# Overloading isunit from Nemo ring/field
**URL:** https://discourse.julialang.org/t/overloading-isunit-from-nemo-ring-field/67777
**Category:** General Usage
**Tags:** nemo
**Created:** [September 6, 2021, 10:01pm UTC](https://discourse.julialang.org/t/overloading-isunit-from-nemo-ring-field/67777 "2021-09-06T22:01:03Z")
**Posts on this page:** 7
**Page:** 1
### Author:  [@Gilles\_Dubois](https://discourse.julialang.org/u/Gilles_Dubois)
#### Post date: [September 6, 2021, 10:01pm UTC](https://discourse.julialang.org/t/overloading-isunit-from-nemo-ring-field/67777/1 "2021-09-06T22:01:03Z")
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 :
```julia
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 :
```julia
#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
```julia
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 :
```julia
println(isunit(one(Z57)))
```
At execution time you receive the error :
```julia
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
---
### Author:  [@jling](https://discourse.julialang.org/u/jling)
#### Post date: [September 6, 2021, 10:09pm UTC](https://discourse.julialang.org/t/overloading-isunit-from-nemo-ring-field/67777/2 "2021-09-06T22:09:46Z")
> [@Gilles\_Dubois](#):
>
> `isunit(C::Z57)=isunit(C.c[1])&&isunit(C.c[2])`
you want to **extend** it instead:
```julia
Nemo.isunit(...
```
---
### Author:  [@jling](https://discourse.julialang.org/u/jling)
#### Post date: [September 6, 2021, 10:13pm UTC](https://discourse.julialang.org/t/overloading-isunit-from-nemo-ring-field/67777/3 "2021-09-06T22:13:07Z")
> [@Gilles\_Dubois](#):
>
> `one(Z57)`
also I think this is what you wanted? you defined:
> [@Gilles\_Dubois](#):
>
> `one(Z57)=couple(1,1)`
but what you wanted is `one(::Type{Z57})`?
---
### Author:  [@Gilles\_Dubois](https://discourse.julialang.org/u/Gilles_Dubois)
#### Post date: [September 6, 2021, 10:16pm UTC](https://discourse.julialang.org/t/overloading-isunit-from-nemo-ring-field/67777/4 "2021-09-06T22:16:23Z")
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) ???
---
### Author:  [@Gilles\_Dubois](https://discourse.julialang.org/u/Gilles_Dubois)
#### Post date: [September 6, 2021, 10:21pm UTC](https://discourse.julialang.org/t/overloading-isunit-from-nemo-ring-field/67777/5 "2021-09-06T22:21:21Z")
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
```julia
in my struct definition...
```
---
### Author:  [@Gilles\_Dubois](https://discourse.julialang.org/u/Gilles_Dubois)
#### Post date: [September 6, 2021, 10:30pm UTC](https://discourse.julialang.org/t/overloading-isunit-from-nemo-ring-field/67777/6 "2021-09-06T22:30:24Z")
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 ?
---
### Author:  [@Gilles\_Dubois](https://discourse.julialang.org/u/Gilles_Dubois)
#### Post date: [September 7, 2021, 6:42am UTC](https://discourse.julialang.org/t/overloading-isunit-from-nemo-ring-field/67777/7 "2021-09-07T06:42:12Z")
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