jell(x)=if(#x,x.j,[]);
vecprint(v)=for(i=1,#v,print(i,": ", v[i]));
{
test(p,f) = setrand(1); my(a = ffgen([p,f], 'a)); vecprint([
ffgen(a^2+a+3),
a^2+3*a+1,
a/(1+a),
2*(a+1)/3,
1/5+a,
if (6*a, 5/6/(a+1)),
if (6*a, 5/6*(a+1)),
shiftmul(a+1,10),
if (2*a, shiftmul(a+1,-10)),
a^-1,
-a,
sqr(a),
sqrt(a^(2^10)),
sqrtn((a^2+a+1)^3,3),
sqrtn((a^2+a+1)^3,3,&z),
z,
if (ispower(a,3), a^(2/3)),
norm(a^2+1),
trace(a),
charpoly(a),
minpoly(a),
conjvec(a),
factor(x^6-a*x^3+1),
jell(ellinit([a,1])),
a/x,
(x+a)/(x-a),
if(1,setrand(1);b=ffprimroot(a)),
fforder(a),
fforder(a,factor(1)),
b^fflog(a,b),
factormod(x^2+x+a),
polrootsmod(x^2+x+a)
]);
}
default(echo,1);

test(2, 20)
test(7, 7)
test(precprime(2^32), 3)
test(nextprime(2^32), 3)

default(echo,0);
stest(p,n)=
{
  my(a=ffgen(ffinit(p,n),'a)^2);
  if(sqrt(a)^2!=a,error([p,n]));
}

ftest(p,n,r)=
{
  my(a=ffgen(ffinit(p,n),'a)^r);
  if(sqrtn(a,r)^r!=a,error([p,n,r]));
}
default(echo,1);

stest(2,1005);
stest(17,2);
stest(17,3);
stest(17,4);

stest(nextprime(2^31),2);
stest(nextprime(2^31),3);
stest(nextprime(2^31),4);


stest(nextprime(2^63),2);
stest(nextprime(2^63),3);
stest(nextprime(2^63),4);

stest(nextprime(2^65),2);
stest(nextprime(2^65),3);
stest(nextprime(2^65),4);

ftest(2,1005,7);
ffgen(ffinit(2^32-5,101),'a)^10000
ffgen(ffinit(2^64-59,101),'a)^10000

for(i=1,10,print(ffnbirred(11,i)));
for(i=1,10,print(ffnbirred(11,i,1)));

t = ffgen(2^64)^((2^64-1)\5);1/t

sqrt(Mod(-1,4296540161))
sqrt(Mod(-1,18446744073944432641))
centerlift(factorcantor(prod(i=-10,10,(x^2-i)),2^64+13)[,1])
conjvec(Mod(x, x^2+Mod(1,3)))

default(echo,0);
test(q)=
{
  my(t = ffgen(q,'t), m=[t,t^2,1+t^3; 1+t,1+t^2,1+t^3]);
  print(matker(m));
  print(matimage(m));
  print(matrank(m));
  my(M = [t,2*t^0,3*t^0; t,t^2,1+t^3; 1+t,1+t^2,1+t^3]);
  print(matdet(M));
  print(M^(-1)*M);
  my(v = [t^0, t^1, t^2]~);
  print(M*v);
  print(M*matsolve(M, v) == v);
  print(M*matinverseimage(M, v) == v);
  print(matsolve(M, matid(3)*t^0) == M^(-1));
  print(matinverseimage(M, matid(3)*t^0) == M^(-1));
  my(N = t*[0, 1; 0, 0]);
  iferr(N^-1, e,, errname(e) == "e_INV");
  iferr(matsolve(N, t*[0, 1]~), e,, errname(e) == "e_INV");
  print(matinverseimage(N, t*[1, 0]~));
  print(matinverseimage(N, t*[0, 1]~));
  print(matinverseimage(N, N^0));
  print(matindexrank(N));
  print(matsupplement(t*[0; 1]));
  print(lindep(t*[1; 1]));
  print(lindep(t*[0, 0; 1, 1]));
}
default(echo,1);
test(2^5)
test(7^5)
test((2^64+13)^5)

default(echo,0);
test(q, n=10)={
  my(t = ffgen(q, 't), M = matrix(n, n, i, j, random(t)));
  if(subst(charpoly(M), 'x, M) != 0, error("test:",[q,n]));
}
default(echo,1);
test(nextprime(2^7)^5)
test(nextprime(2^15)^5)
test(nextprime(2^31)^5)
test(nextprime(2^63)^5)
test(nextprime(2^80)^5)
test(nextprime(2^7)^5, 27)
test(nextprime(2^15)^5, 27)
test(nextprime(2^31)^5, 27)
test(nextprime(2^63)^5, 27)
test(nextprime(2^80)^3, 15)

