This file offers 4 functions: IsLRSDegenerateOrderMod
, IsLRSDegenerateOrder
, IsLRSDegenerateMod
, and IsLRSDegenerate
.
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.
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!
2022