I have two polynomials of degree 20 defining the same number field (I obtained the second from the first using pari's polredbest() routine). I am able to use is_isomorphic() to find isomorphisms between them (there are 2) but embeddings() raises an error since roots() does:
sage: x = polygen(QQ) sage: f = (x^20 - 15*x^19 + 70989*x^18 - 1646113*x^17 + 3890074283*x^16 - 199035549796*x^15 + 203804256639644*x^14 - 10657741285726487*x^13 + 9779630086245476401*x^12 - 457685358591718595073*x^11 + 21 ....: 1985887298317287648516*x^10 - 13621268697129972225420327*x^9 + 3065457104886066023133986949*x^8 - 28110542105571309419720191704*x^7 + 34539665971867983088754678645580*x^6 - 106144538621788123597 ....: 8009629856081*x^5 + 498395492968339432558541006017143039*x^4 - 15789239186368833250097534490638459475*x^3 + 1774782276941552319212370439848636475557*x^2 + 446933009353599830602744826435319514053 ....: 6*x + 4277406750726325717327241436124994515881) sage: g = (x^20 - 5*x^19 - 497395*x^18 + 43617925*x^17 + 92084825461*x^16 - 13577322967760*x^15 - 7694013534722665*x^14 + 1430561593275815035*x^13 + 321534254513790999596*x^12 - 7029914549841232012519 ....: 0*x^11 - 6894702144208513885815805*x^10 + 1786517983436254067840917780*x^9 + 72426826805051978098685836211*x^8 - 24338190557208310471662504670520*x^7 - 255231848841911020332784180965840*x^6 + 17 ....: 2908549561723112381441893500998965*x^5 - 1042438501414486010172621550211101919*x^4 - 555813027721813935650430329326884907050*x^3 + 6754721428610694790490649672796107843280*x^2 + 4708107071244139 ....: 68773034018937652067163520*x + 3896560262532181966922924457358135376686480) sage: sage: Kf.<a>=NumberField(f) sage: Kg.<a>=NumberField(g) sage: flag, isos = Kf.is_isomorphic(Kg, isomorphism_maps=True); flag True sage: len(isos) 2 but sage: Kf.embeddings(Kg) --------------------------------------------------------------------------- PariError Traceback (most recent call last) (...) PariError: inconsistent exact division t_INT , t_INT as a result of sage: f.roots(Kg) raising the same error. I suspect that the root-finding needs higher precision that it is using, but the fact that is_isomorphic() works fine suggests that this can be dealt with. The relevant code seems to be buried in sage/rings/polynomial/polynomial_element.pyx around line 4300 (!). I don't have tim right now to investigate further or even create a trac ticket. John -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
