Sharedwww / talks / bernoulli / sage_log.txtOpen in CoCalc
Author: William A. Stein
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[email protected]:~$ cd papers/talk
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bash: cd: papers/talk: No such fil
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[email protected]:~$ ls
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168 email not
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20b fiction off
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backups grants onh
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bin graphs org
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books hecke pap
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boundless_explorer job pas
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code learn peo
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comp library pho
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computer local pro
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conferences magma pyt
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crypto Mail res
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data mathdiary s
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Desktop misc sag
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diary money sag
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downloads music san
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edu neron sd
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[email protected]:~$ cd papers/bernoulli/
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[email protected]:~/papers/bernoulli$ ls
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auto bern3.tex bern4.tex curren
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[email protected]:~/papers/bernoulli$ cd ta
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[email protected]:~/papers/bernoulli/talk$
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003.gif
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attach.sage
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auth.pdf
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auto
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bern.jpeg
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bernoulli2.jpg
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Bernoulli.pdf
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bern.sage
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buzzard-project_improve.txt
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calcbn12
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current.aux
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current.dvi
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current.log
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current.nav
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current.out
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current.pdf
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current.ps
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current.snm
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current.tex
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current.toc
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current.vrb
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ecm-proc.pdf
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factorial.spyx
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fox-kummer_congruences_for_expresspolynomials.ps
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fresnel-nombres_de_Bernoulli_et_fo
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genber.sage
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LFunctions.pdf
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misc.sage
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notes.txt
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serre-fonctions_zeta_p-adiques.pdf
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t
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these.ps
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[email protected]:~/papers/bernoulli/talk$
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ext = ps
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Opening current.ps using gv --swap
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gv --swap --watch --quiet "current
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[email protected]:~/papers/bernoulli/talk$
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[email protected]:~/papers/bernoulli/talk$
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bash: sag: command not found
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[email protected]:~/papers/bernoulli/talk$
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----------------------------------
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| SAGE Version 1.0.3, Build Date:
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| Distributed under the GNU Genera
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| For help type <object>?, <object
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----------------------------------
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sage: clear
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sage:
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sage:
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sage:
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sage: bernoulli(100)
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_2 = -9459803781912212529522743301533066936133385696204311395415197
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sage: bernoulli(1000)
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_3 = -18243104738661887254572640268670429060521971581576411262572623210697096154899246274955229080874185675822415516684926972441849140109862992465225174097919156372263610228104546530844116137235069692022026260201962026025579005841653927128467639068343422638070295122610817023611889303668166839919156379768122753427426880591799883780255338245895962670442011443630321460259488560543017655574251371150213401051529527491787349736768598347076238825128781905743235312990704069303091768065311836481894518927257264459476758538976992485763097296399763607385878011073153983309981755577515059732295130888490067011333916764610306198429310933121463214168354254815064629129596536997380608256421658268809203555030692846151917069871976510905515966840312411845543616913418528197912335893019941012295746518810594322744943540922319548461929421334360546114754048678863175323642929062590934110003913683363595481408420879424166549229427077592758201421472658482223644369131454584000998591519058404733793433129093995842312746836871169674978646990047126222109345933847358924230963465487604170316077418754242710066906954466338361203745255515267088034037323653333521203382720213197148764600183502703856341178077687454550562191060047315296422920495789
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sage: len(str(bernoulli(1000)))
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_4 = 1790
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sage: bernoulli(2006)
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_5 = 18270523979860326143714702307358225708827354257580788690274124720846038087178060546906746440170274442083367747005667718765819285838794739318387017542153398798175992472528557295572156131245782961643118464286320011835529869281533512017256124614851635837138178545139889422847455164793269258892027468865749496481810438685657450567692009221210176541351847356791525076257495942315588948248727608255228889312043776300309159327247162230600101384300047293620045455954167257361176059307887442090426650556366691308163746438022137878605579701497625797755045298519817835673434868351279714224284385046113285943143066428904732463099708058422021045196822172816069712804265282171031748088326838836930840679549440628538192559882442764259187498605069159007697570876449688665095166284848713337326133954665383616901074138953940759477018662413745383086018699434652006258894615820677963382720117287536325715296711284811179551043915802536705297958371496497307578528394349223067319581092225503905664264686856448810691871480079338433546628851589080424900837549243337263333898700773166168408097898676893244463875198768357465365058743127427581351191017484200369458128893284703319256451636821286967742027096705955881335510092484002324985214739226363594350754072566500782275662704378213317517192384204136616746056520887672342313696706577711481907371955385085376444475500294185415421017241897409594829679592769528196041594977555944583440715527933230172231455003319150218801306076022719357058273346626005188376234033872851818018116435767399934434077914728991005201866875890437097956837032218227939001813445651294058658913234109738283857399622143126872930721408245153972752796480816990076321047852799325995380362965690563538290672919202048449048866911499087605110244491493587977451994000224872929345613894620127200287500830396252867409322232571748731214038906182866937839976321033208467603717717796944945510812870690289147016959294592862555955962695404182884208255736216138748407196392502386815267514716690748275330744531102997219903714143361831697943981384531757164323288365273427882785294039926876860747850516850256331890180666760990394126279097415604271740736984899363114351898726315427737499631537136792178928990897368068154609202803862459201559586128938294437381075589404085973244257905331243762684646265950566370986126199280572916678847722853711121468223254728833756427690771957698078392927278949306124903552332017071351675317294490195852168993955543667859626934615862811172237842828527390144671577839980301464142671370976081407022895183253339977492188545731738933376497524776250775360643279995994999874075180054952376831252602967587859727708837413604172125785334196534905007563299007684397398616273786649064277169698903147152742577325361702556732132261531294082302400793044749568675121489996948433738047827997516067018155738269558943480249727704663753143/6
