\\ $Id: in,v 2.0 1997/11/14 03:52:59 karim Exp karim $
\e
+3
-5
5+3
5-3
5/3
5\3
5\/3
5%3
5^3
\p 57
Pi
\p 38
O(x^12)
padicno=(5/3)*127+O(127^5)
plotinit(0,500,500)
\\ A
abs(-0.01)
acos(0.5)
acosh(3)
addprimes([nextprime(10^9),nextprime(10^10)])
matadjoint([1,2;3,4])
agm(1,2)
agm(1+O(7^5),8+O(7^5))
algdep(2*cos(2*Pi/13),6)
algdep(2*cos(2*Pi/13),6,15)
\\allocatemem(3000000)
nfpol=x^5-5*x^3+5*x+25
nf=nfinit(nfpol)
ba=nfalgtobasis(nf,Mod(x^3+5,nfpol))
apol=x^3+5*x+1
padicappr(apol,1+O(7^8))
padicappr(x^3+5*x+1,Mod(x*(1+O(7^8)),x^2+x-1))
4*arg(3+3*I)
3*asin(sqrt(3)/2)
asinh(0.5)
matcompanion(x^5-12*x^3+0.0005)
3*atan(sqrt(3))
atanh(0.5)
\\ B
nfbasis(x^3+4*x+5)
nfbasis(x^3+4*x+5,2)
nfbasis(x^3+4*x+12,1)
nfbasistoalg(nf,ba)
bernreal(12)
bernvec(6)
bestappr(Pi,10000)
bezout(123456789,987654321)
bigomega(12345678987654321)
binomial(1.1,5)
binary(65537)
bittest(10^100,100)
plotmove(0,0,0);plotbox(0,500,500)
setrand(1);quadclassunit(1-10^7,,[1,1])
setrand(1);bnf=bnfinit(x^2-x-57,2,[0.2,0.2])
bnfcertify(bnf)
bnfunit(bnf)
setrand(1);bnfinit(x^2-x-100000,1)
setrand(1);bnf=bnfinit(x^2-x-57,,[0.2,0.2])
setrand(1);quadclassunit(10^9-3,,[0.5,0.5])
setrand(1);bnfclassunit(x^4-7,2,[0.2,0.2])
setrand(1);bnfclassunit(x^2-x-100000)
setrand(1);bnfclassunit(x^2-x-100000,1)
setrand(1);bnfclassunit(x^4+24*x^2+585*x+1791,,[0.1,0.1])
bnfnarrow(bnf)
bnrclass(bnf,[[5,3;0,1],[1,0]])
bnr=bnrclass(bnf,[[5,3;0,1],[1,0]],2)
bnr2=bnrclass(bnf,[[25,13;0,1],[1,1]],2)
sizebyte(%)
\\ C
ceil(-2.5)
centerlift(Mod(456,555))
contfrac(Pi)
contfrac(Pi,5)
contfrac((exp(1)-1)/(exp(1)+1),[1,3,5,7,9])
changevar(x+y,[z,t])
charpoly([1,2;3,4],z)
charpoly(Mod(x^2+x+1,x^3+5*x+1),z)
charpoly([1,2;3,4],z,1)
charpoly(Mod(1,8191)*[1,2;3,4],z,2)
chinese(Mod(7,15),Mod(13,21))
qfbclassno(-12391)
qfbclassno(1345)
qfbclassno(-12391,1)
qfbclassno(1345,1)
polcoeff(sin(x),7)
Qfb(2,1,3)*Qfb(2,1,3)
component(1+O(7^4),3)
polcompositum(x^4-4*x+2,x^3-x-1)
polcompositum(x^4-4*x+2,x^3-x-1,1)
qfbcompraw(Qfb(5,3,-1,0.),Qfb(7,1,-1,0.))
