#20749: Use PARI nfeltup() for inclusion of base field into relative number
field
-------------------------------------+-------------------------------------
Reporter: pbruin | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-7.3
Component: number fields | Resolution:
Keywords: relative number | Merged in:
field pari | Reviewers: Stephan Ehlen
Authors: Peter Bruin | Work issues:
Report Upstream: N/A | Commit:
Branch: | 9f1d90be8d3f05b6d5de8ee75e36e6d17ad52095
u/pbruin/20749-pari_nfeltup | Stopgaps:
Dependencies: |
-------------------------------------+-------------------------------------
Comment (by ehlen):
@pbruin: I don't think this is really related to this issue but now I
think I also know where the crashes in #20693 come from. Should I open a
new issue for this?
You can get such a crash by taking the example extension from above and
then do the following:
First, before I come to the crash, I observed that the new fast coercion
seems not to be used when doing arithmetic between elements of K and L
(which should also be changed, I guess; create a new issue for this one as
well?):
{{{
sage: a*zeta22
}}}
takes '''extremely long''' (''better do not even try in this case'').
So to make the example work faster for you, redefine
{{{
sage: zeta22 = L(zeta22)
}}}
and then define
{{{
alpha = a^8 + (zeta22^9 - zeta22^6 + 2*zeta22^4 + 33)*a^7 + (31*zeta22^9 +
5*zeta22^8 + 3*zeta22^7 - 31*zeta22^6 - 7*zeta22^5 - 107*zeta22^4 -
7*zeta22^3 + 3*zeta22 + 1059)*a^6 +
(3718477411250739866475244208396740244825243240462255398354618777962943033036197614/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^9
+
3598993609760370116641649296594108177793336273748205490894264408969198182996064521/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^8
+
395515835682657053939335812620537182933299146301044684946734967822987328729996770/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^7
-
5699790756786591231234352859639368530535500068686650515294130239974834139089497358/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^6
+
17297425796252247996017656901940747274345176460026298001221868953832184120342480943/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^5
-
17363940052556552019695963211248247355519164620582388569507136704698531302369871157/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^4
+
9055968516979184171371181551238371584025794515050844857388673892514573091513003290/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^3
-
15040340959361706541983637521956854375291195448848214782596844503078269125044340553/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^2
+
13494420365662811437124466100462970251959171531481521859055299974063740995251772104/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22
+
6244717344446638271677235756972000388998153179319783794204333931828857707898855052/2781215150144642133290297862665034354958449250072837417478217578695339824339427)*a^5
+
(24774162552917688991082130433488385130328970002935037716015871420013133094788422714/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^9
+
79701067568676386611303145273440634808611524849495231394520039468820732638249105800/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^8
+
26568513472358696621594478167874503122978010463520328704511609604190048290318514603/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^7
-
28568346637705610185287947280980997136503568011444674263014607088110550373126222488/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^6
-
39660083727109323104443457044447414454536437867616101135848188026853956400960143227/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^5
-
288506345895399617687343175266113244576300715440934060776626556355537479220650636513/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^4
+
38450957705712699986746557845614915958961186767731353680661029680265167338816527393/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^3
+
38161688129027694214992610734600208295189825414215200641609022074230122499922603243/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^2
-
3191864810403360155650302997604973159366655983340669817286554187937615451268927032/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22
+
47268626458303985980800073875915577424848984965812742485263892593814963540801229150/2781215150144642133290297862665034354958449250072837417478217578695339824339427)*a^4
+
(-937447078652953135161383442869885011608291132795403699637090980208045121301540757748/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^9
+
272895307598582523796743023683576558488087237572381251733653044903614546805704144822/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^8
+
148506657503867941152708044033955240703030804163414655018707004956684533483632072918/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^7
+
646234624710987986053419640141072406503297749358550789304127974747562199499646227564/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^6
-
694272767541738866807839896263173246303852233808156712638352151624760444919113413860/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^5
-
1065299910777172022253542660462029758918982943208973495529175167293206823402147443812/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^4
+
391247849932185372287013557796317033044190817278386930053256314276905903054599189656/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^3
+
