f(x) = 1/x;
g(N) = for(i = -N, N, f(i));
g(10)
print();

f=matsolve;
f(Mat(0), Col(1))
print();

(matsolve)(Mat(0), Col(1))
print();

a.foo=1/(1+a^2);
g(x)=[x.foo];
g(I)
print();

(x->1/x)(0)
print();

ecm(N,t,B)=
{
  for(a=1,t,
     iferr(
       my(E=ellinit([0,0,0,a,1]*Mod(1,N)));
       ellmul(E,[0,1]*Mod(1,N),B),
       err,if(errname(err)=="e_INV",return(gcd(lift(component(err,2)),N))
            ,error(err))));
}
ecm(2^64+1,10,200!)
ecm2(N,t,B)=
{
  for(a=1,t,
     iferr(
       my(E=ellinit([0,0,0,a,1]*Mod(1,N)));
       ellmul(E,[0,1]*Mod(1,N),B),
       err,return(gcd(lift(component(err,2)),N))
          ,errname(err)=="e_INV"));
}
ecm2(2^64+1,10,200!)

rev(A) = my(B=Ser(A)); serreverse(B);
iferr(rev([0,0,0,2,2,4,8,4,16,12]),E,0);
\\ e_COPRIME
T=t^2-2;p=2;A=x^2+1;B=[x+t,x+t];r=polhensellift(A,B,[p,T],6)
\\ e_DIM / e_TYPE
M = matid(2);
M[,1] = 1
M[,3] = 1
M[,1] = [1,2]
M[,1] = [1,2,3]~
M[1,] = 1
M[3,] = 1
M[1,] = [1,2]~
M[1,] = [1,2,3]

[;][1,]
[;][,1]
1[1]
issquare(1,&v[1])
1[1,1]
1[,1]
issquare(1,&v[,1])
1[1,]
issquare(1,&v[1,])

v=Vecsmall([1]);
v[2] = 1
v[1] = Pi
v[1] = 2^64
v[Pi] = 1

\\ RgM_check_ZM
M = [1.,0;0,1]; qflll(M,1)
\\ RgV_check_ZV
addprimes(1.)

\\e_MODULUS
nfalgtobasis(nfinit(t^3-2),Mod(t,t^2+1))
\\e_DIM
vector(-1,i,0)
vectorv(-1,i,0)
vectorsmall(-1,i,0)
matrix(-1,1,i,j,0)
matrix(1,-1,i,j,0)

