\e
default(compatible,3)
+3
-5
5+3
5-3
5/3
5\3
5\/3
5%3
5^3
\precision=57
pi
\precision=38
o(x^12)
padicno=(5/3)*127+O(127^5)
initrect(0,500,500)
\\ A
abs(-0.01)
acos(0.5)
acosh(3)
acurve=initell([0,0,1,-1,0])
apoint=[2,2]
isoncurve(acurve,apoint)
addell(acurve,apoint,apoint)
addprimes([nextprime(10^9),nextprime(10^10)])
adj([1,2;3,4])
agm(1,2)
agm(1+o(7^5),8+o(7^5))
algdep(2*cos(2*pi/13),6)
algdep2(2*cos(2*pi/13),6,15)
\\allocatemem(3000000)
akell(acurve,1000000007)
nfpol=x^5-5*x^3+5*x+25
nf=initalg(nfpol)
ba=algtobasis(nf,mod(x^3+5,nfpol))
anell(acurve,100)
apell(acurve,10007)
apell2(acurve,10007)
apol=x^3+5*x+1
apprpadic(apol,1+O(7^8))
apprpadic(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)
assmat(x^5-12*x^3+0.0005)
3*atan(sqrt(3))
atanh(0.5)
\\ B
basis(x^3+4*x+5)
basis2(x^3+4*x+5)
basistoalg(nf,ba)
bernreal(12)
bernvec(6)
bestappr(pi,10000)
bezout(123456789,987654321)
bigomega(12345678987654321)
mcurve=initell([0,0,0,-17,0])
mpoints=[[-1,4],[-4,2]]~
mhbi=bilhell(mcurve,mpoints,[9,24])
bin(1.1,5)
binary(65537)
bittest(10^100,100)
boundcf(pi,5)
boundfact(40!+1,100000)
move(0,0,0);box(0,500,500)
setrand(1);buchimag(1-10^7,1,1)
setrand(1);bnf=buchinitfu(x^2-x-57,0.2,0.2)
buchcertify(bnf)
buchfu(bnf)
setrand(1);buchinitforcefu(x^2-x-100000)
setrand(1);bnf=buchinitfu(x^2-x-57,0.2,0.2)
setrand(1);buchreal(10^9-3,0,0.5,0.5)
setrand(1);buchgen(x^4-7,0.2,0.2)
setrand(1);buchgenfu(x^2-x-100000)
setrand(1);buchgenforcefu(x^2-x-100000)
setrand(1);buchgenfu(x^4+24*x^2+585*x+1791,0.1,0.1)
buchnarrow(bnf)
buchray(bnf,[[5,3;0,1],[1,0]])
bnr=buchrayinitgen(bnf,[[5,3;0,1],[1,0]])
bnr2=buchrayinitgen(bnf,[[25,13;0,1],[1,1]])
bytesize(%)
\\ C
ceil(-2.5)
centerlift(mod(456,555))
cf(pi)
cf2([1,3,5,7,9],(exp(1)-1)/(exp(1)+1))
changevar(x+y,[z,t])
char([1,2;3,4],z)
char(mod(x^2+x+1,x^3+5*x+1),z)
char1([1,2;3,4],z)
char2(mod(1,8191)*[1,2;3,4],z)
acurve=chell(acurve,[-1,1,2,3])
chinese(mod(7,15),mod(13,21))
apoint=chptell(apoint,[-1,1,2,3])
isoncurve(acurve,apoint)
classno(-12391)
classno(1345)
classno2(-12391)
classno2(1345)
coeff(sin(x),7)
compimag(qfi(2,1,3),qfi(2,1,3))
compo(1+o(7^4),3)
compositum(x^4-4*x+2,x^3-x-1)
compositum2(x^4-4*x+2,x^3-x-1)
comprealraw(qfr(5,3,-1,0.),qfr(7,1,-1,0.))