concat([1,2],[3,4])
bnrconductor(bnf,[[25,13;0,1],[1,1]])
bnrconductorofchar(bnr,[2])
conj(1+I)
%_
conjvec(Mod(x^2+x+1,x^3-x-1))
content([123,456,789,234])
serconvol(sin(x),x*cos(x))
core(54713282649239)
core(54713282649239,1)
coredisc(54713282649239)
coredisc(54713282649239,1)
cos(1)
cosh(1)
plotmove(0,200,150)
plotcursor(0)
truncate(1.7,1)
polcyclo(105)
\\ D
poldegree(x^3/(x-1))
denominator(12345/54321)
lindep(Mod(1,7)*[2,-1;1,3],-1)
deriv((x+y)^5,y)
((x+y)^5)'
matdet([1,2,3;1,5,6;9,8,7])
matdet([1,2,3;1,5,6;9,8,7],1)
matdetint([1,2,3;4,5,6])
matdiagonal([2,4,6])
dilog(0.5)
dz=vector(30,k,1);dd=vector(30,k,k==1);dm=dirdiv(dd,dz)
acurve=ellinit([0,0,1,-1,0])
apoint=[2,2]
ellisoncurve(acurve,apoint)
elladd(acurve,apoint,apoint)
ellak(acurve,1000000007)
ellan(acurve,100)
ellap(acurve,10007)
ellap(acurve,10007,1)
ellan(acurve,100)==deu
deu=direuler(p=2,100,1/(1-ellap(acurve,p)*x+if(acurve[12]%p,p,0)*x^2))
acurve=ellchangecurve(acurve,[-1,1,2,3])
apoint=ellchangepoint(apoint,[-1,1,2,3])
ellisoncurve(acurve,apoint)
mcurve=ellinit([0,0,0,-17,0])
mpoints=[[-1,4],[-4,2]]~
mhbi=ellbil(mcurve,mpoints,[9,24])
dirmul(abs(dm),dz)
dirzetak(nfinit(x^3-10*x+8),30)
poldisc(x^3+4*x+12)
nfdisc(x^3+4*x+12)
nfdisc(x^3+4*x+12,1)
bnrdisc(bnr,Mat(6))
bnrdisc(bnr)
bnrdisc(bnr2,,,2)
lu=ideallist(bnf,55,3);bnrdisclist(bnf,lu)
bnrdisclist(bnf,20,,1)
bnrdisc(bnr,Mat(6),,1)
bnrdisc(bnr,,,1)
bnrdisc(bnr2,,,3)
divisors(8!)
divrem(345,123)
divrem(x^7-1,x^5+1)
sumdiv(8!,x,x)
psdraw([0,0,0])
\\ E
mateigen([1,2,3;4,5,6;7,8,9])
eint1(2)
erfc(2)
eta(q)
euler
z=y;y=x;eval(z)
exp(1)
vecextract([1,2,3,4,5,6,7,8,9,10],1000)
\\ F
10!
factorial(10)
factorcantor(x^11+1,7)
centerlift(lift(factorff(x^3+x^2+x-1,3,t^3+t^2+t-1)))
factormod(x^11+1,7)
factormod(x^11+1,7,1)
factor(17!+1)
factor(100!+1,0)
factor(40!+1,100000)
p=x^5+3021*x^4-786303*x^3-6826636057*x^2-546603588746*x+3853890514072057
fa=[11699,6;2392997,2;4987333019653,2]
nfbasis(p,0,fa)
nfdisc(p,0,fa)
polred(p,0,fa)
polred(p,1,fa)
factornf(x^3+x^2-2*x-1,t^3+t^2-2*t-1)
factorpadic(apol,7,8)
factorpadic(apol,7,8,1)
fibonacci(100)
floor(-1/2)
floor(-2.5)
for(x=1,5,print(x!))