270059737316677284054399797548542667378719651731770017638820261901537292210067430748/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^2
+
591183517951447041155684848874114741342258899601346549805513412737310300574376961340/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22
-
549234386608334176655451066867005934918413936339648030381729208533527232309970754056/2781215150144642133290297862665034354958449250072837417478217578695339824339427)*a^3
+
(3733235692687094353448458915585909509665568180903028164992065763187227802783744366904/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^9
+
4001347101119302151586151100739784824512031744955125627753398604635977129245394082832/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^8
-
142900644218466289026802027389705486824676154666291235714274875202387049736546165496/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^7
-
3140367895112856999469516716889439921902711871458169096781024472877378499868645823464/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^6
+
1548125833062460723167432489350030748656270798599409078100770397214546377977628099392/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^5
-
5555248030204437606615955525547629664582214941617163155200679415001104250314686522904/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^4
+
2338634196530591481118837933605692971586210932289146141551391636565007362205462863632/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^3
+
241065823923473040670468508360923657066538144858067456312163992742504206316110953872/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^2
+
6193407042558447035765092497698058804377114439287850914206888660193032121912761915096/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22
-
1099028159132223312122416248212282152380303533702464885003475741154651056010685127136/2781215150144642133290297862665034354958449250072837417478217578695339824339427)*a^2
+
(-1209474666091626439377287726025063910117768646668537490462602863066374919777158248752/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^9
+
18944377470648440226769591793624192288159925134705324925823731276407685992338482780768/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^8
-
12588022720980067567643175141996157130390089862067396848827764390446478609186744912864/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^7
+
5846397169289048287227403463558979527530805847195272367028420342204317428915118171264/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^6
-
16847241179656718059040202917295887078972805888663869818562994452056221728436316027648/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^5
+
12240286913403964318669326586717222877251387677609611349774686872857040618201006536992/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^4
-
10215645290860597645527053926413672307107960240749347167007546911366807686239483447760/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^3
-
1530790653293321897505424092212210389606218038145729553761965669588546770845494535744/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^2
-
2187147240620525406889619995238280606256936931802838455843775292305350828383843100392/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22
+
19510253615883608973256727849462398241279239407108793464341426177684581140048029643336/2781215150144642133290297862665034354958449250072837417478217578695339824339427)*a
+
16154018655709961475718369484349656491553141143207492785674435352956514805968259987664/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^9
+
2076605038062774454571095952791235830842349738387639911582630151888232765540495947312/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^8
+
4668807939004183895066836782642087347512184354134486123598161763233386792193417033072/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^7
-
23695032293352934150131791676770088928820644994522373184920557704305964271233795745200/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^6
-
30793593484010229493726633495079211970606615963726974062428759270109321834429025890192/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^5
-
15901465043256147712498413364161573071835390049680548208343611460784472680510813931552/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^4
+
30488481430481719467683640329190646090432003826988727071840796540695621523220516840016/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^3
+
30479060480952146242812422067193694873717833966949171930549636681404792808019569151264/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22^2
+
28427288188474291222913119784939698904170993004067585847681058620275056131415057040896/2781215150144642133290297862665034354958449250072837417478217578695339824339427*zeta22
-
15841459674454996185174537876570344446791982788066217107011655814278705184784915491008/2781215150144642133290297862665034354958449250072837417478217578695339824339427
}}}
Now try to invert alpha:
{{{
beta = ~alpha
}}}
I get a crash after a few seconds.
Yes, I know, this example is somewhat huge and it probably shows that the
modular forms should somehow reduce the coefficients of the polynomials of
possible first etc. but anyway... I still think this should be mentioned.
--
Ticket URL: <http://trac.sagemath.org/ticket/20749#comment:9>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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