?2+3
%1 = 5
?factor(18383737373773727282991209202020222112222222111)
%2 =
[3 1]
[11 1]
[13 1]
[231114187 1]
[21092986417 1]
[53128852859 1]
[165455572072019 1]
?gcd(173737372372727272,282818180920202020221111)
%3 = 1
?bezout(173737372372727272,282818180920202020221111)
%4 = [-24662433496369401212531, 15150321588361103, 1]
?%4[1]*173737372372727272+%4[2]*282818180920202020221111
%5 = 1
?v=[173737372372727272,282818180920202020221111]
%6 = [173737372372727272, 282818180920202020221111]
?v[1]
%7 = 173737372372727272
?v[2]
%8 = 282818180920202020221111
?v[1]*v[2]
%9 = 49136087612310489748696032746195539839192
?gcd(v[1],v[2])
%10 = 1
?%2[3,1]
%11 = 13
?%2[3,2]
%12 = 1
?%2[5,2]
%13 = 1
?%2[5,1]
%14 = 21092986417
?factor(18)
%15 =
[2 1]
[3 2]
?w=factor(18)
%16 =
[2 1]
[3 2]
?w[1,]
%17 = [2, 1]
?w[,1]
%18 = [2, 3]~
?w[,1]~
%19 = [2, 3]
??
Help topics: for a list of relevant subtopics, type ?n for n in
0: user-defined functions (aliases, installed and user functions)
1: Standard monadic or dyadic OPERATORS
2: CONVERSIONS and similar elementary functions
3: TRANSCENDENTAL functions
4: NUMBER THEORETICAL functions
5: Functions related to ELLIPTIC CURVES
6: Functions related to general NUMBER FIELDS
7: POLYNOMIALS and power series
8: Vectors, matrices, LINEAR ALGEBRA and sets
9: SUMS, products, integrals and similar functions
10: GRAPHIC functions
11: PROGRAMMING under GP
12: The PARI community
Also:
? functionname (short on-line help)
?\ (keyboard shortcuts)
?. (member functions)
Extended help (if available):
?? (opens the full user's manual in a dvi previewer)
?? tutorial / refcard / libpari (tutorial/reference card/libpari manual)
?? keyword (long help text about "keyword" from the user's manual)
??? keyword (a propos: list of related functions).
??4
addprimes bestappr bezout bezoutres bigomega binomial
chinese content contfrac contfracpnqn core coredisc
dirdiv direuler dirmul divisors eulerphi factor
factorback factorcantor factorff factorial factorint factormod
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gcd hilbert isfundamental ispower isprime ispseudoprime
issquare issquarefree kronecker lcm moebius nextprime
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??bezout
bezout(x,y): returns [u,v,d] such that d=gcd(x,y) and u*x+v*y=d.
??bezout
bezout(x,y): returns [u,v,d] such that d=gcd(x,y) and u*x+v*y=d.
?isprime(3774874874874773878743878378383773374439811)
%20 = 0
?factor(3774874874874773878743878378383773374439811)
%21 =
[17 1]
[25013 1]
[71549 1]
[3360433939 1]
[36922315221269493424481 1]
?3^10000
%22 = 1631350185342625874303256729181154716812132453582537993934820326191825730814319078748015563084784830967325204522323579543340558299917720385238147914536811250145319235516622439102542362884355668655965964501201417744827552999037327442544642575123553734186738760781361993722561687286201650480559317405990952046166850066311892691157177345225585062696852625187913986708508047253964093373024341015218691432891735457685445727419556221801333774562850247067305942699911420254077317598819984248727618368529938892782529678644025299944478569418367532352170443219578580627012338838293177019899084130086150699610894478206501516341034489494580933768915680768667346256303816479219066534012434413398076320559436475496345156407234050260637779058511412381491900163717703445738501993906023292519447111423589297856532241562834414218484289208346622787576050127600980153070303752583915789387574119249770530046969106245436992679597545634023677773435466713907260157496983431276965355718439614758707126044394794486223574445971120447306293776415377003021033218363553181817345661802274597505531321259851442958754554729653460959719483603654687049177192762521435295750345494840363582234572877488517580950015845183738941379809532971199309210141742840677432612645000546788873654625494865860248449453593888865654274697742436838533549608316492131860193497702509578037010430798027635685735034920586607837180606554239353610167340201798095159894698066433039150584580367424834887807101041291866733582384989962348621505030405257778984851241026383481171923694931142341182358531640508530616493667113745698539428567732477177504605097086552089359615168701715385575519734819965907019295477130834762711105247113447632598636283858595955220964538208905518287185486674463373753321752488011840178759509406085571701014408713649553241854424148943708007471615840489591413645180203244670796105875763334569169674329386962374541087005185159067285934706121257344657204508846546061682608257973168600458521828433345239615773003630637942182243581800150590520391820920696966232670695262351242738024046878411453510149673398340124021984004895673368930962032161379375715672756246165193339754026679596386592159091332206057267334984925330339787424238196077533718273003778369870874878173841974769888032160118631050633286970493130307683944479096833930630127337101408724806094685179369797311443270675928854607762283100252680055484969686771028094594660366959379735464213662223119269502732122951191295294032087976312315176055595949696116314145568827884294958728839910027369188001877414756889265018615206533521911307258241769961690199553024993773521909978675895489253436583523584315611279972816412346121981734390478240251711160320657533052785075256464299531806498590081555797994588593112435130325281125525429579708228194665879870597907749246984964418316658595084495316472689614616829780817839847045156132052618054231084074484310746936895970772683660847181706059877173017075544647344077403137122743765104842160622475752708595851594727315102740066294816111128477782810353149948891367280078316788805117715542728510386173665806940479769590075882046523867397088266016228510759922141874365700687253784267788370880751585039769181243388056177265236484729701950802584896483388322516566898693508127459629398312186404627726859040158020905998850051126247016715049526190813668869386132408155904633628896303709031203352240072236088249492818280907540691431995704492750442079727811783767743144697908575643299075358258810244024061103908451640108994886843335374844410463973407451916506763294141934798562443556734207281591075448412381291748731293828067040322818881300397838408133224248464657141757440485296267516561610152736742565486950871200178839384617178045745596304576494356596488751839648129615990247199673550885429296453679677940437723096572336162518203079829773478585460606032341909164671113867849092884010744992[+++]
??default
default({key},{val}): returns the current value of the default key. If val is present, set opt
to val first. If no argument is given, print a list of all defaults as well as their values.
