id summary reporter owner description type status priority milestone component resolution keywords cc merged author reviewer upstream work_issues branch commit dependencies stopgaps
13215 Skew polynomials caruso tbd "If R is a ring equipped with an endomorphism sigma, the ring of skew polynomials over (R,sigma) is the ring of usual polynomials over R with the modified multiplication given by the rule X*a = sigma(a)*X.
Skew polynomials play an important role in several domains like coding theory or Galois representations theory in positive characteristic.
The attached patch provides:
1. a basic implementation of skew polynomials over any commutative ring (including addition, multiplication, euclidean division, gcd...)
1. a more complete implementation of skew polynomials over finite fields (including factoring)
NB: This ticket depends on tickets #13214 (which implements Frobenius endomorphisms over finite fields) and #13303 (which fixes a bug in quotient_polynomial_ring_element.pyx). For convenience, I reattach the corresponding patches here (you need to apply these two patches first).
Apply: attachment:trac_13215_skew_polynomials.patch" enhancement needs_review major sage-5.11 algebra skew polynomials tfeulner caruso burcin Xavier Caruso N/A #13214, #13303