fordiv(10,x,print(x))
forprime(p=1,30,print(p))
forstep(x=0,Pi,Pi/12,print(sin(x)))
forvec(x=[[1,3],[-2,2]],print1([x[1],x[2]]," "));print(" ");
frac(-2.7)
\\ G
polgalois(x^6-3*x^2-1)
nf3=nfinit(x^6+108);nfgaloisconj(nf3)
nfgaloisconj(nf3,1)
aut=%[2];nfgaloisapply(nf3,aut,Mod(x^5,x^6+108))
gammah(10)
gamma(10.5)
matsolve(mathilbert(10),[1,2,3,4,5,6,7,8,9,0]~)
matsolvemod([2,3;5,4],[7,11],[1,4]~)
matsolvemod([2,3;5,4],[7,11],[1,4]~,1)
gcd(12345678,87654321)
gcd(x^10-1,x^15-1,2)
getheap
getrand
ellglobalred(acurve)
getheap
\\ H
qfbhclassno(2000003)
ellheight(acurve,apoint)
ellheight(acurve,apoint,1)
mathnf(amat=1/mathilbert(7))
mathnf(amat,1)
mathnf(amat,2)
mathnfmod(amat,matdetint(amat))
mathnf(amat,3)
mathess(mathilbert(7))
hilbert(2/3,3/4,5)
mathilbert(5)
hilbert(Mod(5,7),Mod(6,7))
hyperu(1,1,1)
\\ I
I^2
nf1=nfinit(nfpol,2)
nfinit(nfpol,3)
nfinit(nfpol,4)
vp=idealprimedec(nf,3)[1]
idx=idealmul(nf,matid(5),vp)
idealinv(nf,idx)
idy=idealred(nf,idx,[1,5,6])
idealadd(nf,idx,idy)
idealaddtoone(nf,idx,idy)
idealaddtoone(nf,[idy,idx])
idealappr(nf,idy)
idealappr(nf,idealfactor(nf,idy),1)
idealcoprime(nf,idx,idx)
idz=idealintersect(nf,idx,idy)
idealfactor(nf,idz)
ideallist(bnf,20)
idx2=idealmul(nf,idx,idx)
idt=idealmul(nf,idx,idx,1)
idealdiv(nf,idy,idt)
idealdiv(nf,idx2,idx,1)
idealhnf(nf,vp)
idealhnf(nf,vp[2],3)
idealnorm(nf,idt)
idp=idealpow(nf,idx,7)
idealpow(nf,idx,7,1)
idealtwoelt(nf,idy)
idealtwoelt(nf,idy,10)
idealval(nf,idp,vp)
matid(5)
if(3<2,print("bof"),print("ok"));
imag(2+3*I)
matimage([1,3,5;2,4,6;3,5,7])
matimage(Pi*[1,3,5;2,4,6;3,5,7])
incgam(2,1)
incgam(4,1,6)
matindexrank([1,1,1;1,1,1;1,1,2])
vecindexsort([8,7,6,5])
ellinit([0,0,0,-1,0])
ellinit([0,0,0,-17,0],1)
plotinit(1,700,700)
nfz=zetakinit(x^2-2);
intformal(sin(x),x)
intformal((-x^2-2*a*x+8*a)/(x^4-14*x^3+(2*a+49)*x^2-14*a*x+a^2),x)
matintersect([1,2;3,4;5,6],[2,3;7,8;8,9])
\p 19
intnum(x=0,Pi,sin(x),1)
sqr(2*intnum(x=0,4,exp(-x^2),1))
4*intnum(x=1,10^20,1/(1+x^2),2)
intnum(x=-0.5,0.5,1/sqrt(1-x^2))
2*intnum(x=0,100,sin(x)/x,3)
\p 38
matinverseimage([1,1;2,3;5,7],[2,2,6]~)
matisdiagonal([1,0,0;0,5,0;0,0,0])
isfundamental(12345)
nfisideal(bnf[7],[5,1;0,1])
nfisincl(x^2+1,x^4+1)
nfisincl(nfinit(x^2+1),nfinit(x^4+1),1)
polisirreducible(x^5+3*x^3+5*x^2+15)
nfisisom(x^3+x^2-2*x-1,x^3+x^2-2*x-1)
nfisisom(nfinit(x^3-2),nfinit(x^3-6*x^2-6*x-30),1)
isprime(12345678901234567)
bnfisprincipal(bnf,[5,1;0,1],0)
bnfisprincipal(bnf,[5,1;0,1])
bnrisprincipal(bnr,idealprimedec(bnf,7)[1])
ispseudoprime(73!+1)
sqrtint(10!^2+1)
setisset([-3,5,7,7])
issquarefree(123456789876543219)