concat([1,2],[3,4])
conductor(bnf,[[25,13;0,1],[1,1]])
conductorofchar(bnr,[2])
conj(1+i)
conjvec(mod(x^2+x+1,x^3-x-1))
content([123,456,789,234])
convol(sin(x),x*cos(x))
core(54713282649239)
core2(54713282649239)
coredisc(54713282649239)
coredisc2(54713282649239)
cos(1)
cosh(1)
move(0,200,150)
cursor(0)
cvtoi(1.7)
cyclo(105)
\\ D
degree(x^3/(x-1))
denom(12345/54321)
deplin(mod(1,7)*[2,-1;1,3])
deriv((x+y)^5,y)
((x+y)^5)'
det([1,2,3;1,5,6;9,8,7])
det2([1,2,3;1,5,6;9,8,7])
detint([1,2,3;4,5,6])
diagonal([2,4,6])
dilog(0.5)
dz=vector(30,k,1);dd=vector(30,k,k==1);dm=dirdiv(dd,dz)
deu=direuler(p=2,100,1/(1-apell(acurve,p)*x+if(acurve[12]%p,p,0)*x^2))
anell(acurve,100)==deu
dirmul(abs(dm),dz)
dirzetak(initalg(x^3-10*x+8),30)
disc(x^3+4*x+12)
discf(x^3+4*x+12)
discrayabs(bnr,mat(6))
discrayabs(bnr)
discrayabscond(bnr2)
lu=ideallistunitgen(bnf,55);discrayabslist(bnf,lu)
discrayabslistlong(bnf,20)
discrayrel(bnr,mat(6))
discrayrel(bnr)
discrayrelcond(bnr2)
divisors(8!)
divres(345,123)
divres(x^7-1,x^5+1)
divsum(8!,x,x)
\\draw([0,0,0])
postdraw([0,0,0])
\\ E
eigen([1,2,3;4,5,6;7,8,9])
eint1(2)
erfc(2)
eta(q)
euler
z=y;y=x;eval(z)
exp(1)
extract([1,2,3,4,5,6,7,8,9,10],1000)
\\ F
10!
fact(10)
factcantor(x^11+1,7)
centerlift(lift(factfq(x^3+x^2+x-1,3,t^3+t^2+t-1)))
factmod(x^11+1,7)
factor(17!+1)
p=x^5+3021*x^4-786303*x^3-6826636057*x^2-546603588746*x+3853890514072057
fa=[11699,6;2392997,2;4987333019653,2]
factoredbasis(p,fa)
factoreddiscf(p,fa)
factoredpolred(p,fa)
factoredpolred2(p,fa)
factornf(x^3+x^2-2*x-1,t^3+t^2-2*t-1)
factorpadic(apol,7,8)
factorpadic2(apol,7,8)
factpol(x^15-1,3,1)
factpol(x^15-1,0,1)
factpol2(x^15-1,0)
fibo(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
galois(x^6-3*x^2-1)
nf3=initalg(x^6+108);galoisconj(nf3)
aut=%[2];galoisapply(nf3,aut,mod(x^5,x^6+108))
gamh(10)
gamma(10.5)
gauss(hilbert(10),[1,2,3,4,5,6,7,8,9,0]~)
gaussmodulo([2,3;5,4],[7,11],[1,4]~)
gaussmodulo2([2,3;5,4],[7,11],[1,4]~)
gcd(12345678,87654321)
getheap()
getrand()
getstack()
\\gettime()isattheend
globalred(acurve)
getstack()
\\ H
hclassno(2000003)
hell(acurve,apoint)
hell2(acurve,apoint)
hermite(amat=1/hilbert(7))
hermite2(amat)
hermitehavas(amat)
hermitemod(amat,detint(amat))
hermiteperm(amat)
hess(hilbert(7))
hilb(2/3,3/4,5)
hilbert(5)
hilbp(mod(5,7),mod(6,7))
hvector(10,x,1/x)
hyperu(1,1,1)
\\ I
i^2
nf1=initalgred(nfpol)
initalgred2(nfpol)
vp=primedec(nf,3)[1]
idx=idealmul(nf,idmat(5),vp)
idealinv(nf,idx)
idy=ideallllred(nf,idx,[1,5,6])
idealadd(nf,idx,idy)
idealaddone(nf,idx,idy)
idealaddmultone(nf,[idy,idx])
idealappr(nf,idy)
idealapprfact(nf,idealfactor(nf,idy))
idealcoprime(nf,idx,idx)
idz=idealintersect(nf,idx,idy)
idealfactor(nf,idz)
ideallist(bnf,20)
idx2=idealmul(nf,idx,idx)
idt=idealmulred(nf,idx,idx)
idealdiv(nf,idy,idt)
idealdivexact(nf,idx2,idx)
idealhermite(nf,vp)
idealhermite2(nf,vp[2],3)
idealnorm(nf,idt)
idp=idealpow(nf,idx,7)
idealpowred(nf,idx,7)
idealtwoelt(nf,idy)
idealtwoelt2(nf,idy,10)
idealval(nf,idp,vp)
idmat(5)
if(3<2,print("bof"),print("ok"));
imag(2+3*i)
image([1,3,5;2,4,6;3,5,7])
image(pi*[1,3,5;2,4,6;3,5,7])
incgam(2,1)
incgam1(2,1)
incgam2(2,1)
incgam3(2,1)
incgam4(4,1,6)
indexrank([1,1,1;1,1,1;1,1,2])
