padicprec(1,2)
padicappr(x,O(2))
padicappr(x^2+1+O(3), Mod(-1+O(5^10),y^2-2))
padicappr(x^2+1+O(3), -1+O(5^10))
factorpadic(y^2+3^5,3,5)
p=2^64+13; liftint(padicappr((x-1)^30+p^30, 1+O(p^40)))

test(p, e = 1)=
{ my (N = 7*p^2);
  for (i=0,10,if (!ispower(i+O(p^e), N), print([i,p,e])));
  for (i=1,10,if (!ispower((i+O(p^e))^N, N), error([i,p,e])));
}
test(2)
test(2,2)
test(2,3)
test(3)
test(3,3)
test(11,3)
test(nextprime(2^64),3)
polrootspadic(x^3-x+8, 2, 6)
f = subst(x^3-x+8, x, x + Mod(y,y^2+y+1));
padicappr(f, Mod(1+O(2^10)-y, y^2+y+1))
\\#1424
lift(1/2 + O(2))

s=3+3^2+O(3^5)
t=2+2^2+O(2^5)
f=[cosh,sinh,tanh,cotanh];
{
for (i=1,#f,
  print(f[i](s));
  print(f[i](O(x)));
)
}
gamma(s)
gamma(t)
p=2^64+13;
gamma(3 + O(p^2))
gamma(-3 + O(p^2))
lngamma(17+O(3^5))
gamma(1/5+O(2^2))
gamma(1/5+O(2^3))
gamma(123+O(2^7))
gamma(123+O(2^8))
gamma(29+O(2^5))
gamma(29+O(2^6))

I + O(5^3)
log(1+4+O(2^10))
log(1+3+O(3^10))
log(1+5+O(5^10))
log(1+101+O(101^10))

T = x^12 + 208*x^6 + 64; phi = polcyclo(9);
prec = 10; p = 3;
v = factorpadic(T, p, prec)[,1];
liftall( padicappr(phi, Mod(-2+O(p^prec),  v[1])) )

T = teichmuller([17,10]);
for(i=1,16,if (teichmuller(i+O(17^10),T) != teichmuller(i+O(17^10)), error(i)))

\\#1793
padicappr(x^3+1,-2+O(2^5))
padicappr(x^3+1,Mod(-2+O(2^5),y^3+3))

newtonpoly(x^4+3*x^2+27*x+x+81,3)
newtonpoly(x^4+3*x^2+27*x,3)
newtonpoly(x^4+y*x^2+y^3*x,y)

