Pari/GP Reference Documentation
Contents
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Global index
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GP keyboard shortcuts
Index
A
abs
acos
acosh
addhelp
addprimes
agm
airy
alarm
algadd
algalgtobasis
algaut
algb
algbasis
algbasistoalg
algcenter
algcentralproj
algchar
algcharpoly
algdegree
algdep
algdim
algdisc
algdivl
algdivr
alggroup
alggroupcenter
alghasse
alghassef
alghassei
algindex
alginit
alginv
alginvbasis
algisassociative
algiscommutative
algisdivision
algisdivl
algisinv
algisramified
algissemisimple
algissimple
algissplit
alglatadd
alglatcontains
alglatelement
alglathnf
alglatindex
alglatinter
alglatlefttransporter
alglatmul
alglatrighttransporter
alglatsubset
algmakeintegral
algmul
algmultable
algneg
algnorm
algpoleval
algpow
algprimesubalg
algquotient
algradical
algramifiedplaces
algrandom
algrelmultable
algsimpledec
algsplit
algsplittingdata
algsplittingfield
algsqr
algsub
algsubalg
algtableinit
algtensor
algtomatrix
algtrace
algtype
alias
allocatemem
apply
arg
arity
asin
asinh
asympnum
asympnumraw
atan
atanh
B
bernfrac
bernpol
bernreal
bernvec
besselh1
besselh2
besseli
besselj
besseljh
besseljzero
besselk
besseln
bessely
besselyzero
bestapprPade
bestappr
bestapprnf
bezout
bezoutres
bigomega
binary
binomial
bitand
bitneg
bitnegimply
bitor
bitprecision
bittest
bitxor
bnfcertify
bnfdecodemodule
bnfinit
bnfisintnorm
bnfisnorm
bnfisprincipal
bnfissunit
bnfisunit
bnflog
bnflogdegree
bnflogef
bnfnarrow
bnfsignunit
bnfsunit
bnfunits
bnrL1
bnrchar
bnrclassfield
bnrclassno
bnrclassnolist
bnrcompositum
bnrconductor
bnrconductorofchar
bnrdisc
bnrdisclist
bnrgaloisapply
bnrgaloismatrix
bnrinit
bnrisconductor
bnrisgalois
bnrisprincipal
bnrmap
bnrrootnumber
bnrstark
bnrstarkunit
break
breakloop
breakpoint
C
Catalan
Col
Colrev
Comparison
call
ceil
centerlift
characteristic
charconj
chardiv
chareval
chargalois
charker
charmul
charorder
charpoly
charpow
chinese
cmp
colors
compatible
component
concat
conj
conjvec
content
contfrac
contfraceval
contfracinit
contfracpnqn
core
coredisc
cos
cosh
cotan
cotanh
D
datadir
dbg_down
dbg_err
dbg_up
dbg_x
debug
debugfiles
debugmem
default
denominator
deriv
derivn
derivnum
diffop
digits
dilog
dirdiv
direuler
dirmul
dirpowers
dirpowerssum
dirzetak
divisors
divisorslenstra
divrem
E
Equality
Euler
echo
eint1
ell2cover
ellE
ellK
ellL1
elladd
ellak
ellan
ellanalyticrank
ellap
ellbil
ellbsd
ellcard
ellchangecurve
ellchangepoint
ellchangepointinv
ellconvertname
elldivpol
elleisnum
elleta
ellformaldifferential
ellformalexp
ellformallog
ellformalpoint
ellformalw
ellfromeqn
ellfromj
ellgenerators
ellglobalred
ellgroup
ellheegner
ellheight
ellheightmatrix
ellidentify
ellinit
ellintegralmodel
elliscm
ellisdivisible
ellisisom
ellisogeny
ellisogenyapply
ellisomat
ellisoncurve
ellisotree
ellissupersingular
ellj
elllocalred
elllog
elllseries
ellmaninconstant
ellminimaldisc
ellminimalmodel
ellminimaltwist
ellmoddegree
ellmodulareqn
ellmul
ellneg
ellnonsingularmultiple
ellorder
ellordinate
ellpadicL
ellpadicbsd
ellpadicfrobenius
ellpadicheight
ellpadicheightmatrix
ellpadiclambdamu
ellpadiclog
ellpadicregulator
ellpadics2
ellperiods
ellpointtoz
ellpow
ellrank