indsort([8,7,6,5])
initell([0,0,0,-1,0])
initrect(1,700,700)
nfz=initzeta(x^2-2);
integ(sin(x),x)
integ((-x^2-2*a*x+8*a)/(x^4-14*x^3+(2*a+49)*x^2-14*a*x+a^2),x)
intersect([1,2;3,4;5,6],[2,3;7,8;8,9])
\precision=19
intgen(x=0,pi,sin(x))
sqr(2*intgen(x=0,4,exp(-x^2)))
4*intinf(x=1,10^20,1/(1+x^2))
intnum(x=-0.5,0.5,1/sqrt(1-x^2))
2*intopen(x=0,100,sin(x)/x)
\precision=38
inverseimage([1,1;2,3;5,7],[2,2,6]~)
isdiagonal([1,0,0;0,5,0;0,0,0])
isfund(12345)
isideal(bnf[7],[5,1;0,1])
isincl(x^2+1,x^4+1)
isinclfast(initalg(x^2+1),initalg(x^4+1))
isirreducible(x^5+3*x^3+5*x^2+15)
isisom(x^3+x^2-2*x-1,x^3+x^2-2*x-1)
isisomfast(initalg(x^3-2),initalg(x^3-6*x^2-6*x-30))
isprime(12345678901234567)
isprincipal(bnf,[5,1;0,1])
isprincipalgen(bnf,[5,1;0,1])
isprincipalraygen(bnr,primedec(bnf,7)[1])
ispsp(73!+1)
isqrt(10!^2+1)
isset([-3,5,7,7])
issqfree(123456789876543219)
issquare(12345678987654321)
isunit(bnf,mod(3405*x-27466,x^2-x-57))
\\ J
jacobi(hilbert(6))
jbesselh(1,1)
jell(i)
\\ K
kbessel(1+i,1)
kbessel2(1+i,1)
x
y
ker(matrix(4,4,x,y,x/y))
ker(matrix(4,4,x,y,sin(x+y)))
keri(matrix(4,4,x,y,x+y))
kerint(matrix(4,4,x,y,x*y))
kerint1(matrix(4,4,x,y,x*y))
kerint2(matrix(4,6,x,y,2520/(x+y)))
f(u)=u+1;
print(f(5));kill(f);
f=12
killrect(1)
kro(5,7)
kro(3,18)
\\ L
laplace(x*exp(x*y)/(exp(x)-1))
lcm(15,-21)
length(divisors(1000))
legendre(10)
lex([1,3],[1,3,5])
lexsort([[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)])
lindep2([(1-3*sqrt(2))/(3-2*sqrt(3)),1,sqrt(2),sqrt(3),sqrt(6)],14)
move(0,0,900);line(0,900,0)
lines(0,vector(5,k,50*k),vector(5,k,10*k*k))
m=1/hilbert(7)
mp=concat(m,idmat(7))
lll(m)
lll1(m)
lllgram(m)
lllgram1(m)
lllgramint(m)
lllgramkerim(mp~*mp)
lllint(m)
lllintpartial(m)
lllkerim(mp)
lllrat(m)
\precision=96
ln(2)
lngamma(10^50*i)
\precision=2000
log(2)
logagm(2)
\precision=19
bcurve=initell([0,0,0,-3,0])
localred(bcurve,2)
ccurve=initell([0,0,-1,-1,0])
l=lseriesell(ccurve,2,-37,1)
lseriesell(ccurve,2,-37,1.2)-l
\\ M
sbnf=smallbuchinit(x^3-x^2-14*x-1)
makebigbnf(sbnf)
concat(mat(vector(4,x,x)~),vector(4,x,10+x)~)
matextract(matrix(15,15,x,y,x+y),vector(5,x,3*x),vector(3,y,3*y))
ma=mathell(mcurve,mpoints)
gauss(ma,mhbi)
(1.*hilbert(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)
matrixqz2([1/3,1/4,1/6;1/2,1/4,-1/4;1/3,1,0])
matrixqz3([1,3;3,5;5,7])
max(2,3)
min(2,3)
minim([2,1;1,2],4,6)
mod(-12,7)
modp(-12,7)
mod(10873,49649)^-1
modreverse(mod(x^2+1,x^3-x-1))
move(0,243,583);cursor(0)
mu(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,vvector(5,l,random()\10^8))
aid=[idx,idy,idz,idmat(5),idx]
bb=algtobasis(nf,mod(x^3+x,nfpol))
da=nfdetint(nf,[a,aid])
nfdiv(nf,ba,bb)
nfdiveuc(nf,ba,bb)
nfdivres(nf,ba,bb)
nfhermite(nf,[a,aid])
nfhermitemod(nf,[a,aid],da)
nfmod(nf,ba,bb)
nfmul(nf,ba,bb)
nfpow(nf,bb,5)
nfreduce(nf,ba,idx)
setrand(1);as=matrix(3,3,j,k,vvector(5,l,random()\10^8))
vaid=[idx,idy,idmat(5)]
haid=[idmat(5),idmat(5),idmat(5)]
nfsmith(nf,[as,haid,vaid])
nfval(nf,ba,vp)
norm(1+i)
norm(mod(x+5,x^3+x+1))
norml2(vector(10,x,x))
nucomp(qfi(2,1,9),qfi(4,3,5),3)
form=qfi(2,1,9);nucomp(form,form,3)
numdiv(2^99*3^49)
numer((x+1)/(x-1))
nupow(form,111)
\\ O
1/(1+x)+o(x^20)
omega(100!)
