cyclotomic

• Examples
• User documentation
  • Operations
• Maintainer documentation
• Bugs, shortcomings and other ideas
• Main changes

Examples

• ex-cyclotomic.C

User documentation

This file offers 2 main functions: cyclotomic and CyclotomicIndex.

Operations

Let f be two RingElem values representing univariate polynomials in a polynomial ring P over ZZ or QQ. Let n be a positive integer.

• cyclotomic(n,x) -- returns the n-th cyclotomic polynomial in the indet x
• CyclotomicTest(f) -- returns an unsigned long n indicating that f is the n-th cyclotomic polynomial; if f is not cyclotomic, returns 0.
• CyclotomicIndex(f) -- if f is cyclotomic, returns n its index. If f is not cyclotomic it may return 0 or some other value. Faster than CyclotomicTest.

Maintainer documentation

• Details about the InversePhiBound can be found in OEIS sequence A355667.
• Basics are taken from Bradford and Davenport (DOI:10.1007/3-540-51084-2_22).

Bugs, shortcomings and other ideas

• Are there any criterions when the Graeffe approach is faster?

Main changes

2022

• August (v0.99802): first release