Cyclic polynomial:Cyclotomic polynomial

Cyclotomic polynomial

Cyclotomic polynomial

Thecyclotomicpolynomialsaremonicpolynomialswithintegercoefficientsthatareirreducibleoverthefieldoftherationalnumbers.。其他文章還包含有:「Apolynomial...」、「CyclicandSymmetricPolynomials」、「Cyclicpolynomialsarisingfromthefunctionalequationfor...」、「CyclicPolynomialsinDirichlet」、「CyclicPolynomials」、「FactorizationofCyclicandSymmetricpolynomials」、「Factorizationofcyclicpolynomial」...

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Minimal polynomialMonic polynomial
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A polynomial...
A polynomial...

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A polynomial is called cyclic if after changing all its variables cyclically, the resulting polynomial does not change.

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Cyclic and Symmetric Polynomials
Cyclic and Symmetric Polynomials

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Cyclic polynomials are unchanged by cyclic permutations of their variables, while symmetric polynomials are unchanged by any permutation of their variables. 2.

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Cyclic polynomials arising from the functional equation for ...
Cyclic polynomials arising from the functional equation for ...

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In this paper, we study algebraic properties of a family of certain polynomials arising from the functional equation for Dickson polynomials.

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Cyclic Polynomials in Dirichlet
Cyclic Polynomials in Dirichlet

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Our purpose is to characterize the polynomials that are cyclic for the shift operators on these spaces in two variables.

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Cyclic Polynomials
Cyclic Polynomials

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Cyclic polynomials are polynomial functions that are invariant under cyclic permutation of the arguments. This gives them interesting properties that are useful in factorization and problem solving.

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Factorization of Cyclic and Symmetric polynomials
Factorization of Cyclic and Symmetric polynomials

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Product of cyclic polynomials is cyclic. We therefore need a cyclic polynomial of degree 1. Use the table in 2 above to help. f(2, 1, 0) = (2 – 1)(1 – 0) (0 ...

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Factorization of cyclic polynomial
Factorization of cyclic polynomial

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The method to factor cyclic expressions is to arrange the expression with the highest powers of the first variable.

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Structure of the ring of cyclic polynomials
Structure of the ring of cyclic polynomials

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It may be tempting to conjecture that elementary symmetric polynomials together with the numerator might generate the ring of polynomial invariants.