ellrankinit
ellratpoints
ellrootno
ellsaturation
ellsea
ellsearch
ellsigma
ellsub
ellsupersingularj
elltamagawa
elltaniyama
elltatepairing
elltors
elltrace
elltwist
ellweilcurve
ellweilpairing
ellwp
ellxn
ellzeta
ellztopoint
erfc
errname
error
eta
eulerfrac
eulerianpol
eulerphi
eulerpol
eulerreal
eulervec
eval
exp
expm1
exponent
export
exportall
extern
externstr
F
factor
factor_add_primes
factor_proven
factorback
factorcantor
factorff
factorial
factorint
factorlimit
factormodDDF
factormodSQF
factormod
factormodcyclo
factornf
factorpadic
ffcompomap
ffembed
ffextend
fffrobenius
ffgen
ffinit
ffinvmap
fflog
ffmap
ffmaprel
ffnbirred
fforder
ffprimroot
fft
fftinv
fibonacci
fileclose
fileextern
fileflush
fileopen
fileread
filereadstr
filewrite1
filewrite
floor
fold
for
forcomposite
fordiv
fordivfactored
foreach
forell
forfactored
format
forpart
forperm
forprime
forprimestep
forqfvec
forsquarefree
forstep
forsubgroup
forsubset
forvec
frac
fromdigits
G
galoischardet
galoischarpoly
galoischartable
galoisconjclasses
galoisexport
galoisfixedfield
galoisgetgroup
galoisgetname
galoisgetpol
galoisidentify
galoisinit
galoisisabelian
galoisisnormal
galoispermtopol
galoissplittinginit
galoissubcyclo
galoissubfields
galoissubgroups
gamma
gammah
gammamellininv
gammamellininvasymp
gammamellininvinit
gcd
gcdext
gcharalgebraic
gcharconductor
gcharduallog
gchareval
gcharidentify
gcharinit
gcharisalgebraic
gcharlocal
gcharlog
gcharnewprec
genus2igusa
genus2red
getabstime
getcache
getenv
getheap
getlocalbitprec
getlocalprec
getrand
getstack
gettime
getwalltime
global
graphcolormap
graphcolors
H
halfgcd
hammingweight
harmonic
help
hgmalpha
hgmbydegree
hgmcoef
hgmcoefs
hgmcyclo
hgmeulerfactor
hgmgamma
hgminit
hgmissymmetrical
hgmparams
hgmtwist
hilbert
histfile
histsize
hyperellchangecurve
hyperellcharpoly
hyperelldisc
hyperellisoncurve
hyperellminimaldisc
hyperellminimalmodel
hyperellordinate
hyperellpadicfrobenius
hyperellratpoints
hyperellred
hypergeom
hyperu
I
I
idealadd
idealaddtoone
idealappr
idealchinese
idealcoprime
idealdiv
idealdown
idealfactor
idealfactorback
idealfrobenius
idealhnf
idealintersect
idealinv
idealismaximal
idealispower
ideallist
ideallistarch
ideallog
idealmin
idealmul
idealnorm
idealnumden
idealpow
idealprimedec
idealprincipalunits
idealramgroups
idealred
idealredmodpower
idealstar
idealtwoelt
idealval
if
iferr
imag
incgam
incgamc
inline
input
install
intcirc
intformal
intfuncinit
intnum
intnumgauss
intnumgaussinit
intnuminit
intnumosc
intnumromb
isfundamental
ispolygonal
ispower
ispowerful
isprime
isprimepower
ispseudoprime
ispseudoprimepower
issquare
issquarefree
istotient
K
kill
kronecker
L
List
lambertw
laurentseries
lcm
length
lerchphi
lerchzeta
lex
lfun
lfunan
lfunartin
lfuncheckfeq
lfunconductor
lfuncost
lfuncreate
lfundiv
lfundual
lfunetaquo
lfuneuler
lfungenus2
lfunhardy
lfunhgm
lfuninit
lfunlambda
lfunmf
lfunmfspec
lfunmul
lfunorderzero
lfunparams
lfunqf
lfunrootres
lfunshift
lfunsympow
lfuntheta
lfunthetacost
lfunthetainit
lfuntwist
lfunzeros
lift
liftall
liftint
liftpol
limitnum
lindep
lines
linewrap
listcreate
listinsert
listkill
listpop
listput
listsort
lngamma
localbitprec
localprec
log1p
log
log
logfile
logint
M
