Ticket #13672 (closed defect: fixed)
resultant over GF(q)[t][x] is plain wrong!!!
|Reported by:||zimmerma||Owned by:||malb|
|Cc:||cremona, wstein, malb, robertwb, mmarco, SimonKing, saraedum||Work issues:|
|Report Upstream:||N/A||Reviewers:||Paul Zimmermann|
|Authors:||Jeroen Demeyer||Merged in:||sage-5.7.beta0|
Description (last modified by zimmerma) (diff)
Consider the following:
sage: R.<t> = GF(2); S.<x> = R sage: f=(t^2 + t)*x + t^2 + t; g=(t + 1)*x + t^2 sage: f.resultant(g) t^3 + t
This is wrong: the resultant of f and g is t^4+t.
Plenty of failures can be found with the following code which computes the resultant as the determinant of the Sylvester matrix:
def Resultant(f,g): df = f.degree() dg = g.degree() K = f.base_ring() M = matrix(K,df+dg,df+dg) for i in range(dg): for j in range(df+1): M[i,i+j] = f.coeffs()[df-j] for i in range(df): for j in range(dg+1): M[dg+i,i+j] = g.coeffs()[dg-j] return M.det() def check(df,dg): f = S.random_element(degree=df) g = S.random_element(degree=dg) r1 = f.resultant(g) r2 = Resultant(f,g) if r1 <> r2: print f, g, r1, r2 raise ValueError
- Summary changed from resultant over GF(2)[t][x] is plain wrong!!! to resultant over GF(q)[t][x] is plain wrong!!!
- Cc robertwb, mmarco, SimonKing, saraedum added
- Priority changed from blocker to critical
- Milestone changed from sage-5.5 to sage-5.6
- Status changed from new to needs_review
- Authors set to Jeroen Demeyer
- Status changed from needs_review to positive_review
- Reviewers set to Paul Zimmermann
- Description modified (diff)