cyclotomic polynomial
English
Noun
cyclotomic polynomial (plural cyclotomic polynomials)
- (algebra) For a positive integer n, a polynomial whose roots are the primitive nth roots of unity, so that its degree is the Euler's totient function of n. In symbols, letting
be the first primitive nth root of unity, then
is the nth such polynomial.
- For a prime number , the th cyclotomic polynomial is .
- Cyclotomic polynomials can be shown to be irreducible through the Eisenstein irreducibility criterion, after replacing with .
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