Add a function for multiplicative order

[davidamarquis]

@btime bench_mult_order_eric1(1009)
210.208 μs (8056 allocations: 188.81 KiB)

The function in this PR is the result for bench_mult_order:

@btime bench_mult_order(1009)
727.166 μs (28 allocations: 1.05 KiB

##########
[Unimportant] Here's the benchmark code:

function mult_order_eric1(n::Int, q::Int)
    (q <= 0 || n <= 0) && 
        throw(DomainError("q and n both need to be positive. Passed: q = $q, n = $n"))

    # finite stop instead of while
    for i in 0:n-1
        if mod(BigInt(q)^i, n) == 1
            return i
        end
    end
    error("Unable to compute ord($n, $q).")
end

function bench_mult_order_eric1(n::Int)
    for x in 2:(n-1) 
        mult_order_eric1(x,n) 
    end 
end

function bench_mult_order(n::Int)
    data = prepare_mult_order(n)
    for x in 2:(n-1)
        mult_order(x, data) 
    end 
end

[davidamarquis]

merged so I have a mult order function which I need to run

q = 2;
l = 9;
m = 35;
Fq = GF(q)
R_base, (x, y) = polynomial_ring(Fq, [:x, :y])
grid_x = x^l - 1
grid_y = y^m - 1
R, _ = quo(R_base, ideal(R_base, [grid_x, grid_y]));
deg = lcm(mult_order(q, l), mult_order(q, m))
K = GF(q, deg)
α = _nth_root(K, l)
β  = _nth_root(K, m)
R_K, (xk, yk) = polynomial_ring(K, [:x, :y])
S = orbit_cross(q, l, m, 7, 5);
e_S_ext = s_selected_idempotent(S, q, l, m, α, β, xk, yk)
e_S_dual = R(1 - map_coefficients(c -> Fq(coeff(c, 0)), e_S_ext, parent = R_base))
I_dual = ideal(R_base, [e_S_dual, grid_x, grid_y])
GB = groebner_basis(I_dual)
generators = typeof(e_S_dual)[]
for g in GB
    if g != grid_x && g != grid_y && !iszero(g)
        push!(generators, R(g))
    end
end
G = generator_matrix_2dcc(I_dual, l, m, Fq);
rank(G) == size(G, 1)
wts = [];
for i in 1:size(G, 1)
    push!(wts, wt(G[i, :]))
end
println("Minimum weight: ", minimum(wts))

Ω = q_Frobenius_orbits(q, l, m);
S_c = Ω[setdiff(1:length(Ω), [1, 4, 5])];
S_c_idem = s_selected_idempotent(S_c, q, l, m, α, β, xk, yk);
S_d = Ω[setdiff(1:length(Ω), [1, 5, 6])];
S_d_idem = s_selected_idempotent(S_d, q, l, m, α, β, xk, yk);
BCH_bound_2D(S_c, l, m, 1, l, m)
BCH_bound_2D(S_d, l, m, 1, l, m)