LRSDegeneracy

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

Examples

• ex-LRSDegeneracy.C

User documentation

This file offers 4 functions: IsLRSDegenerateOrderMod, IsLRSDegenerateOrder, IsLRSDegenerateMod, and IsLRSDegenerate.

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. Let VerifLev be an instance of VerificationLevel.

• IsLRSDegenerateOrderMod(f,n,VerifLev) -- returns a bool indicating whether f is the characteristic polynomial of a n-degenerate LRS - using a modular approach.
• IsLRSDegenerateOrder(f,n) -- returns a bool indicating whether f is the characteristic polynomial of a n-degenerate LRS.
• IsLRSDegenerateMod(f,VerifLev) -- returns an unsigned long n indicating that f is the characteristic polynomial of a n-degenerate LRS - using a modular approach.
• IsLRSDegenerate(f) -- returns a bool: true means that f is the characteristic polynomial of a n-degenerate LRS for some n. Otherwise false.
• LRSDegeneracyOrder(f) -- returns an unsigned long n indicating that f is the characteristic polynomial of a n-degenerate LRS.

Maintainer documentation

• The approaches are taken from Cipu et al. (DOI:10.1007/s00200-011-0150-8).
• Details about the modular approach have been provided by John Abbott.

Bugs, shortcomings and other ideas

• Cipu et al. suggest using Q_n = Res_y(f(xy), Phi_n(y)) and then deg(gcd(P,Q_n)) > 0 in the modular/iterative approach. But resultant can be slow!

Main changes

2022

• August (v0.99802): first release