Map
Mat
Mod
Motives
mapapply
mapdelete
mapget
mapisdefined
mapput
matadjoint
matalgtobasis
matbasistoalg
matcompanion
matconcat
matdet
matdetint
matdetmod
matdiagonal
mateigen
matfrobenius
mathess
mathilbert
mathnf
mathnfmod
mathnfmodid
mathouseholder
matid
matimage
matimagecompl
matimagemod
matindexrank
matintersect
matinverseimage
matinvmod
matisdiagonal
matker
matkerint
matkermod
matmuldiagonal
matmultodiagonal
matpascal
matpermanent
matqr
matrank
matreduce
matrix
matrixqz
matsize
matsnf
matsolve
matsolvemod
matsupplement
mattranspose
max
mfDelta
mfEH
mfEk
mfTheta
mfatkin
mfatkineigenvalues
mfatkininit
mfbasis
mfbd
mfbracket
mfcoef
mfcoefs
mfconductor
mfcosets
mfcuspisregular
mfcusps
mfcuspval
mfcuspwidth
mfderivE2
mfderiv
mfdescribe
mfdim
mfdiv
mfeigenbasis
mfeigensearch
mfeisenstein
mfembed
mfeval
mffields
mffromell
mffrometaquo
mffromlfun
mffromqf
mfgaloisprojrep
mfgaloistype
mfhecke
mfheckemat
mfinit
mfisCM
mfisequal
mfisetaquo
mfkohnenbasis
mfkohnenbijection
mfkohneneigenbasis
mflinear
mfmanin
mfmul
mfnumcusps
mfparams
mfperiodpol
mfperiodpolbasis
mfpetersson
mfpow
mfsearch
mfshift
mfshimura
mfslashexpansion
mfspace
mfsplit
mfsturm
mfsymbol
mfsymboleval
mftaylor
mftobasis
mftocoset
mftonew
mftraceform
mftwist
min
minpoly
modreverse
moebius
msatkinlehner
mscosets
mscuspidal
msdim
mseisenstein
mseval
msfarey
msfromcusp
msfromell
msfromhecke
msgetlevel
msgetsign
msgetweight
mshecke
msinit
msissymbol
mslattice
msnew
msomseval
mspadicL
mspadicinit
mspadicmoments
mspadicseries
mspathgens
mspathlog
mspetersson
mspolygon
msqexpansion
mssplit
msstar
mstooms
N
nbthreads
new_galois_format
newtonpoly
next
nextprime
nfalgtobasis
nfbasis
nfbasistoalg
nfcertify
nfcompositum
nfdetint
nfdisc
nfdiscfactors
nfeltadd
nfeltdiv
nfeltdiveuc
nfeltdivmodpr
nfeltdivrem
nfeltembed
nfeltispower
nfeltissquare
nfeltmod
nfeltmul
nfeltmulmodpr
nfeltnorm
nfeltpow
nfeltpowmodpr
nfeltreduce
nfeltreducemodpr
nfeltsign
nfelttrace
nfeltval
nffactor
nffactorback
nffactormod
nfgaloisapply
nfgaloisconj
nfgrunwaldwang
nfhilbert
nfhnf
nfhnfmod
nfinit
nfisideal
nfisincl
nfisisom
nfislocalpower
nfkermodpr
nflist
nfmodpr
nfmodprinit
nfmodprlift
nfnewprec
nfpolsturm
nfresolvent
nfroots
nfrootsof1
nfsnf
nfsolvemodpr
nfsplitting
nfsubfields
nfsubfieldscm
nfsubfieldsmax
nfweilheight
norm
norml2
normlp
numbpart
numdiv
numerator
numtoperm
O
O
omega
oo
op=
output
P
Pi
Pol
Polrev
padicappr
padicfields
padicprec
parapply
pareval
parfor
parforeach
parforprime
parforprimestep
parforstep
parforvec
parisize
parisizemax
parploth
parplothexport
parselect
parsum
partitions
parvector
path
permcycles
permorder
permsign
permtonum
plot
plotarc
plotbox
plotclip
plotcolor
plotcopy
plotcursor
plotdraw
plotexport
ploth
plothexport
plothraw
plothrawexport
plothsizes
plothsizes
plotinit
plotkill
plotlines
plotlinetype
plotmove
plotpoints
plotpointsize
plotpointtype
plotrbox
plotrecth
plotrecthraw
plotrline
plotrmove
plotrpoint
plotscale
plotstring
polchebyshev
polclass
polcoef
polcoeff
polcompositum
polcyclo
polcyclofactors
poldegree
poldisc
poldiscfactors
poldiscreduced
polfromroots
polgalois
polgraeffe
polhensellift
polhermite
polinterpolate
polisclass
poliscyclo
poliscycloprod
polisirreducible
