''Homfly polynomial, Homflypt polynomial, skein polynomial''
...[[Alexander–Conway polynomial|Alexander–Conway polynomial]] and the Jones polynomial.
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$#C+1 = 50 : ~/encyclopedia/old_files/data/P073/P.0703730 Polynomial of best approximation
A polynomial furnishing the best approximation of a function $ x ( t) $
6 KB (907 words) - 08:06, 6 June 2020
$#C+1 = 12 : ~/encyclopedia/old_files/data/K110/K.1100100 Kharitonov polynomial theory
...rned with the root locations for a family of polynomials (cf. [[Polynomial|Polynomial]]). A good general reference for this area is [[#References|[a1]]]. The mot
5 KB (695 words) - 22:14, 5 June 2020
It is a Laurent polynomial of one variable associated to ambient isotopy classes of unoriented framed
...^ { ( 1 ) } \rangle = - A ^ { 3 } \langle L \rangle$. The Kauffman bracket polynomial is also considered as an invariant of regular isotopy (Reidemeister moves:
7 KB (1,054 words) - 07:42, 10 February 2024
...polynomials $\sigma_k(x_1,\ldots,x_n)$ for $k=0,\ldots,n$ where the $k$-th polynomial is obtained by summing all distinct [[monomial]]s which are products of $k$
...] $S_n$, so that any symmetric polynomial in the $x_i$ can be written as a polynomial in the $\sigma_k$.
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$#C+1 = 35 : ~/encyclopedia/old_files/data/N066/N.0606230 Negative polynomial distribution,
The [[Generating function|generating function]] of the negative polynomial distribution with parameters $ r, p _ {0}, \dots, p _ {k} $
3 KB (418 words) - 16:50, 1 February 2022
$#C+1 = 17 : ~/encyclopedia/old_files/data/A011/A.0101620 Algebraic polynomial of best approximation
A polynomial deviating least from a given function. More precisely, let a measurable fun
4 KB (571 words) - 16:10, 1 April 2020
...teger programming problems in a fixed number of variables can be solved in polynomial time.
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...]]], [[#References|[a2]]] and generalized by L.H. Kauffman (the [[Kauffman polynomial]]; cf. also [[Link]]).
...> <TD valign="top"> R.D. Brandt, W.B.R. Lickorish, K.C. Millett, "A polynomial invariant for unoriented knots and links" ''Invent. Math.'' , '''84''' (1
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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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''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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...g $w_1=w_2=w$, then the resulting polynomial is called the simple matching polynomial of $G$.
...e been investigated [[#References|[a8]]]. The analytical properties of the polynomial have also been investigated [[#References|[a10]]].
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$#C+1 = 209 : ~/encyclopedia/old_files/data/P073/P.0703700 Polynomial and exponential growth in groups and algebras
is of polynomial growth, or power growth, $ r $
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A divisor of a polynomial $A(x)$ is a polynomial $B(x)$ that divides $A(x)$ without remainder (cf. [[Division|Division]]).
...e of $a$, then $a$ is ''irreducible''. For polynomials, see [[Irreducible polynomial]]; for integers, the traditional terminology is [[prime number]].
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''polynomial regression''
exist). The regression is called parabolic (polynomial) if the components of the vector $ {\mathsf E} \{ Y \mid X \} = f( x)
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...omial'' (also, companion or auxiliary polynomial) of the recurrence is the polynomial
It is the characteristic polynomial of the left shift operator acting on the space of all sequences. If $\alph
2 KB (283 words) - 16:38, 30 December 2018
...e polynomials one can calculate an approximation of two roots of the given
polynomial. An advantage of the method is that it uses real arithmetic only.
be a given
polynomial with real coefficients and <img align="absmiddle" border="0" src="https://w
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...le of topology has ultimately been reduced to the single assumption that a polynomial of odd degree with real coefficients has a real root.
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''Bernstein form, Bézier polynomial''
The Bernstein polynomial of order $n$ for a function $f$, defined on the closed interval $[0,1]$, is
4 KB (598 words) - 16:55, 1 July 2020
''(algebraic) polynomial''
is called the degree of the polynomial; the polynomial $ P ( z) \equiv 0 $
2 KB (328 words) - 19:37, 5 June 2020
A field $k$ is algebraically closed if any polynomial of non-zero degree over $k$ has at
field $k$ each polynomial of degree $n$ over $k$ has exactly $n$ roots
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...g $w_1=w_2=w$, then the resulting polynomial is called the simple matching polynomial of $G$.
...e been investigated [[#References|[a8]]]. The analytical properties of the polynomial have also been investigated [[#References|[a10]]].
6 KB (1,005 words) - 20:14, 15 March 2023
...perfect matching exists. (It should be noted that this is not the [[Tutte polynomial]] of $G$.)
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* A [[divisor (of an integer or of a polynomial)]]
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...gebraic number]]. An algebraic irrationality is the root of an irreducible polynomial of a degree at least two, with rational coefficients.
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be a [[Polynomial|polynomial]] of degree $ \geq 1 $
is irreducible (cf. [[Irreducible polynomial|Irreducible polynomial]]) and, trivially, that the leading coefficient is positive. Are these cond
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$#C+1 = 17 : ~/encyclopedia/old_files/data/A011/A.0101620 Algebraic polynomial of best approximation
A polynomial deviating least from a given function. More precisely, let a measurable fun
4 KB (571 words) - 16:10, 1 April 2020
A method for calculating the roots of a polynomial
...mials of degree 3. The parabola method allows one to find all zeros of the polynomial without preliminary information about initial approximations. The convergen
4 KB (619 words) - 08:04, 6 June 2020
...ferential equations; it is an analogue of the [[Hilbert polynomial|Hilbert polynomial]].
There exists (see [[#References|[2]]]) a polynomial whose value at points $ s \in \mathbf Z $
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A form in four variables, that is, a homogeneous polynomial (cf. [[Homogeneous function|Homogeneous function]]) in four unknowns with c
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A conjecture on the asymptotic behaviour of a polynomial satisfying the Bunyakovskii condition (cf. also [[Bunyakovskii conjecture|B
be polynomials (cf. [[Polynomial|Polynomial]]) with integer coefficients, of degrees $ d _ {1} \dots d _ {r} \geq 1 $
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''polynomial deviating least from zero''
An algebraic polynomial of degree $n$, with leading coefficient 1, having minimal norm in the space
3 KB (552 words) - 15:05, 14 February 2020
...next to the knot $8_9$ is written $7-5+3-1$. This means that the Alexander polynomial equals $\Delta(t)=-t^6+3t^5-5t^4+7t^3-5t^2+3t-1$. Non-alternating knots are
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...l and its generalizations (e.g. the [[Jones–Conway polynomial|Jones–Conway polynomial]]).
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