issquare(12345678987654321)
bnfisunit(bnf,Mod(3405*x-27466,x^2-x-57))
\\ J
qfjacobi(mathilbert(6))
besseljh(1,1)
ellj(I)
\\ K
besselk(1+I,1)
besselk(1+I,1,1)
x
y
matker(matrix(4,4,x,y,x/y))
matker(matrix(4,4,x,y,sin(x+y)))
matker(matrix(4,4,x,y,x+y),1)
matkerint(matrix(4,4,x,y,x*y))
matkerint(matrix(4,4,x,y,x*y),1)
matkerint(matrix(4,6,x,y,2520/(x+y)),2)
f(u)=u+1;
print(f(5));kill(f);
f=12
plotkill(1)
kronecker(5,7)
kronecker(3,18)
\\ L
serlaplace(x*exp(x*y)/(exp(x)-1))
lcm(15,-21)
length(divisors(1000))
pollegendre(10)
lex([1,3],[1,3,5])
veclexsort([[1,5],[2,4],[1,5,1],[1,4,2]])
lift(chinese(Mod(7,15),Mod(4,21)))
lindep([(1-3*sqrt(2))/(3-2*sqrt(3)),1,sqrt(2),sqrt(3),sqrt(6)])
lindep([(1-3*sqrt(2))/(3-2*sqrt(3)),1,sqrt(2),sqrt(3),sqrt(6)],14)
plotmove(0,0,900);plotlines(0,900,0)
plotlines(0,vector(5,k,50*k),vector(5,k,10*k*k))
m=1/mathilbert(7)
mp=concat(m,matid(7))
qflll(m)
qflll(m,7)
qflllgram(m)
qflllgram(m,7)
qflllgram(m,1)
qflllgram(mp~*mp,4)
qflll(m,1)
qflll(m,2)
qflll(mp,4)
qflll(m,3)
\p 96
alias(ln,log)
ln(2)
lngamma(10^50*I)
\p 2000
log(2)
log(2,1)
\p 19
bcurve=ellinit([0,0,0,-3,0])
elllocalred(bcurve,2)
ccurve=ellinit([0,0,-1,-1,0])
l=elllseries(ccurve,2,-37,1)
elllseries(ccurve,2,-37,1.2)-l
\\ M
setrand(1);sbnf=bnfinit(x^3-x^2-14*x-1,3)
bnfmake(sbnf)
concat(Mat(vector(4,x,x)~),vector(4,x,10+x)~)
vecextract(matrix(15,15,x,y,x+y),vector(5,x,3*x),vector(3,y,3*y))
ma=ellheightmatrix(mcurve,mpoints)
matsolve(ma,mhbi)
(1.*mathilbert(7))^(-1)
matsize([1,2;3,4;5,6])
matrix(5,5,x,y,gcd(x,y))
matrixqz([1,3;3,5;5,7],0)
matrixqz([1/3,1/4,1/6;1/2,1/4,-1/4;1/3,1,0],-1)
matrixqz([1,3;3,5;5,7],-2)
max(2,3)
min(2,3)
qfminim([2,1;1,2],4,6)
Mod(-12,7)
Mod(-12,7,1)
Mod(10873,49649)^-1
modreverse(Mod(x^2+1,x^3-x-1))
plotmove(0,243,583);plotcursor(0)
moebius(3*5*7*11*13)
\\ N
newtonpoly(x^4+3*x^3+27*x^2+9*x+81,3)
nextprime(100000000000000000000000)
setrand(1);a=matrix(3,5,j,k,vectorv(5,l,random\10^8))
aid=[idx,idy,idz,matid(5),idx]
bb=nfalgtobasis(nf,Mod(x^3+x,nfpol))
da=nfdetint(nf,[a,aid])
nfeltdiv(nf,ba,bb)
nfeltdiveuc(nf,ba,bb)
nfeltdivrem(nf,ba,bb)
nfhnf(nf,[a,aid])
nfhnfmod(nf,[a,aid],da)
nfeltmod(nf,ba,bb)
nfeltmul(nf,ba,bb)
nfeltpow(nf,bb,5)
nfeltreduce(nf,ba,idx)
setrand(1);as=matrix(3,3,j,k,vectorv(5,l,random\10^8))
vaid=[idx,idy,matid(5)]
haid=[matid(5),matid(5),matid(5)]
nfsnf(nf,[as,haid,vaid])
nfeltval(nf,ba,vp)
norm(1+I)
norm(Mod(x+5,x^3+x+1))
norml2(vector(10,x,x))
qfbnucomp(Qfb(2,1,9),Qfb(4,3,5),3)
form=Qfb(2,1,9);qfbnucomp(form,form,3)
numdiv(2^99*3^49)
numerator((x+1)/(x-1))
qfbnupow(form,111)
\\ O
1/(1+x)+O(x^20)
omega(100!)