pollaguerre
pollead
pollegendre
polmodular
polrecip
polred
polredabs
polredbest
polredord
polresultant
polresultantext
polroots
polrootsbound
polrootsff
polrootsmod
polrootspadic
polrootsreal
polsturm
polsubcyclo
polsubcyclofast
polsylvestermatrix
polsym
poltchebi
polteichmuller
poltomonic
poltschirnhaus
polylog
polylogmult
polzagier
powers
precision
precprime
prettyprinter
prime
primecert
primecertexport
primecertisvalid
primelimit
primepi
primes
print1
print
printf
printp
printsep1
printsep
printtex
prod
prodeuler
prodeulerrat
prodinf
prodnumrat
prompt
prompt_cont
psdraw
psfile
psi
psploth
psplothraw
Q
Qfb
qfauto
qfautoexport
qfbclassno
qfbcomp
qfbcompraw
qfbcornacchia
qfbhclassno
qfbil
qfbnucomp
qfbnupow
qfbpow
qfbpowraw
qfbprimeform
qfbred
qfbredsl2
qfbsolve
qfcholesky
qfcvp
qfeval
qfgaussred
qfisom
qfisominit
qfjacobi
qflll
qflllgram
qfminim
qfminimize
qfnorm
qforbits
qfparam
qfperfection
qfrep
qfsign
qfsolve
quadclassunit
quaddisc
quadgen
quadhilbert
quadpoly
quadray
quadregulator
quadunit
quadunitindex
quadunitnorm
quit
R
Reduction
ramanujantau
random
randomprime
read
readline
readstr
readvec
real
realbitprecision
realprecision
recover
removeprimes
return
rnfalgtobasis
rnfbasis
rnfbasistoalg
rnfcharpoly
rnfconductor
rnfdedekind
rnfdet
rnfdisc
rnfeltabstorel
rnfeltdown
rnfeltnorm
rnfeltreltoabs
rnfelttrace
rnfeltup
rnfequation
rnfhnfbasis
rnfidealabstorel
rnfidealdown
rnfidealfactor
rnfidealhnf
rnfidealmul
rnfidealnormabs
rnfidealnormrel
rnfidealprimedec
rnfidealreltoabs
rnfidealtwoelt
rnfidealup
rnfinit
rnfisabelian
rnfisfree
rnfislocalcyclo
rnfisnorm
rnfisnorminit
rnfkummer
rnflllgram
rnfnormgroup
rnfpolred
rnfpolredabs
rnfpolredbest
rnfpseudobasis
rnfsteinitz
rootsof1
round
S
Ser
Set
Str
Strchr
Strexpand
Strprintf
Strtex
secure
select
self
seralgdep
serchop
serconvol
serdiffdep
seriesprecision
serlaplace
serprec
serreverse
setbinop
setdebug
setdelta
setintersect
setisset
setminus
setrand
setsearch
setunion
shift
shiftmul
sigma
sign
simplify
simplify
sin
sinc
sinh
sizebyte
sizedigit
snfrank
solve
solvestep
sopath
sqr
sqrt
sqrtint
sqrtn
sqrtnint
stirling
strchr
strexpand
strictargs
strictmatch
strjoin
strprintf
strsplit
strtex
strtime
subcyclohminus
subcycloiwasawa
subcyclopclgp
subgrouplist
subst
substpol
substvec
sum
sumalt
sumdedekind
sumdigits
sumdiv
sumdivmult
sumeulerrat
sumformal
suminf
sumnum
sumnumap
sumnumapinit
sumnuminit
sumnumlagrange
sumnumlagrangeinit
sumnummonien
sumnummonieninit
sumnumrat
sumnumsidi
sumpos
system
T
TeXstyle
Templates
tan
tanh
taylor
teichmuller
theta
thetanullk
threadsize
threadsizemax
thue
thueinit
timer
trace
trap
truncate
type
U
unexport
unexportall
uninline
until
V
Vec
Vecrev
Vecsmall
valuation
varhigher
variable
variables
varlower
vecextract
vecmax
vecmin
vecprod
vecsearch
vecsort
vecsum
vector
vectorsmall
vectorv
version
W
warning
weber
whatnow
while
write1
write
writebin
writetex
Z
zeta
zetahurwitz
zetamult
zetamultall
zetamultconvert
zetamultdual
znchar
zncharconductor
znchardecompose
znchargauss
zncharinduce
zncharisodd
znchartokronecker
znchartoprimitive
znconreychar
znconreyconductor
znconreyexp
znconreylog
zncoppersmith
znlog
znorder
znprimroot
znstar
znsubgroupgenerators