my(a=ffgen([2,100]));(0*a*x)*x

default(echo,0);
test(p=3,f=10,d=2,e=2)=
{
  my(Pa,Pb);
  my(q = p^f);
  my(a = ffgen([p,f],'a), b = ffgen([p,d*f],'b), c = ffgen([p,e*d*f],'c));
  my(m = ffembed(a, b),   n = ffembed(b, c),     k = ffembed(a, c));
  my(rm = ffinvmap(m), rn = ffinvmap(n), rk = ffinvmap(k));
  my(nm = ffcompomap(n,m), rmrn =ffcompomap(rm,rn));
  my(rnk = ffcompomap(rn,k), rkn = ffcompomap(rk,n));
  my(rmm = ffcompomap(rm,m), mrm = ffcompomap(m,rm));
  my(fr=fffrobenius(b,f));
  my(z = b); for(i=1,d-1,z = b + ffmap(fr,z));
  if (ffmap(m,ffmap(rm,z))!=z,error("fffrobenius"));
  if (minpoly(ffmap(m,a),'a) != a.mod,error("minpoly"));
  Pa = a^2+a+3;
  Pb = ffmap(m,Pa);
  if (ffmap(rm,Pb)!=Pa, error("ffmap"));
  if (ffmap(rm,b)!=[],error("ffmap"));
  my(Qa = [Pa,x^2+x*Pa+1], Qb = ffmap(m,Qa), Qc = ffmap(n,Qb));
  if (ffmap(rm,Qb)!=Qa,error("ffmap: rm"));
  if (ffmap(nm,Qa)!=Qc,error("ffmap: n o m"));
  if (ffmap(rmm,Qa)!=Qa,error("ffmap: rm o m"));
  if (ffmap(mrm,Qb)!=Qb,error("ffmap: m o m"));
  if (ffmap(rmrn,Qc)!=Qa,error("ffmap: rm o rn"));
  if (ffmap(rnk,Qa)!=ffmap(rn,ffmap(k,Qa)),error("ffmap: rn o k"));
  if (ffmap(rkn,Qb)!=ffmap(rk,ffmap(n,Qb)),error("ffmap: rk o n"));
  iferr(ffcompomap(m,n),E,print(E));
  iferr(ffcompomap(rn,rm),E,print(E));
  iferr(ffcompomap(m,rn),E,print(E));
  iferr(ffcompomap(rm,n),E,print(E));
  R=factor(b.mod*a^0)[1,1];
  [d,l]=ffextend(a,R);
  if(subst(ffmap(l,R),'b,d),error("ffextend"));
  if(minpoly(ffmap(l,a))!=minpoly(a),error("ffextend"));
  iferr(ffextend(a,x^2+b*x+1),E,print(E));
  if (ffmaprel(m,Pa).pol!=Pb, error("ffmaprel"));
  if (ffmaprel(rm,Pb).pol!=Pa, error("ffmaprel"));
  if (ffmaprel(rm,b).pol!='b, error("ffmaprel"));
  mPa = ffmaprel(m,Pa); if (subst(minpoly(mPa),x,mPa)!=0, error("minpoly"));
  rmPb = ffmaprel(rm,Pb); if (subst(minpoly(rmPb),x,rmPb)!=0, error("minpoly"));
  rmb = ffmaprel(rm,b); if (subst(minpoly(rmb),x,rmb)!=0, error("minpoly"));
}
default(echo,1);
test(2,1,5,3)
test(2,5,5,3)
test(3,1,2,3)
test(3,10,2,3)
test(nextprime(2^100),1,3,2)
test(nextprime(2^100),3,3,2)

a=ffgen(('a^4+'a^3+'a^2+'a+1)*Mod(1,3));
for(i=1,1000,setrand(i);iferr(sqrt(2*a^2+1);print(i),E,E))

/* error */
ffinit(1,1)
ffinit(4,2)
ffinit(2^64,2)
ffgen(x^2+x+Mod(1,3))
ffembed(ffgen([3,5],'b),ffgen([3,6],'a));
a=ffgen(3^3,'a); ffinvmap(ffextend(a,x^2+x+a));
fforder(ffgen(8)*0)