ellordinate(acurve,1)
tcurve=ellinit([1,0,1,-19,26],1)
ellorder(tcurve,[1,2])
ellztopoint(acurve,ellpointtoz(acurve,apoint))
ellpow(acurve,apoint,10)
cmcurve=ellinit([0,-3/4,0,-2,-1])
ellpow(cmcurve,[x,y],quadgen(-7))
ellpointtoz(acurve,apoint)
polredord(x^3-12*x+45*x-1)
\\ P
padicprec(padicno,127)
matpascal(8)
qfperfection([2,0,1;0,2,1;1,1,2])
numtoperm(7,1035)
permtonum([4,7,1,6,3,5,2])
qfbprimeform(-44,3)
eulerphi(257^2)
Pi
plot(x=-5,5,sin(x))
contfracpnqn([2,6,10,14,18,22,26])
contfracpnqn([1,1,1,1,1,1,1,1;1,1,1,1,1,1,1,1])
plotpoints(0,225,334)
plotpoints(0,vector(10,k,10*k),vector(10,k,5*k*k))

polinterpolate([0,2,3],[0,4,9],5)
polred(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
polred(x^4-28*x^3-458*x^2+9156*x-25321,3)
polred(x^4+576,1)
polred(x^4+576,3)
polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568,1)
polsym(x^17-1,17)
variable(name^4-other)
Pol(sin(x),x)
polylog(5,0.5)
polylog(-4,t)
polylog(5,0.5,1)
polylog(5,0.5,2)
polylog(5,0.5,3)
Pol([1,2,3,4,5],x)
Polrev([1,2,3,4,5],x)
polzagier(6,3)
psdraw([0,20,20])
psploth(x=-5,5,sin(x))
psploth(t=0,2*Pi,[sin(5*t),sin(7*t)],1,100)
psplothraw(vector(100,k,k),vector(100,k,k*k/100))
qfbpowraw(Qfb(5,3,-1,0.),3)
print((x-12*y)/(y+13*x));
print([1,2;3,4])
print1(x+y);print(x+y);
\p 96
Pi
precision(Pi,20)
precision(cmcurve)
\p 38
prime(100)
idealprimedec(nf,2)
idealprimedec(nf,3)
idealprimedec(nf,11)
primes(100)
forprime(p=2,100,print(p," ",lift(znprimroot(p))))
idealprincipal(nf,Mod(x^3+5,nfpol))
ideleprincipal(nf,Mod(x^3+5,nfpol))
print((x-12*y)/(y+13*x));
print([1,2;3,4])
print1(x+y);print1(" equals ");print(x+y);
prod(k=1,10,1+1/k!)
prod(k=1,10,1+1./k!)
Pi^2/6*prodeuler(p=2,10000,1-p^-2)
prodinf(n=0,(1+2^-n)/(1+2^(-n+1)))
prodinf(n=0,-2^-n/(1+2^(-n+1)),1)
psi(1)
\\ Q
quaddisc(-252)
quadgen(-11)
quadpoly(-11)
quadregulator(17)
\\ R
matrank(matrix(5,5,x,y,x+y))
bnrclassno(bnf,[[5,3;0,1],[1,0]])
bnrclassnolist(bnf,lu)
plotmove(0,50,50);plotrbox(0,50,50)
print1("give a value for s? ");s=input();print(1/s)
37.
real(5-7*I)
polrecip(3*x^7-5*x^3+6*x-9)
qfbred(Qfb(3,10,12),,-1)
qfbred(Qfb(3,10,-20,1.5))
qfbred(Qfb(3,10,-20,1.5),2,,18)
qfbred(Qfb(3,10,-20,1.5),1)
qfbred(Qfb(3,10,-20,1.5),3,,18)
poldiscreduced(x^3+4*x+12)
kill(y);print(x+y);reorder([x,y]);print(x+y);
polresultant(x^3-1,x^3+1)
polresultant(x^3-1.,x^3+1.,1)
serreverse(tan(x))
plotrline(0,200,150)
plotcursor(0)
plotrmove(0,5,5);plotcursor(0)
round(prod(k=1,17,x-exp(2*I*Pi*k/17)),1)
qpol=y^3-y-1;setrand(1);bnf2=bnfinit(qpol);nf2=bnf2[7];
un=Mod(1,qpol);w=Mod(y,qpol);p=un*(x^5-5*x+w)
aa=rnfpseudobasis(nf2,p)
rnfbasis(bnf2,aa)
rnfdisc(nf2,p)
rnfequation(nf2,p)
rnfequation(nf2,p,1)
rnfhnfbasis(bnf2,aa)
rnfisfree(bnf2,aa)
rnfsteinitz(nf2,aa)
polrootsmod(x^16-1,41)
polrootspadic(x^4+1,41,6)
polroots(x^5-5*x^2-5*x-5)
polroots(x^4-1000000000000000000000,1)
round(prod(k=1,17,x-exp(2*I*Pi*k/17)))
rounderror(prod(k=1,17,x-exp(2*I*Pi*k/17)))
plotrpoint(0,20,20)
\\ S
plotinit(3,600,600);plotscale(3,-7,7,-2,2);plotcursor(3)
q*Ser(ellan(acurve,100),q)
aset=Set([5,-2,7,3,5,1])
bset=Set([7,5,-5,7,2])
setintersect(aset,bset)
setminus(aset,bset)
default(realprecision,28)
setrand(10)
setsearch(aset,3)
setsearch(bset,3)
default(seriesprecision,12)
setunion(aset,bset)
arat=(x^3+x+1)/x^3;type(arat,14)
shift(1,50)
shift([3,4,-11,-12],-2)
shiftmul([3,4,-11,-12],-2)
sigma(100)
sigma(100,2)
sigma(100,-3)
sign(-1)
sign(0)
sign(0.)
