default(realprecision,38);
setrand(1429412696);bnfinit(x^2+29051222508*x-12).clgp
setrand(1); bnfinit(x^8 + 12*x^6 + 30*x^4 + 24*x^2 + 4).reg
setrand(1); bnfinit(x^4 - 3*x^2 + 49).reg
bnfinit(x-1/2).clgp
bnfinit(x^2-1/2).clgp

nfinit(factor(polzagier(9,5))[2,1],2).disc
nfinit(Pol([1,0,42,112,728,3248,14224,3392,289478,-804944,2966908,-11015200,17342836,-108601584,381107816,-1679988352,6252186465,-14812800240,28868620970,-27997506768,-33428758132,98285772160,-51592356424,-39975211584,55983352320,-24670808064,5337884160,-733917184,87744512])).disc

setrand(3);bnfinit(x^2-(1130481^2+4)).clgp
setrand(2);bnfinit(x^4 - x^3 + 63*x^2 - 22*x + 1004).clgp
setrand(1);bnfinit(x^8 - 8*x^6 + 38*x^4 - 143*x^2 + 121).clgp
bnfcertify(bnfinit(x^2-40!));
bnfcertify(bnfinit(x^8-2));
\\#1736
setrand(1);bnfinit(x^3-87156*x^2-6728799*x-456533).cyc

nf=nfinit(y^5-4*y^3+2*y+11);
v = [4/3, -1, y^2+y+1, Mod(y,nf.pol),Mod(1/2,nf.pol),[1,2,3,4,5]~];
for (i=1, #v, print( nfelttrace(nf,v[i]) ))
for (i=1, #v, print( nfeltnorm(nf,v[i]) ))
nfeltnorm(nf,[3,3;y,2])
for (i=1, #v, print( nfbasistoalg(nf,v[i]) ))
for (i=1, #v, print( nfalgtobasis(nf,v[i]) ))
funs = [nfeltadd, nfeltdiv, nfeltdiveuc, nfeltdivrem, nfeltmod, nfeltmul];

try(f) = for (i=1, #v, for (j=1,#v, print( f(nf, v[i],v[j])) ))
for (i = 1, #funs, try(funs[i]))

nfisincl(nfinit(x-1),y)
p=x^2+3;nfbasis([p, factor(poldisc(p))])

\\#1253
k=bnfinit(z^2+19*z+6,1); bnfisunit(k,k.fu[1]^2)

\\#1158
nf=nfinit(x^2+x+1);
nfinit(nf)

\\#1180
setrand(1);quadclassunit(572).no

bnf=bnfinit(x^3-2); S=bnfsunit(bnf,idealfactor(bnf,2*3*5*7)[,1]);
bnfissunit(bnf,S,x)
bnfissunit(bnf,S,x+2)
bnfissunit(bnf,S,x+100)
bnfisunit(bnf, x+100)

\\#1247
setrand(1);bnfinit(x^2+1635847).no

\\#1381
K = bnfinit(x^2+23); L = bnrdisclist(K, 10); s = L[1][2];
bnfdecodemodule(K, s[1][1])

default(realprecision,19);
K=bnfinit(x^5-x^4+x^3+100*x+20,1);
A=idealpow(K,idealprimedec(K,5)[2],150);
bnfisprincipal(K,A);
default(realprecision,173);
K=nfnewprec(K);
bnfisprincipal(K,A)

l=ideallist(K,4,0);ideallistarch(K,l,[1])
l=ideallist(K,4,3);L=ideallistarch(K,l,[1])
bnrdisclist(K,l)
bnrdisclist(K,L)
bnrdisclist(K,4,[1])
nfinit([y^3+2,[1,x]])
nfinit([y^3+2,[1,x,x^2]])
nfinit([y^3+2,[1,y^5,y]])
K=nfinit([x^5-x^4+x^3+100*x+20,[1,x,x^2-x,1/2*x^4-1/2*x^3+1/2*x^2+40,x^3-x^2+x]]);
K.index

K=nfinit([x^5+9*x^4+851*x^3+18890*x^2+252376*x+529348, 39820]);
nfcertify(K)

nfnewprec(x)
nfnewprec(quadgen(5))
nfnewprec(vector(5))
nfnewprec(vector(6))
nfnewprec(vector(8))
nfnewprec(vector(9))
nfnewprec(vector(16))

g=polcyclo(13);
f=x^12-2*x^11+17*x^10-73*x^9+198*x^8-578*x^7+1533*x^6-3404*x^5+5716*x^4-8260*x^3+18652*x^2-25578*x+15601;
nfisincl(f,g)

\\#1631
setrand(1);bnfinit(x^16-48*x^14+934*x^12-9632*x^10+57251*x^8-198568*x^6+386172*x^4-377776*x^2+137288).no

K = nfinit(y^2-5);
L = nfcompositum(K, x^5-y, polcyclo(5))
L = nfcompositum(K, x^5-y, polcyclo(5), 1);
[R,a,b,k] = L[1]
a^5 - y
liftall(b^5)
L = nfcompositum(K, x^5-y, x^5-y)
L = nfcompositum(K, x^5-y, polcyclo(3),2)
L = nfcompositum(K, x^5-y, polcyclo(3),3)

nfcompositum(nfinit(y),x,x^2+x+1,3)

p=10^62+447;
q=10^42+63;
nf=nfinit([polcompositum(x^2-p,x^2-q,2), [2,p,q]]);
idealprimedec(nf,25339)[1].gen \\ overflow in get_norm

\\#1777
nfcompositum(nfinit(x-1),x^3-2,x^3-1)
nfcompositum(nfinit(x^2+1),x^3-2,x^3-1)
nfcompositum(nfinit(x-1),y^3-2,y^3-1)
nfcompositum(nfinit(y-1),x^3-2,x^3-1)

\\#1796
nfcompositum(bnfinit(x),x^3-2,x^3-1)
nfcompositum(bnfinit(y),x^3-2,x^3-1)
