I've had time to find the origin of the bug: It appears to be a bug in
Pari 2.11.0 (cf below). I've submitted a bug report.
? 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 +
211985887298317287648516*x^10 - 13621268697129972225420327*x^9 +
3065457104886066023133986949*x^8 - 28110542105571309419720191704*x^7 +
34539665971867983088754678645580*x^6 - 1061445386217881235978009629856081*x^5 +
498395492968339432558541006017143039*x^4 -
15789239186368833250097534490638459475*x^3 +
1774782276941552319212370439848636475557*x^2 +
4469330093535998306027448264353195140536*x +
4277406750726325717327241436124994515881;
? g = y^20 - 5*y^19 - 497395*y^18 + 43617925*y^17 + 92084825461*y^16 -
13577322967760*y^15 - 7694013534722665*y^14 + 1430561593275815035*y^13 +
321534254513790999596*y^12 - 70299145498412320125190*y^11 -
6894702144208513885815805*y^10 + 1786517983436254067840917780*y^9 +
72426826805051978098685836211*y^8 - 24338190557208310471662504670520*y^7 -
255231848841911020332784180965840*y^6 +
172908549561723112381441893500998965*y^5 -
1042438501414486010172621550211101919*y^4 -
555813027721813935650430329326884907050*y^3 +
6754721428610694790490649672796107843280*y^2 +
470810707124413968773034018937652067163520*y +
3896560262532181966922924457358135376686480;
? nffactor(g,f)
*** at top-level: nffactor(g,f)
*** ^-------------
*** nffactor: bug in LLL_cmbf [no factor], please report.
*** Break loop: type 'break' to go back to GP prompt
Bruno
Le 14/09/2018 à 13:40, Dima Pasechnik a écrit :
One could use 'git bisect' to narrow the problem down to a particular commit.
Just in case...
On Fri, Sep 14, 2018 at 12:16 PM Bruno Grenet <bruno.gre...@gmail.com> wrote:
I've also tested on Ubuntu with gcc. Actually, I run new tests: The bug
appears between 8.4beta2 (where it's still ok) and 8.4beta3. I'll try to
find the the origin of the bug.
Bruno
Le 14/09/2018 à 10:38, Dima Pasechnik a écrit :
It might be a platform dependent bug. I guess John is working on some
Ubunty machine, using gcc.
Please provide compiler details you're using, too...
On Fri, Sep 14, 2018 at 9:25 AM Bruno Grenet <bruno.gre...@gmail.com> wrote:
Which version of SageMath are you using? I am unable to reproduce the
bug neither on 8.3beta7 nor on 8.4beta2.
Bruno
Example with 8.4beta2:
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 - 10
....: 657741285726487*x^13 + 9779630086245476401*x^12 -
457685358591718595073*x^11 + 211985887298317287648516*x^10 - 1
....: 3621268697129972225420327*x^9 + 3065457104886066023133986949*x^8 -
28110542105571309419720191704*x^7 + 345396659
....: 71867983088754678645580*x^6 -
1061445386217881235978009629856081*x^5 +
498395492968339432558541006017143039*x^4
....: - 15789239186368833250097534490638459475*x^3 +
1774782276941552319212370439848636475557*x^2 + 446933009353599830
....: 6027448264353195140536*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 -
70299145498412320125190*x^11 - 6894702144208513885815
....: 805*x^10 + 1786517983436254067840917780*x^9 +
72426826805051978098685836211*x^8 - 243381905572083104716625046705
....: 20*x^7 - 255231848841911020332784180965840*x^6 +
172908549561723112381441893500998965*x^5 - 10424385014144860101
....: 72621550211101919*x^4 -
555813027721813935650430329326884907050*x^3 +
6754721428610694790490649672796107843280*x
....: ^2 + 470810707124413968773034018937652067163520*x +
3896560262532181966922924457358135376686480
....:
sage: Kf.<a> = NumberField(f)
sage: Kg.<a> = NumberField(g)
sage: embeddings = Kf.embeddings(Kg)
sage: len(embeddings)
2
Le 13/09/2018 à 16:16, John Cremona a écrit :
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
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