id,summary,reporter,owner,description,type,status,priority,milestone,component,resolution,keywords,cc,work_issues,upstream,reviewer,author,merged,dependencies,stopgaps
8558,add a fast gcd algorithm for univariate polynomials over absolute number fields,lftabera,AlexGhitza,"Question arised here,

http://groups.google.com/group/sage-devel/browse_thread/thread/0f5b029970e1a4e2/fcec7d0e35474fbd#fcec7d0e35474fbd

univariate gcd is performed using euclidean algorithm, which causes explosion of coefficients and is slow but for trivial examples. Instead we should use pari that performs better.

 1. Make `_pari_()` work for polynomials over absolute number fields, see #11904.
 2. Add gcd using pari for absolute number fields
 3. For relative number fields, pass to an absolute representation. This may be slow. But for the cases where this is slow the current implementation may be unfeasible.

Apply: [attachment:trac-8558.2.2.patch]",enhancement,needs_review,major,sage-5.11,algebra,,"gcd, pari, ntl, number field",,,N/A,Jeroen Demeyer,Luis Felipe Tabera Alonso,,#14186,