ordell(acurve,1)
order(mod(33,2^16+1))
tcurve=initell([1,0,1,-19,26]);
orderell(tcurve,[1,2])
ordred(x^3-12*x+45*x-1)
\\ P
padicprec(padicno,127)
pascal(8)
perf([2,0,1;0,2,1;1,1,2])
permutation(7,1035)
permutation2num([4,7,1,6,3,5,2])
pf(-44,3)
phi(257^2)
pi
plot(x=-5,5,sin(x))
\\ploth(x=-5,5,sin(x))
\\ploth2(t=0,2*pi,[sin(5*t),sin(7*t)])
\\plothraw(vector(100,k,k),vector(100,k,k*k/100))
pnqn([2,6,10,14,18,22,26])
pnqn([1,1,1,1,1,1,1,1;1,1,1,1,1,1,1,1])
point(0,225,334)
points(0,vector(10,k,10*k),vector(10,k,5*k*k))
pointell(acurve,zell(acurve,apoint))
polint([0,2,3],[0,4,9],5)
polred(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
polred2(x^4-28*x^3-458*x^2+9156*x-25321)
polredabs(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
polredabs2(x^5-2*x^4-4*x^3-96*x^2-352*x-568)
polsym(x^17-1,17)
polvar(name^4-other)
poly(sin(x),x)
polylog(5,0.5)
polylog(-4,t)
polylogd(5,0.5)
polylogdold(5,0.5)
polylogp(5,0.5)
poly([1,2,3,4,5],x)
polyrev([1,2,3,4,5],x)
polzag(6,3)
\\draw([0,20,20])
postdraw([0,20,20])
postploth(x=-5,5,sin(x))
postploth2(t=0,2*pi,[sin(5*t),sin(7*t)])
postplothraw(vector(100,k,k),vector(100,k,k*k/100))
powell(acurve,apoint,10)
cmcurve=initell([0,-3/4,0,-2,-1])
powell(cmcurve,[x,y],quadgen(-7))
powrealraw(qfr(5,3,-1,0.),3)
pprint((x-12*y)/(y+13*x));
pprint([1,2;3,4])
pprint1(x+y);pprint(x+y);
\precision=96
pi
prec(pi,20)
precision(cmcurve)
\precision=38
prime(100)
primedec(nf,2)
primedec(nf,3)
primedec(nf,11)
primes(100)
forprime(p=2,100,print(p," ",lift(primroot(p))))
principalideal(nf,mod(x^3+5,nfpol))
principalidele(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(1,k=1,10,1+1/k!)
prod(1.,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)))
prodinf1(n=0,-2^-n/(1+2^(-n+1)))
psi(1)
\\ Q
quaddisc(-252)
quadgen(-11)
quadpoly(-11)
\\ R
rank(matrix(5,5,x,y,x+y))
rayclassno(bnf,[[5,3;0,1],[1,0]])
rayclassnolist(bnf,lu)
move(0,50,50);rbox(0,50,50)
print1("give a value for s? ");s=read();print(1/s)
37.
real(5-7*i)
recip(3*x^7-5*x^3+6*x-9)
redimag(qfi(3,10,12))
redreal(qfr(3,10,-20,1.5))
redrealnod(qfr(3,10,-20,1.5),18)
reduceddisc(x^3+4*x+12)
regula(17)
kill(y);print(x+y);reorder([x,y]);print(x+y);
resultant(x^3-1,x^3+1)
resultant2(x^3-1.,x^3+1.)
