MethodError

using Nemo
function lift(x::FinFieldElem)
Fl = parent(x)
@Assert Nemo.isprime(order(Fl))
i = 0
while i != x
i += 1
end
return i
end

function order(x::FinFieldElem)
K = parent(x)
if x == Nemo.zero(K)
throw(ArgumentError(“Argument must be non-zero”))
else
k = 1
z = x
while z != Nemo.one(K)
z *= x
k += 1
end
return k
end
end
function roots(f::PolyElem{T}) where {T <: FinFieldElem}
fac = Nemo.factor(f)
res = Dict{T, Int}()
for index in fac
P, exp = index
if degree§ == 1
res[- coeff(P, 0)] = exp
end
end
res = collect(res)
return res
end
p = ZZ(2)^128 + 51
F, _ = FiniteField(p, 1, “u”)
FX, X = PolynomialRing(F, “X”)

E0 = EllipticCurve(F(1), F(9))
ZZY, Y = PolynomialRing(ZZ, “Y”)
frob_poly = Y^2 + ZZ(13815554068038022463)*Y + ZZ(340282366920938463463374607431768211507)
Card = ZZ(340282366920938463477190161499806233971)
primes_use_step = []
eigenvalues = Dict()
primes_use_step_torsion = []
orders = Dict()

for ell in primes(2, 100)
Fl, _ = FiniteField(ell, 1, “u”)
FlZ, Z = PolynomialRing(Fl, “Z”)
frob_poly_mod_ell = FlZ(frob_poly)
rts = roots(frob_poly_mod_ell)
if length(rts)==2
rts = (rts[1][1], rts[2][1])
order1 = order(rts[1])
order2 = order(rts[2])
if ((order1 != order2) & (min(order1, order2) < 10))
append!(primes_use_step_torsion, [ell])
orders[ell] = min(order1, order2)
else
append!(primes_use_step, ell)
eigenvalues[ell] = (lift(rts[1]), lift(rts[2]))
end
end
end

When I run this I get the error message as follows:

LoadError: MethodError: no method matching order(::FqNmodFiniteField)
Closest candidates are:
order(::FinFieldElem) at /home/cssc/exp.jl:13
Stacktrace:
[1] lift(::fq_nmod) at /home/cssc/exp.jl:4
[2] top-level scope at /home/cssc/exp.jl:65
[3] include at ./boot.jl:317 [inlined]
[4] include_relative(::Module, ::String) at ./loading.jl:1038
[5] include(::Module, ::String) at ./sysimg.jl:29
[6] include(::String) at ./client.jl:388
[7] top-level scope at none:0
in expression starting at /home/cssc/exp.jl:51

I don’t understand the problem. can any one help with this?

I can’t get your code to run but it looks like your problem is here:

order1 = order(rts[1])
order2 = order(rts[2])

I’m not sure what typeof(rts[1]) gives, but it seems that it is FqNmodFiniteField, while your order function is only defined for FinFieldElem inputs.

Your roots function seems to accept subtypes of FinFieldElem, you might want to define the order function in a saimilar way? (Note that I have no understanding of the type hierarchy here given that I can’t get Nemo to work on 0.7!)