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sage: bernoulli(2006)
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_6 = 182705239798603261437147023087947393183870175421533987981759924228474551647932692588920274688657437763003091593272471622306001013877550452985198178356734348683512798388369308406795494406285381925598770186624137453830860186994346520092230673195810922255039056642646868751987683574653650587431274275813635943507540725665007822756627043772418974095948296795927695281960418180181164357673999344340779147289082451539727527964808169900763210493456138946201272002875008303962
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59286255595596269540418288420
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2328836527342788278529403
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6792178928990897368068
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847722853711121468223
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111722378428285273901
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518005495237683125260
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556732132261531294082
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sage: bernoulli(10)
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_7 = 5/66
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sage: G=DirichletGroup(13)
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sage: G
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_9 = Group of Dirichlet chara
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cters of modulus 13 over Cyclo
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tomic Field of order 12 and de
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gree 4
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sage: e = G.0
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sage: e
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_11 = [zeta_12]
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sage: e.bernoulli(2)
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_12 = 0
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sage: e.bernoulli(3)
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_13 = -6*zeta_12^3 + 30*zeta_1
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2^2 + 12*zeta_12 - 6
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sage: e.bernoulli(4)
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_14 = 0
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sage: e(-1)
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_15 = -1
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sage: e.bernoulli(5)
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_16 = 7430/13*zeta_12^3 - 3475
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0/13*zeta_12^2 - 11380/13*zeta
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_12 + 9110/13
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sage: time e.bernoulli(7)
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CPU times: user 0.29 s, sys: 0
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.03 s, total: 0.32 s
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Wall time: 0.34
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_17 = -1373582/13*zeta_12^3 +
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6295030/13*zeta_12^2 + 1944964 /13*zeta_12 - 1709582/13
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sage: time e.bernoulli(9)
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CPU times: user 0.38 s, sys: 0 .05 s, total: 0.42 s
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Wall time: 0.45
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_18 = 32799798*zeta_12^3 - 149 483790*zeta_12^2 - 45491508*ze ta_12 + 40864806
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sage: e.bernoulli (7)
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_19 = -1373582/13*zeta_12^3 + 6295 1944964/13*zeta_12 - 1709582/13
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sage: e.bernoulli (19)
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_20 = -205981347635108520197894/136949631296096034030/13*zeta_12^2 +0026388/13*zeta_12 - 2566150080784
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sage:
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sage:
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sage:
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sage: test1(100, 10
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....: )
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group: Group of Dirichlet charactver Cyclotomic Field of order 2 an
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chi = [-1]
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1.2500000000000000000000000000000e
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0.0000000000000000000000000000000e
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8.9999999999999999999999999996971e
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3.3061224489795918367346938770856e
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d = 9
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K = 4.050000000000000000000000000
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L = 8.844126777849974731066349000
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a = 3.100627668029982017547631506
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g = -2.36658271566303541623518569508075688772935274463415062e0*I
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B3 = 6.002639291135028057592666841956531491175072449301379e-30*I
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_21 =
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([-1],
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6.002639291135028057592666845765531491175072449301379e-30*I)
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sage: test1(100, 20)
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group: Group of Dirichlet charactver Cyclotomic Field of order 2 an
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chi = [-1]
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1.2500000000000000000000000000000e
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0.0000000000000000000000000000000e
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8.9999999999999999999999999996971e
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3.3061224489795918367346938770856e
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8.4950704549287784234655545131227e
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5.1504022967524500956104317700978e
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2.3021134629896968064238770939658e
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1.6493053735429902473781793361746e
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d = 9
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K = 4.050000000000000000000000000
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L = 8.841001113807802471255999374
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a = 3.100627668029982017547631506
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g = -2.36658271566303541623518569508075688772935274463415062e0*I
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B3 = 6.000517856847425921093568235799222970695685668397101e-30*I
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_22 =
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([-1],
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6.000517856847425921093568233152722970695685668397101e-30*I)
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sage:
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sage: test1(100, 20)
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group: Group of Dirichlet charactver Cyclotomic Field of order 2 an
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chi = [-1]
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2 1.250000000000000000000000000000
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3 0.000000000000000000000000000000
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5 8.999999999999999999999999999697
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7 3.306122448979591836734693877085
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11 8.49507045492877842346555451312
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13 5.15040229675245009561043177009
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17 2.30211346298969680642387709396
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19 1.64930537354299024737817933617
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d = 9
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K = 4.050000000000000000000000000
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L = 8.841001113807802471255999374
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a = 3.100627668029982017547631506
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g = -2.36658271566303541623518569508075688772935274463415062e0*I
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B3 = 6.000517856847425921093568235799222970695685668397101e-30*I
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_23 =
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([-1],
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6.000517856847425921093568233152722970695685668397101e-30*I)
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sage:
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sage: test1(200, 15)
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group: Group of Dirichlet charactver Cyclotomic Field of order 2 an