# Problem with \`cat\`

**URL:** <https://discourse.julialang.org/t/problem-with-cat/35964>\
**Category:** General Usage\
**Created:** [March 14, 2020, 11:37am UTC](https://discourse.julialang.org/t/problem-with-cat/35964 "2020-03-14T11:37:29Z")\
**Posts on this page:** 10\
**Page:** 1

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**Author:** ![Jean\_Michel](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jean_michel/32/8282_2.png) [@Jean\_Michel](https://discourse.julialang.org/u/Jean_Michel)\
**Post date:** [March 14, 2020, 11:37am UTC](https://discourse.julialang.org/t/problem-with-cat/35964/1 "2020-03-14T11:37:29Z")

</div>

I have a problem with `cat`. I am using polynomials (my own package but this is not the problem)

```julia
julia> q=Pol(:q)
Pol{Int64}: q

julia> (q+1)^3
Pol{Int64}: q³+3q²+3q+1

```

and I am all the time using `cat` to construct block-diagonal matrices:

```julia
julia> m=[q 0; 1 q+1]
2×2 Array{Pol{Int64},2}:
 q 0  
 1 q+1

julia> cat(m,m;dims=(1,2))
4×4 Array{Pol{Int64},2}:
    q 0 #undef #undef
    1 q+1 #undef #undef
 #undef #undef q 0  
 #undef #undef 1 q+1

```

here is the problem: why is `cat` putting `#undef` in my matrix instead of polynomial 0?

```julia
julia> zero(q)
Pol{Int64}: 0

```

I tracked down the problem to lines 1443–1445 of `abstractarray.jl`:

```julia
  if T <: Number && count(!iszero, catdims) > 1
        fill!(A, zero(T))
    end

```

Is not the test `T<:Number` wrong? Should not the right test be that `T` has the method `zero`?

Thank you for help on what to do…

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**Author:** ![Sukera](https://avatars.discourse-cdn.com/v4/letter/s/ce7236/32.png) [@Sukera](https://discourse.julialang.org/u/Sukera)\
**Post date:** [March 14, 2020, 11:57am UTC](https://discourse.julialang.org/t/problem-with-cat/35964/2 "2020-03-14T11:57:49Z")

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Can’t you simply declare your polynomial type to be `<: Number`, or is that abstraction wrong?

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**Author:** ![hendri54](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/hendri54/32/9621_2.png) [@hendri54](https://discourse.julialang.org/u/hendri54)\
**Post date:** [March 14, 2020, 12:01pm UTC](https://discourse.julialang.org/t/problem-with-cat/35964/3 "2020-03-14T12:01:13Z")

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Why not simply roll your own function to construct a diagonal matrix?

```julia
function diagm(m, n)
     l = size(m)[1]
     nd = l * n
     d = fill(0, nd, nd);
     for j = 1 : n
           idx1 = 1 + (j-1) * l
           idx2 = idx1 + (l-1)
           d[idx1:idx2, idx1:idx2] = m
      end
      return d 
end

```

where the `0` in the `fill` would have to be replaced with the `zero` for your polynomial.

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<div class="post-metadata">

**Author:** ![Jean\_Michel](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jean_michel/32/8282_2.png) [@Jean\_Michel](https://discourse.julialang.org/u/Jean_Michel)\
**Post date:** [March 14, 2020, 12:27pm UTC](https://discourse.julialang.org/t/problem-with-cat/35964/4 "2020-03-14T12:27:25Z")

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I would say it is wrong. I distinguish polynomials from their coefficients by saying that the coefficients are `<:Number`

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<div class="post-metadata">

**Author:** ![Sukera](https://avatars.discourse-cdn.com/v4/letter/s/ce7236/32.png) [@Sukera](https://discourse.julialang.org/u/Sukera)\
**Post date:** [March 14, 2020, 12:36pm UTC](https://discourse.julialang.org/t/problem-with-cat/35964/5 "2020-03-14T12:36:14Z")

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> [@Jean\_Michel](#):
>
> I distinguish polynomials from their coefficients by saying that the coefficients are `<:Number`

That reads like an implementation detail, not like a hard requirement of `Poly{T} where T`.

In any case, you can also of course overload `cat` for your type.

EDIT:

I agree with you in that this probably should not just check for `<: Number`, but making your type `<: Number` is a valid fix until this can be fixed in Base. Moreover, polynomials do very much feel like numbers to me, so not having that parent type and all the associated methods available seems weird to me.

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<div class="post-metadata">

**Author:** ![Jean\_Michel](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jean_michel/32/8282_2.png) [@Jean\_Michel](https://discourse.julialang.org/u/Jean_Michel)\
**Post date:** [March 14, 2020, 12:38pm UTC](https://discourse.julialang.org/t/problem-with-cat/35964/6 "2020-03-14T12:38:25Z")

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The question is not whether I can write myself functions from julia Base (I can) but whether `cat` is properly designed. By the way your code is wrong

- It assumes `m` is square
- You cannot initialize `d` to `0`. One should rather use `zero(promote_type(eltype(m),eltype(n)))`

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<div class="post-metadata">

**Author:** ![leethargo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/leethargo/32/6004_2.png) [@leethargo](https://discourse.julialang.org/u/leethargo)\
**Post date:** [March 14, 2020, 12:44pm UTC](https://discourse.julialang.org/t/problem-with-cat/35964/7 "2020-03-14T12:44:43Z")

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> [@Sukera](#):
>
> I agree with you in that this probably should not just check for `<: Number`

Well, if the `cat` code uses the `zero` function, then it makes sense to check for `Number` subtypes, because that’s how `zero` is defined (in addition to some other types).

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<div class="post-metadata">

**Author:** ![Jean\_Michel](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jean_michel/32/8282_2.png) [@Jean\_Michel](https://discourse.julialang.org/u/Jean_Michel)\
**Post date:** [March 14, 2020, 12:45pm UTC](https://discourse.julialang.org/t/problem-with-cat/35964/8 "2020-03-14T12:45:50Z")

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I tried to make a system where I do not distinguish polynomials from their coefficients, to get free  
multi-variate polynomials (polynomials with coefficients another polynomial) but this did not work (too long to explain here why). In my system I have many numbers: integers, rationals, BigInts, Cyclotomics, field extensions; I think my type system is ok.

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<div class="post-metadata">

**Author:** ![Sukera](https://avatars.discourse-cdn.com/v4/letter/s/ce7236/32.png) [@Sukera](https://discourse.julialang.org/u/Sukera)\
**Post date:** [March 14, 2020, 1:01pm UTC](https://discourse.julialang.org/t/problem-with-cat/35964/9 "2020-03-14T13:01:14Z")

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I don’t know how your package is structured, but are you sure things break as soon as you add `<: Number` to the type definition? Because other than that, I don’t see how this could be resolved, if the `<: Number` check for `zero` is intended.

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<div class="post-metadata">

**Author:** ![Jean\_Michel](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jean_michel/32/8282_2.png) [@Jean\_Michel](https://discourse.julialang.org/u/Jean_Michel)\
**Post date:** [March 14, 2020, 8:37pm UTC](https://discourse.julialang.org/t/problem-with-cat/35964/10 "2020-03-14T20:37:23Z")

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In my mind `Number` means “some subfield of the complex numbers” or perhaps also “element of a finite field”. If you think it should mean “any element of a ring” then that’s a completely different viewpoint.  
Anyway, thinking in terms of “duck typing”, I think the logical test should be the existence or not of a `zero` method. I would like some authoritative answer (like a sound argument why it should not be so).