next(-1)
break(-1)
v[-1]
v[#v+1]
subst(x,1,0)
exp(1/x)
cos(1/x)
sin(1/x)
tan(1/x)
cotan(1/x)
atan(1/x)
asin(1/x)
acos(1/x)
asinh(1/x)
acosh(1/x)
atanh(1/x)
lngamma(x)
besselj(2,1/x)
besseljh(2,1/x)
besselk(2,1/x)
besselk(1/3,O(x))
besseln(2,1/x)
besseln(1/3,O(x))
polylog(2,1/x)
sqrt(x)
sqrt(2+O(2^2))
sqrtn(x,3)
sqrtn(2+O(2^2),3)
log(x)
log(0)
abs(x+O(x^2))
vecmax([])
vecmax([], &i)
vecmin([])
vecmmin([], &i)
vecmax(matrix(0,2))
L=List();
listput(L, x, -1)
listinsert(L,x,-1)
listinsert(L,x,10)
listpop(L)
ellj(Mod(1,2))
ellj(Qfb(1,1,1))
eta(1+O(2))
eta(1/x)
K = nfinit(y^2+1);
idealhnf(K, Qfb(1,1,1))
idealfactor(K, [;])
idealval(K, [;], idealprimedec(K,2)[1]);
idealdiv(K,2,0, 1);
valuation(Pi,2)
x^Pi
x^x
0^0.
agm([],[])
sin(1/2+O(2^1))
cos(1/9+O(3^1))
exp(1/9+O(3^1))
G=[[Vecsmall([6,11,14,16,17,1,21,24,26,27,2,29,30,3,31,4,5,34,36,37,7,39,40,8,41,9,10,42,12,13,15,44,45,18,46,19,20,47,22,23,25,28,48,32,33,35,38,43]),Vecsmall([5,10,13,15,1,17,20,23,25,2,27,28,3,30,4,31,6,33,35,7,37,38,8,40,9,41,11,12,42,14,16,43,18,45,19,46,21,22,47,24,26,29,32,48,34,36,39,44]),Vecsmall([15,25,28,1,4,31,35,38,2,9,41,3,12,42,5,6,16,43,7,19,46,8,22,47,10,11,26,13,14,29,17,18,32,48,20,21,36,23,24,39,27,30,33,34,44,37,40,45]),Vecsmall([30,40,1,42,14,13,45,2,47,24,23,4,5,6,29,28,3,7,48,34,33,9,10,11,39,38,8,15,16,17,12,19,20,21,44,43,18,25,26,27,22,31,35,36,37,32,41,46]),Vecsmall([7,1,44,18,37,20,2,29,3,17,5,35,43,48,45,33,21,39,8,27,10,15,28,42,30,13,6,36,19,32,34,25,38,47,40,23,11,16,4,12,14,46,26,9,22,24,31,41])],Vecsmall([2,2,2,2,3])]; galoissubgroups(G)
bnrstark(bnrinit(bnfinit(y^2+1),2,1))
bnrstark(bnrinit(bnfinit(y^2-2),[4,[1,1]],1))
quadray(-16,1)
quadray(bnfinit(x^3-2),1)
galoissubcyclo(-1)
galoissubcyclo(6,Mod(1,3))
galoissubcyclo(6,[;])
galoissubcyclo(6,Mat(1))
galoissubcyclo(znstar(5),matid(2))
galoissubcyclo( [3, [3], [3]], Mat(3))
galoissubcyclo(bnrinit(bnfinit(y^2+1),1,1), 2)
polsubcyclo(-1,2);
polsubcyclo(2,-1);
random(-1)
znprimroot(0)
sqrtint(-1)
sqrtnint(-1,2)
sqrtnint(2,-2)
znprimroot(8)
polroots(x^2+Mod(1,2))
polroots(0)
polroots(Mod(1,2))
prime(-2)
addprimes(-1)
padicappr(x^2+1+O(3^5), 1+O(5))
factorpadic(x^2+1,2,-1)
polrootspadic(x^2+1,2,-1)
ellinit([1+O(3),1+O(5)])
ellwp([1,I],I)
ellsigma([1,I],x,1)
ellsigma([1,I],1,1)
E=ellinit([1,1]);
ellap(E)
ellap(E,1)
ellap(E,'x)
elltaniyama(E,-1)
ellheight(E,[2,2])
Qfb(0,0,0)
quadpoly(2)
qfbprimeform(2,5)
qfbcomp(Qfb(1,1,1),Qfb(1,0,2))
\\qfbcompraw(Qfb(21,1,2),Qfb(112,0,2))
galoisinit(x^2)
galoisinit(2*x)
ellL1(1,-1)
ellheegner(ellinit([0,-1,1,-10,-20]))
ellheegner(ellinit([0,0,1,-7,6]))
substpol(x+O(x^2),x^3,x)
intformal(1/(x^2+1))
component(x,-1)
component(O(x),2)
component(Vecsmall([]),1)
component(x->x,6)
polcoeff(O(x),2)
polcoeff(x+O(x^2),2)
polcoeff([],2)
polcoeff([],-1)
polcoeff("",2)
matcompanion(0*x)
matrixqz(Mat([1,2]))
matrixqz(Mat(0))
vecextract([1],[-1]);
vecextract([1],[2]);
idealfrobenius(K,galoisinit(K),idealprimedec(K,2)[1])
nfisincl(x^2,x^2)
polcompositum(x^2,x)
rnfdedekind(K, x^2+x-1/3)
hilbert(Mod(1,2),1)
hilbert(Mod(1,3),Mod(1,5))
hilbert(Mod(1,3),2,0)
znorder(0)
znorder(Mod(2,4))
contfrac(1e100)
contfrac(1.,[1],10)
contfrac(1,,-1)
contfracpnqn(matrix(3,1));
divisors(1/2)
idealstar(K,0)
idealstar(K,1/2)
idealaddtoone(K,[[;]])
idealdiv(K,1,2,1)
idealred(K,matid(2),[])
idealtwoelt(K,matid(2),1/2)
rnf=rnfinit(K,x^2-y); rnfeltdown(rnf, x)
matid(-1)
polinterpolate([1,1],[2,3],Pi)
modreverse(Mod(-x^3+9*x,x^4-10*x^2+1))
rnfnormgroup(bnrinit(bnfinit(K),9), x^3-2)
concat([1,2],[3,4]~)
concat([])
concat(List())
mathnfmod([1;2],2)
polsturm(x^2*1.)
removeprimes(2)
forstep(a=1,2,0,)
e=ellinit([1,1+O(31^2)]);
e.omega
e.eta
e.area
e=ellinit([0,1]);
e.tate
ellorder(e, [0,0]*Mod(1,2))
thue(x*(x^3-2),0);
direuler(p=2, 10, 2/(1-p*X))
solve(x=0,1,x^2+1)
warning(1)
iferr(1/0,E,1,errname(E)=="e_DOMAIN")
\\ backward compatibility. Eventually remove
inv(x) = trap (e_INV, INFINITY, 1/x)
inv(2)
inv(0)
trap (e_INV, INFINITY, log(0))
a=1;
notafunc('a)
a
n=1<<10000;
znlog(Mod(1,n),Mod(1,n+1))
Mod(0,n)^(-1)
