V = [1,2,3];
f(V,x) = V[x]++;
f(V,1)
V
f(~V,x) = V[x]++;
f(~V,1)
V

L = List([1,2,3]);
f(~L,x) = listput(~L,x^2);
f(~L,5)
L

a.inc=a[1]++;
V.inc
V

W=vector(1000,i,i!);
f(x)=x[1];
g(~x)=x[1];
x.b = x[1];
default(timer,1);
for(i=1,10^5,W[1])
for(i=1,10^5,f(W))
for(i=1,10^5,g(~W))
for(i=1,10^5,W.b)
default(timer,0);

T = y^2+y+1; p = 2;
lift(polrootspadic(x^3-x^2+64*y, [T,p], 5))

qfbsolve(Qfb(1,0,1),65,0)
qfbsolve(Qfb(1,0,1),65,1)
qfbsolve(Qfb(1,0,1),65,2)
qfbsolve(Qfb(1,0,1),65,3)

qfbsolve(Qfb(1,0,1),20,0)
qfbsolve(Qfb(1,0,1),20,1)
qfbsolve(Qfb(1,0,1),20,2)
qfbsolve(Qfb(1,0,1),20,3)

M = matconcat([factor(12),factor(20)]~)
F=matreduce(M)
factorback(F)

P = x^3+2*x^2+3*x+4; w = rootsof1(4)
f = fft(w, P)
apply(z->subst(P,x,z),w)
fi = fftinv(w, f)
Polrev(fi/#fi)

w = powers(znprimroot(5),3)
f = fft(w, P)
apply(z->subst(P,x,z),w)
fi = fftinv(w, f)
lift(Polrev(fi/#fi))

serlaplace(1/cosh(t+O(t^10)))
vector(10,i,eulerfrac(i))

eulervec(5)
eulerpol(5)
vector(4,i,eulerianpol(i))

f(n) = n! / (n^n * exp(-n) * sqrt(n));
asympnum(f)
v = asympnumraw(f, 3)
bestappr(v / v[1])

a = ffgen([3,5],'a);
b = ffgen([3,10],'b);
m = ffembed(a, b);
mi= ffinvmap(m);

R = ffmaprel(mi,b)

minpoly(R)
trace(R)
norm(R)

P = x^8+3*x^4+5;
nfsubfields(P)
nfsubfieldsmax(P)
nfsubfieldscm(P)

nfdiscfactors(x^3+3*x+7)

nfbasis(x^3+3*x+7,&dK)
dK

a = 'a;
nf = nfinit(a^3-2);
idealismaximal(nf,7)
idealismaximal(nf,5)

id2 = idealprimedec(nf,2)[1];
id3 = idealprimedec(nf,3)[1];
idealdown(nf, idealmul(nf, id2, id3))

bnf=bnfinit(a^2+41); bnf.cyc
P=bnrclassfield(bnf,,1)
rnfdisc(bnf,P)

bnf = bnfinit(x^2-nextprime(2^38), 1);
sizebyte(bnf.fu)
sizebyte(bnfunits(bnf))

ellheight(ellinit([1,3]))
ellheight(ellinit([1,a],nfinit(a^2+1)))

lfun(1,-7)
lfun(-4,-8)
lfun(5,-9)

L = lfunshift(1,1); \\ zeta(s-1)
lfun(L,1)
M = lfunshift(1,1,1); \\ zeta(s)*zeta(s-1)
lfun(M,2)

G=znstar(7,1); chi=[2]; \\ cubic char of cond 7
V=[rootsof1(3)~,3];
r=sqrtn((-13-sqrt(-27))/14,6); \\ root number
an(V)=n->vector(n,i,chareval(G,chi,i,V));
L=lfuncreate([an(V),1,[0],1,7,r]);
lfuncheckfeq(L)
localbitprec(256); lfuncheckfeq(L)

F() =
{ 
  my(V=[rootsof1(3)~,3]);
  my(r=sqrtn((-13-sqrt(-27))/14,6));
  [an(V),1,[0],1,7,r];
}
L = lfuncreate(F);
lfuncheckfeq(L)
localbitprec(256); lfuncheckfeq(L)

G=znstar(17,1); C=[[1],[3],[5],[7]];
lfun([G,C],1)
lfunrootres([G,C])

default(timer,1);
localprec(1000); lfun([G,C],1);
localprec(1000); [lfun([G,c],1)|c<-C];
default(timer,0);

bnf = bnfinit(x^2+47); bnr = bnrinit(bnf,1);
lfun([bnr,[[1],[2]]],1)

find(a,b)=
  {
    forell(e,a,b,
      my(E=ellinit(e[1]));
      my(F=mffromell(E)[2]);
      my(Q=mfisetaquo(F));
      if(Q,print(e[1],":",Q)),1);
  }
find(1,100)

print(strtime(12345678))
derivn((x*(1-x))^4,4)
arity((x,y)->x^2+y^2)
arity(sin)
L=List([1,2,3]);L[1..2]
L=List([1,2,3]);L[^1]
svg=parplothexport("svg",x=1,10,1/gamma(x));