, binomial or trinomial.
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...the basis $v_1,\dots,v_n$. If here $C$ is an infinite integral domain, the polynomial $F$ is defined uniquely.
The polynomial functions on a module $V$ form an associative-commutative $C$-algebra $P(V)
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''additive polynomial''
A [[polynomial]] over a [[field]] of [[Characteristic of a field|characteristic]] $p \ne 0
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...nd and older results. The paper [[#References|[a24]]] is an early study on polynomial convexity.
Polynomial convexity arises naturally in the context of function algebras (cf. also [[
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..., $P_M(n) = h_M(n) = \dim_K M_n$. This polynomial is called the ''Hilbert polynomial''.
...e Hilbert polynomial of the ring $R$ is also the name given to the Hilbert polynomial of the projective variety $X$ with respect to the imbedding $X \subset \mat
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...[Matroid|matroid]] with rank function $r$ on the ground set $E$. The Tutte polynomial $t ( M ; x , y )$ of $M$ is defined by
Some standard evaluations of the Tutte polynomial are:
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#REDIRECT [[Jones-Conway polynomial]]
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...)c(g_2)$. In particular, a product of primitive polynomials is a primitive polynomial.
...he theory of finite, or [[Galois field]]s, a ''primitive polynomial'' is a polynomial $f$ over a finite field $F$ whose roots are primitive elements, in the sens
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The Dickson polynomial of the first kind of degree $n$ with parameter $a$ is defined by
...ssical [[Chebyshev polynomials|Chebyshev polynomials]]. In particular, the polynomial $D _ { n } ( x , a )$ satisfies
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#REDIRECT [[Alexander-Conway polynomial]]
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The polynomial
The values of the Taylor polynomial and of its derivatives up to order $n$ inclusive at the point $x=x_0$ coinc
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where $M$ is a finite set of natural numbers, is called the Dirichlet polynomial with coefficients $a _ { m }$ (complex numbers) and exponents $\lambda _ {
...esis (cf. [[Riemann hypotheses|Riemann hypotheses]]) is that the Dirichlet polynomial $\sum _ { { m } = 1 } ^ { { n } } m ^ { - s }$ should have no zeros in $\
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#REDIRECT [[Brandt-Lickorish-Millett-Ho polynomial]]
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$#C+1 = 32 : ~/encyclopedia/old_files/data/C021/C.0201720 Characteristic polynomial
The polynomial
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#REDIRECT [[Jones-Conway polynomial]]
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...$\mathbf{Z}\langle X \rangle$ becomes the [[Leibniz–Hopf algebra]]. A Lie polynomial is an element $P$ of $\mathbf{Z}\langle X \rangle$ such that $\mu(P) = 1 \o
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''minimum polynomial of a matrix''
...l|characteristic polynomial]] of $A$ and, more generally, it divides every polynomial $f$ such that $f(A)=0$.
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See [[Characteristic polynomial|Characteristic polynomial]].
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...so [[Eigen value|Eigen value]]; [[Characteristic polynomial|Characteristic polynomial]]).
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...xactly, an extension $L$ of a field $K$ is called the splitting field of a polynomial $f$ over the field $K$ if $f$ decomposes over $L$ into linear factors:
...tsc,a_n)$ (see [[Extension of a field]]). A splitting field exists for any polynomial $f\in K[x]$, and it is defined uniquely up to an isomorphism that is the id
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...ots in Jones' construction of his polynomial invariant of links, the Jones polynomial, and Drinfel'd's work on quantum groups (cf. also [[Quantum groups|Quantum
For references, see [[Kauffman polynomial|Kauffman polynomial]]; [[Knot and link diagrams|Knot and link diagrams]].
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The polynomial
The values of the Taylor polynomial and of its derivatives up to order $n$ inclusive at the point $x=x_0$ coinc
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...)c(g_2)$. In particular, a product of primitive polynomials is a primitive polynomial.
...he theory of finite, or [[Galois field]]s, a ''primitive polynomial'' is a polynomial $f$ over a finite field $F$ whose roots are primitive elements, in the sens
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#REDIRECT [[Linearised polynomial]]
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#REDIRECT [[Hilbert polynomial]]
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...s. This theorem can also be used to find the number of negative roots of a polynomial $f(x)$ by considering $f(-x)$.
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#REDIRECT [[Alexander-Conway polynomial]]
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#REDIRECT [[Elementary symmetric polynomial]]
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#REDIRECT [[Jones-Conway polynomial]]
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#REDIRECT [[Jones-Conway polynomial]]
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...t–Lickorish–Millett–Ho polynomial]] and the [[Kauffman polynomial|Kauffman polynomial]]:
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...the basis $v_1,\dots,v_n$. If here $C$ is an infinite integral domain, the polynomial $F$ is defined uniquely.
The polynomial functions on a module $V$ form an associative-commutative $C$-algebra $P(V)
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A trigonometric polynomial of the form
or a similar polynomial in sines. Fejér polynomials are used in constructing continuous functions
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...[[characteristic polynomial]] and [[Minimal polynomial of a matrix|minimal polynomial]] coincide (up to a factor $\pm1$). Equivalently, for each of its distinct
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...ts an element $\alpha \in K$ such that the [[ring of integers]] $O_K$ is a polynomial ring $\mathbb{Z}[\alpha]$. The powers of such a element $\alpha$ constitut
...lynomial|discriminant]] of the [[Minimal polynomial (field theory)|minimal polynomial]] of $\alpha$.
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It is a polynomial of two variables associated to homotopy classes of links in $\mathbf{R}^3$,
...f the graph associated to $D$ (cf. also [[Graph colouring]]). The homotopy polynomial can be generalized to homotopy skein modules of three-dimensional manifolds
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