bnfsunit

default(realprecision,38);
default(parisize,"80M");
bnf=bnfinit(x^3-2); S=idealfactor(bnf,2*3*5*7)[,1];
B=bnfsunit(bnf,S);
B[1]
B[4]
B[5]
bnfissunit(bnf,B,x)
bnfissunit(bnf,B,x+2)
bnfissunit(bnf,B,x+100)
bnfissunit(bnf,B,[x+2,20;x,17])
bnfisunit(bnf, x+100)
B=bnfunits(bnf)
bnfisunit(bnf,x,B)
B=bnfunits(bnf,S)
bnfisunit(bnf,x+2,B)
bnfisunit(bnf,x+100,B)
bnfisunit(bnf,[x+2,20;x,17],B)

S=bnfsunit(bnf,[]);
bnfissunit(bnf,S,2)
bnfissunit(bnf,S,-1)
bnfissunit(bnf,S,bnf.fu[1])

bnf=bnfinit(x^2+23); S=bnfsunit(bnf,idealprimedec(bnf,2)[1..1]);
S[1]
S[4]
S[5]

bnf=bnfinit(x^2-210); S=bnfsunit(bnf,idealprimedec(bnf,2)[1..1]);
S[1]
S[4]
S[5]

\\ #2207
setrand(1);
L=bnfinit(x^6-68463*x^4-5120808*x^3+1250774892*x^2+192368273328*x+7520491439712,1);
S2=vecextract(idealprimedec(L,2), [3,2,1]);
S7=idealprimedec(L,7);
S13=vecextract(idealprimedec(L,13), [1,3,2]);
S5=idealprimedec(L,5);
S=concat([S2,S7,S13,S5]);
U=bnfunits(L,S);
foreach(U[1],u,print(bnfisunit(L,u,U)))

\\ from D. Broadhurst's examples
P=x^7-22*x^6+169*x^5-568*x^4+1263*x^3-1506*x^2+2295*x+2;
setrand(1); bnf=bnfinit(P,1);
US=bnfunits(bnf,idealprimedec(bnf,2)); u=US[1];
t=4*(x^2-18*x+85)/x^2*Mod(1,bnf.pol);
v=bnfisunit(bnf,t,US);
for(i=1,#u,u[i][,2] *= v[i]);
P=nfmodprinit(bnf,idealprimedec(bnf,2^32+15)[1]);
nfmodpr(bnf,matreduce(matconcat(u~)), P) / nfmodpr(bnf,t,P)