?3^10000%101
%23 = 1
?3^10000%103
%24 = 81
?Mod(3,101)^10000
%25 = Mod(1, 101)
?3^100000000000%103
at top-level: ^100000000000%103
^-----------------
*** _^s: the PARI stack overflows !
current stack size: 8000000 (7.629 Mbytes)
[hint] you can increase GP stack with allocatemem()
*** Break loop: type 'break' to go back to GP
break> break
?allocatemem()
*** Warning: new stack size = 16000000 (15.259 Mbytes).
?allocatemem()
*** Warning: new stack size = 32000000 (30.518 Mbytes).
?allocatemem()
*** Warning: new stack size = 64000000 (61.035 Mbytes).
?allocatemem()
*** Warning: new stack size = 128000000 (122.070 Mbytes).
?allocatemem()
*** Warning: new stack size = 256000000 (244.141 Mbytes).
?3^100000000000%103
at top-level: ^100000000000%103
^-----------------
*** _^s: the PARI stack overflows !
current stack size: 256000000 (244.141 Mbytes)
[hint] you can increase GP stack with allocatemem()
*** Break loop: type 'break' to go back to GP
break>break
?Mod(3,103)^100000000000
%26 = Mod(76, 103)
?Mod(3^100000000000,103)
at top-level: ^100000000000,103)
^------------------
*** _^s: the PARI stack overflows !
current stack size: 256000000 (244.141 Mbytes)
[hint] you can increase GP stack with allocatemem()
*** Break loop: type 'break' to go back to GP
at top-level: ^100000000000,103)
^------------------
*** _^s: user interrupt after
at top-level: ^100000000000,103)
^------------------
break> break
?Mod(3723727277272727272727272,1039299292929292929292)^10000000000000000
%27 = Mod(652690466722500883612, 1039299292929292929292)
?Mod(3,101)*(Mod(5,101)
syntax error, unexpected $end, expecting )-> or ',' or ')': )
^-
?Mod(3,101)*Mod(5,101)
%28 = Mod(15, 101)
?Mod(3,101)*Mod(5,103)
%29 = Mod(0, 1)
?for(n=1,10,print(Mod(3,1001)^n))
Mod(3, 1001)
Mod(9, 1001)
Mod(27, 1001)
Mod(81, 1001)
Mod(243, 1001)
Mod(729, 1001)
Mod(185, 1001)
Mod(555, 1001)
Mod(664, 1001)
Mod(991, 1001)
?for(n=1,10,print(n,"hello ",Mod(3,1001)^n))
1hello Mod(3, 1001)
2hello Mod(9, 1001)
3hello Mod(27, 1001)
4hello Mod(81, 1001)
5hello Mod(243, 1001)
6hello Mod(729, 1001)
7hello Mod(185, 1001)
8hello Mod(555, 1001)
9hello Mod(664, 1001)
10hello Mod(991, 1001)
?for(n=1,1000,if(Mod(3,1001)^n==Mod(1,1001),print(n)))
30
60
90
120
150
180
210
240
270
300
330
360
390
420
450
480
510
540
570
600
630
660
690
720
750
780
810
840
870
900
930
960
990
?for(n=1,1000,if(Mod(3,1001)^n==Mod(1,1001),print(n);break))
30
?znorder(Mod(3,1001))
%30 = 30
??znorder
znorder(x,{o}): order of the integermod x in (Z/nZ)*. Optional o represents a multiple of the
order of the element.
?p=nextprime(100000000)
%31 = 100000007
?znprimroot(p)
%32 = Mod(5, 100000007)
?lift(%)
%33 = 5
??zeta
zeta(s): Riemann zeta function at s with s a complex or a p-adic number.
?zeta(2)
%34 = 1.6449340668482264364724151666460251892
?Pi^2/6
%35 = 1.6449340668482264364724151666460251892
?myfunction(p)=if(isprime(p),return(znprimroot(p)^2))
%36 = (p)->if(isprime(p),return(znprimroot(p)^2))
?myfunction(100)
?myfunction(101)
%37 = Mod(4, 101)
?\rmyfile
*** error opening input file: `myfile'.
*** Break loop: type 'break' to go back to GP
break>break
?\q
?for(n=1,10,if(n%2==0&&n%3==0,print(n," yes"),print(n," no")))
1 no
2 no
3 no
4 no
5 no
6 yes
7 no
8 no
9 no
10 no
?for(n=1,10,if(n%2==0||n%3==0,print(n," yes"),print(n," no")))
1 no
2 yes
3 yes
4 yes
5 no
6 yes
7 no
8 yes
9 yes
10 yes
?\q