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cyclotomic polynomial

cyclotomic polynomial noun: for a positive integer n, a polynomial whose roots are the primitive nᵗʰ roots of unity, so that its degree is Euler's totient function of n. That is, letting ζₙ=e^(i 2π/n) be the first primitive nᵗʰ root of unity, then Φₙ(x)=∏_( stackrel )1<m<ngcd (n,m)=1(x-ζₙᵐ) is the nᵗʰ such polynomial.

Noun

cyclotomic polynomial (plural cyclotomic polynomials)

  1. For a positive integer n, a polynomial whose roots are the primitive nᵗʰ roots of unity, so that its degree is Euler's totient function of n. That is, letting ζₙ=e^(i 2π/n) be the first primitive nᵗʰ root of unity, then Φₙ(x)=∏_( stackrel )1<m<ngcd (n,m)=1(x-ζₙᵐ) is the nᵗʰ such polynomial.
    • For a prime number p, the pᵗʰ cyclotomic polynomial is #123;xᵖ-1#92;overx-1#125;#61;x#123;p-1#125;#43;x#123;p-2#125;#43;...#43;x²#43;x#43;1.
    • Cyclotomic polynomials can be shown to be irreducible through the Eisenstein irreducibility criterion, after replacing x with x#43;1.

cyclotomic polynomial meaning in Tamil

cyclotomic polynomial in Tamil

சுழல் நுண்ம அடுக்குகோவை

Forms of cyclotomic polynomial

pluralcyclotomic polynomials

Questions about cyclotomic polynomial

What does cyclotomic polynomial mean?
Cyclotomic polynomial means for a positive integer n, a polynomial whose roots are the primitive nᵗʰ roots of unity, so that its degree is Euler's totient function of n. That is, letting ζₙ=e^(i 2π/n) be the first primitive nᵗʰ root of unity, then Φₙ(x)=∏_( stackrel )1<m<ngcd (n,m)=1(x-ζₙᵐ) is the nᵗʰ such polynomial.
What is cyclotomic polynomial in Tamil?
Cyclotomic polynomial in Tamil is சுழல் நுண்ம அடுக்குகோவை. See Cyclotomic polynomial meaning in Tamil.
What part of speech is cyclotomic polynomial?
Cyclotomic polynomial is a noun.
What is the plural of cyclotomic polynomial?
The plural of cyclotomic polynomial is cyclotomic polynomials.

Words near cyclotomic polynomial in the dictionary

  1. cyclotides
  2. cyclotol
  3. cyclotomic
  4. cyclotomic field
  5. cyclotomic fields
  6. cyclotomic polynomial
  7. cyclotomic polynomials
  8. cyclotomically
  9. cyclotomics
  10. cyclotomy
  11. cyclotornid

Source and license

Adapted from Wiktionary: cyclotomic polynomial (page history and authors); cyclotomic polynomial (Tamil Wiktionary) (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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