Overloading isunit from Nemo ring/field

General Usage
1

Hi everybody !
My first attempt was quite successful !
I wanted to check experimentally that Z/nZ is a field if and only if n is a prime number. This is easy to prove but it was just an opportunity to use the Nemo residue fields.
So I wrote :

using Nemo

#vérification que Z/pZ corps ssi p premier
function test(n)
    R = ResidueRing( ZZ , n)
    K=[R(i) for i in 0:n-1]
    return all((isunit(x)||iszero(x) for x in K))
end

println([n for n in 2:20 if test(n)])

which gives the desired result…
But the story doesn’t end here. I’m using now Nemo residue rings to study products of such rings.
Everything works more or less and I decided to redefine isunit for a couple given that a couple has inverse if and only if every coordinate has one according multiplication law in product rings. So I wrote a lot of things working correctly :

#http://nemocas.github.io/Nemo.jl/v0.6/types/#the-abstract-type-hierarchy-in-nemo
using Nemo
R5 = ResidueRing( ZZ , 5)
R7= ResidueRing( ZZ , 7)
struct Z_sur_5ZxZ_sur_7Z <:RingElem
   c::Tuple{nmod, nmod}
end
const Z57=Z_sur_5ZxZ_sur_7Z #alias
Base.show(io::IO, C::Z57) = print(io,C.c)
couple(x::Int64,y::Int64)=Z57((R5(x),R7(y)))
println(couple(12,13))
zero(Z57)=couple(0,0) #neutre de l'addition
println(zero(Z57))
println(couple(5,7))
one(Z57)=couple(1,1)
println(one(Z57))
Base.:(==)(C1::Z57,C2::Z57)=C1.c==C2.c
iszero(C::Z57)=C==zero(Z57)
println(iszero(couple(5,7)))
Base.:+(C1::Z57,C2::Z57)=Z57((C1.c[1]+C2.c[1],C1.c[2]+C2.c[2]))
println(zero(Z57)+one(Z57))
Base.:*(C1::Z57,C2::Z57)=Z57((C1.c[1]*C2.c[1],C1.c[2]*C2.c[2]))
println(zero(Z57)*one(Z57))
Base.:*(n::Int64,C::Z57)=Z57((n*C.c[1],n*C.c[2]))
println(5one(Z57))
Base.:^(C::Z57,n::Int64) = Z57((C.c[1]^n,C.c[2]^n))
println(one(Z57)^3)

But now if I want to define isunit for my couples :
it is logical to write

isunit(C::Z57)=isunit(C.c[1])&&isunit(C.c[2])

which is accepted by the compiler without any error.
Now if you want to test with the line :

println(isunit(one(Z57)))

At execution time you receive the error :

ERROR: LoadError: MethodError: no method matching isunit(::nmod)

This error is more or less clear but contradicts the correct execution of first program assuming method matching isunit(::nmod)
I would be glad if somebody can explain to me what happens and why.
Thank you !
Gilles

2

you want to extend it instead:

Nemo.isunit(...
3

also I think this is what you wanted? you defined:

but what you wanted is one(::Type{Z57})?

4

Thank you, what you propose works quite well but I still don’t understand the error message because in the right part of the assignation isunit can only refer to the Nemo definition given the type of the argument (nmod) ???

5

Yes actually I want to define the multiplying neutral of couples (elements whose type is Z57). It’s not what I did ? I got what I wanted, my ‘one’ works as it should, but I have the feeling that I don’t use the derivation ```
<:RingElem

in my struct definition...
6

I thought a little more and I understand now. I redefine isunit so the Nemo.isunit is forgotten even for elements of nmod types. In the first case it was called by default.
Subtle but logical.
No need to explain. But I would appreciate if you can develop the zero is it the same mistake ?

7

Thank you again jiling for your help.
I thought and searched a lot by myself after your remark.
Everything is clear now. No need to answer any of my previous questions.
This topic is closed

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