qfsign(mathilbert(5)-0.11*matid(5))
bnfsignunit(bnf)
simplify(((x+I+1)^2-x^2-2*x*(I+1))^2)
sin(Pi/6)
sinh(1)
sizedigit([1.3*10^5,2*I*Pi*exp(4*Pi)])
matsnf(matrix(5,5,j,k,random))
matsnf(1/mathilbert(6))
matsnf(x*matid(5)-matrix(5,5,j,k,1),2)
solve(x=1,4,sin(x))
vecsort(vector(17,x,5*x%17))
sqr(1+O(2))
qfgaussred(mathilbert(5))
sqrt(13+O(127^12))
plotmove(0,100,100);plotstring(0,Pi)
plotmove(0,200,200);plotstring(0,"(0,0)")
psdraw([0,10,10])
apol=0.3+pollegendre(10)
polsturm(apol)
polsturm(apol,0.91,1)
polsubcyclo(31,5)
ellsub(ellinit([0,0,0,-17,0]),[-1,4],[-4,2])
subst(sin(x),x,y)
subst(sin(x),x,x+x^2)
sum(k=1,10,2^-k)
sum(k=1,10,2.^-k)
polsylvestermatrix(a2*x^2+a1*x+a0,b1*x+b0)
\p 38
4*sumalt(n=0,(-1)^n/(2*n+1))
4*sumalt(n=0,(-1)^n/(2*n+1),1)
suminf(n=1,2.^-n)
6/Pi^2*sumpos(n=1,n^-2)
matsupplement([1,3;2,4;3,6])
\\ T
sqr(tan(Pi/3))
tanh(1)
elltaniyama(bcurve)
taylor(y/(x-y),y)
poltchebi(10)
teichmuller(7+O(127^12))
printtex((x+y)^3/(x-y)^2)
theta(0.5,3)
thetanullk(0.5,7)
elltors(tcurve)
trace(1+I)
trace(Mod(x+5,x^3+x+1))
mattranspose(vector(2,x,x))
%*%~
truncate(-2.7)
truncate(sin(x^2))
poltschirnhaus(x^5-x-1)
type(Mod(x,x^2+1))
\\ U
quadunit(17)
n=33;until(n==1,print1(n," ");if(n%2,n=3*n+1,n=n/2));print(1)
\\ V
valuation(6^10000-1,5)
Vec(sin(x))
vecmax([-3,7,-2,11])
vecmin([-3,7,-2,11])
vector(10,x,1/x)
vecsort([[1,8,5],[2,5,8],[3,6,-6],[4,8,6]],2)
vecsort([[1,8,5],[2,5,8],[3,6,-6],[4,8,6]],[2,1])
\\ W
ellwp(acurve)
weber(I)
weber(I,1)
weber(I,2)
m=5;while(m<20,print1(m," ");m=m+1);print()
\\ Z
zeta(3)
zeta(0.5+14.1347251*I)
zetak(nfz,-3)
zetak(nfz,1.5+3*I)
idealstar(nf2,54)
bid=idealstar(nf2,54,1)
ideallog(nf2,w,bid)
znstar(3120)
znorder(Mod(33,2^16+1))
getheap
print("Total time spent: ",gettime);
\q
