I know, I know, not clear if we can do something about this, but sometimes is_norm returns "large" elements:
julia> k, _a = Hecke.number_field(x^3 + 11*x^2 + 8*x - 1)
julia> ky, y = k[:y]
julia> l, _b = Hecke.number_field(y^3 + (3*_a - 2)*y^2 + (3*_a^2 - 4*_a - 8)*y - 13*_a^2 - 16*_a + 9)
# _, n1 = Hecke.is_norm(l, k(-2))
julia> n1 = (-94298461707737030787129//16384*_a^2 - 2080417641007139625138849//32768*_a - 1586977050802009659961479//32768)*_b^2 + (393422482194948133205409//16384*_a^2 + 2174529619712306886603447//8192*_a + 1702234347536301306440155//8192)*_b - 23232913862876524680321//2048*_a^2 - 2117168264649881482131805//16384*_a - 4493697201581404452050543//32768
julia> n2 = (5//8*_a^2 + 29//4*_a + 71//8)*_b^2 + (15//4*_a^2 + 79//2*_a + 47//4)*_b - 6*_a^2 - 511//8*_a - 133//8
julia> Hecke.norm(n1) == Hecke.norm(n2) == -2
Just posting it so that we don't forget.
I know, I know, not clear if we can do something about this, but sometimes
is_normreturns "large" elements:Just posting it so that we don't forget.