reverse(tan(x))
rhoreal(qfr(3,10,-20,1.5))
rhorealnod(qfr(3,10,-20,1.5),18)
rline(0,200,150)
cursor(0)
rmove(0,5,5);cursor(0)
rndtoi(prod(1,k=1,17,x-exp(2*i*pi*k/17)))
qpol=y^3-y-1;setrand(1);bnf2=buchinit(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)
rnfdiscf(nf2,p)
rnfequation(nf2,p)
rnfequation2(nf2,p)
rnfhermitebasis(bnf2,aa)
rnfisfree(bnf2,aa)
rnfsteinitz(nf2,aa)
rootmod(x^16-1,41)
rootpadic(x^4+1,41,6)
roots(x^5-5*x^2-5*x-5)
rootsold(x^4-1000000000000000000000)
round(prod(1,k=1,17,x-exp(2*i*pi*k/17)))
rounderror(prod(1,k=1,17,x-exp(2*i*pi*k/17)))
rpoint(0,20,20)
\\ S
initrect(3,600,600);scale(3,-7,7,-2,2);cursor(3)
q*series(anell(acurve,100),q)
aset=set([5,-2,7,3,5,1])
bset=set([7,5,-5,7,2])
setintersect(aset,bset)
setminus(aset,bset)
setprecision(28)
setrand(10)
setsearch(aset,3)
setsearch(bset,3)
setserieslength(12)
setunion(aset,bset)
arat=(x^3+x+1)/x^3;settype(arat,14)
shift(1,50)
shift([3,4,-11,-12],-2)
shiftmul([3,4,-11,-12],-2)
sigma(100)
sigmak(2,100)
sigmak(-3,100)
sign(-1)
sign(0)
sign(0.)
signat(hilbert(5)-0.11*idmat(5))
signunit(bnf)
simplefactmod(x^11+1,7)
simplify(((x+i+1)^2-x^2-2*x*(i+1))^2)
sin(pi/6)
sinh(1)
size([1.3*10^5,2*i*pi*exp(4*pi)])
smallbasis(x^3+4*x+12)
smalldiscf(x^3+4*x+12)
smallfact(100!+1)
smallinitell([0,0,0,-17,0])
smallpolred(x^4+576)
smallpolred2(x^4+576)
smith(matrix(5,5,j,k,random()))
smith(1/hilbert(6))
smithpol(x*idmat(5)-matrix(5,5,j,k,1))
solve(x=1,4,sin(x))
sort(vector(17,x,5*x%17))
sqr(1+o(2))
sqred(hilbert(5))
sqrt(13+o(127^12))
srgcd(x^10-1,x^15-1)
move(0,100,100);string(0,pi)
move(0,200,200);string(0,"(0,0)")
\\draw([0,10,10])
postdraw([0,10,10])
apol=0.3+legendre(10)
sturm(apol)
sturmpart(apol,0.91,1)
subcyclo(31,5)
subell(initell([0,0,0,-17,0]),[-1,4],[-4,2])
subst(sin(x),x,y)
subst(sin(x),x,x+x^2)
sum(0,k=1,10,2^-k)
sum(0.,k=1,10,2^-k)
sylvestermatrix(a2*x^2+a1*x+a0,b1*x+b0)
\precision=38
4*sumalt(n=0,(-1)^n/(2*n+1))
4*sumalt2(n=0,(-1)^n/(2*n+1))
suminf(n=1,2.^-n)
6/pi^2*sumpos(n=1,n^-2)
supplement([1,3;2,4;3,6])
\\ T
sqr(tan(pi/3))
tanh(1)
taniyama(bcurve)
taylor(y/(x-y),y)
tchebi(10)
teich(7+o(127^12))
texprint((x+y)^3/(x-y)^2)
theta(0.5,3)
thetanullk(0.5,7)
torsell(tcurve)
trace(1+i)
trace(mod(x+5,x^3+x+1))
trans(vector(2,x,x))
%*%~
trunc(-2.7)
trunc(sin(x^2))
tschirnhaus(x^5-x-1)
type(mod(x,x^2+1))
\\ U
unit(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])
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
weipell(acurve)
wf(i)
wf2(i)
m=5;while(m<20,print1(m," ");m=m+1);print()
\\ Z
zell(acurve,apoint)
zeta(3)
zeta(0.5+14.1347251*i)
zetak(nfz,-3)
zetak(nfz,1.5+3*i)
zidealstar(nf2,54)
bid=zidealstarinit(nf2,54)
zideallog(nf2,w,bid)
znstar(3120)
getstack()
getheap()
print("Total time spent: ",gettime());
\q