More generally uf all the coefficients can be coerced into AA then the roots in QQbar not in AA come in pairs.
On Wed, 22 Sep 2021, 09:23 Dima Pasechnik, <dimp...@gmail.com> wrote: > > > On Wed, Sep 22, 2021 at 9:19 AM Dima Pasechnik <dimp...@gmail.com> wrote: > >> >> >> On Wed, Sep 22, 2021 at 8:10 AM Tracy Hall <h.tr...@gmail.com> wrote: >> >>> I ran into an assertion error when trying to return a sorted list whose >>> key was a certain linear combination of eigenvalues of the Laplacian matrix >>> over graphs on nine vertices. Digging into it a bit, the failure happened >>> when comparing an algebraic real number against the same number that was >>> constructed differently (starting with the graph complement). Digging >>> further, the error happens when finding roots of a certain degree 56 >>> polynomial over AA (all the roots are real) but there is no error doing the >>> same thing over QQbar. >>> >>> Here is a minimal working example: >>> >>> P.<z> = QQ[] >>> rootlist = (z^8 - 32*z^7 + 425*z^6 - 3044*z^5 + 12789*z^4 - 32090*z^3 + >>> 46672*z^2 - 35734*z + 10917).roots(AA) >>> problem = rootlist[-1][0] - rootlist[0][0] - 9 >>> >>> problem.minpoly().roots(AA) >>> >> >> indeed, problem.minpoly().roots(QQbar) produces a list of 56 QQbar >> elements, more precisely, pairs (t,1)), each t convertible into AA. >> One funny discrepancy is that one of the elements of this list is shown as >> (-6.390396068452545? + 0.?e-170*I, 1) >> >> sage: rrr=problem.minpoly().roots(QQbar) >> sage: rrr[-1] >> (-6.390396068452545? + 0.?e-170*I, 1) >> sage: AA(rrr[-1][0]) >> -6.390396068452545? >> >> Not sure whether this is the cause of the bug, though. >> > > The behaviour of QQbar is not very consistent there. Only one root is > shown with an imaginary part, but > the polynomial has integer coefficients --- it ought to "know" that > complex roots come in pairs :-) > > >> Dima >> >> -- > You received this message because you are subscribed to the Google Groups > "sage-nt" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-nt+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-nt/CAAWYfq35Omovg-jPnG6a3eKLLa%2BpaL-%3D%3DCRFpgPRasn%2BwBf8qA%40mail.gmail.com > <https://groups.google.com/d/msgid/sage-nt/CAAWYfq35Omovg-jPnG6a3eKLLa%2BpaL-%3D%3DCRFpgPRasn%2BwBf8qA%40mail.gmail.com?utm_medium=email&utm_source=footer> > . > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/CAD0p0K5jv%2BjrVz3p2TBvsGmfySJGTrCgm7KPJAR4tmze7%3DKRUQ%40mail.gmail.com.
