# Strange inconsistent in complex algebra
**URL:** https://discourse.julialang.org/t/strange-inconsistent-in-complex-algebra/36851
**Category:** General Usage
**Created:** [April 1, 2020, 2:27pm UTC](https://discourse.julialang.org/t/strange-inconsistent-in-complex-algebra/36851 "2020-04-01T14:27:47Z")
**Posts on this page:** 7
**Page:** 3
### Author:  [@gangchern](https://discourse.julialang.org/u/gangchern)
#### Post date: [April 4, 2020, 10:18am UTC](https://discourse.julialang.org/t/strange-inconsistent-in-complex-algebra/36851/41 "2020-04-04T10:18:13Z")
I just test in the Python3. It seems there is no such inconsistency.
```julia
complex((-0.5) * 0.5**2)**(-0.2)
(1.2262404609625575-0.8909158444501956j)
((-0.5) * complex(0.5)**2)**(-0.2)
(1.2262404609625575-0.8909158444501956j)
```
The reason is in Python, the complex function seems redefined. They always use the integral zero in the imagine part. It is not changed even under the product with a float number. The power function is also redefined.
```julia
complex((-0.5) * 0.5**2)
(-0.125+0j)
((-0.5) * complex(0.5)**2)
(-0.125+0j)
```
PS. I do not use any external package.
---
### Author:  [@yuyichao](https://discourse.julialang.org/u/yuyichao)
#### Post date: [April 4, 2020, 12:08pm UTC](https://discourse.julialang.org/t/strange-inconsistent-in-complex-algebra/36851/42 "2020-04-04T12:08:09Z")
> [@gangchern](#):
>
> They always use the integral zero in the imagine part. It is not changed even under the product with a float number.
AFAICT that’s just printing.
---
### Author:  [@antoine-levitt](https://discourse.julialang.org/u/antoine-levitt)
#### Post date: [April 4, 2020, 1:41pm UTC](https://discourse.julialang.org/t/strange-inconsistent-in-complex-algebra/36851/43 "2020-04-04T13:41:09Z")
It’s not just printing. python does some _weird_ things here:
```julia
In [13]: (-0.0j).imag
Out[13]: -0.0
In [14]: (1.0-0.0j).imag
Out[14]: 0.0
```
so I’m not actually sure how to check what it does for branch cuts… It behaves as if they’ve imposed no signed zeros for complex numbers.
---
### Author:  [@antoine-levitt](https://discourse.julialang.org/u/antoine-levitt)
#### Post date: [April 4, 2020, 1:48pm UTC](https://discourse.julialang.org/t/strange-inconsistent-in-complex-algebra/36851/44 "2020-04-04T13:48:08Z")
OK no it’s weirdness in parsing: [Issue 22548: Bogus parsing of negative zeros in complex literals - Python tracker](https://bugs.python.org/issue22548)
It behaves correctly wrt branch cuts:
```julia
In [24]: cmath.log(complex(-.2, -0.0j))
Out[24]: (-1.6094379124341003-3.141592653589793j)
In [25]: cmath.log(complex(-.2, 0.0j))
Out[25]: (-1.6094379124341003+3.141592653589793j)
```
I’m not sure I would call the behavior more sensible though:
```julia
In [31]: -complex(.25)
Out[31]: (-0.25-0j)
In [32]: (-1)*complex(.25)
Out[32]: (-0.25+0j)
```
(and therefore a different sign in the imaginary part of the log). I’m guessing this is because `(-1)*complex(.25)` promotes the -1 to a complex number, which possibly changes the sign of the zero sign. In any case: signed zeros are a mess, and it looks like julia is more consistent here.
---
### Author:  [@DNF](https://discourse.julialang.org/u/DNF)
#### Post date: [April 4, 2020, 2:04pm UTC](https://discourse.julialang.org/t/strange-inconsistent-in-complex-algebra/36851/45 "2020-04-04T14:04:06Z")
> [@gangchern](#):
>
> They always use the integral zero in the imagine part.
Python 3.8:
```julia
In [25]: z = complex(1.0)
In [26]: z
Out[26]: (1+0j)
In [27]: z.imag
Out[27]: 0.0
```
> [@yuyichao](#):
>
> AFAICT that’s just printing.
Yup.
---
### Author:  [@chakravala](https://discourse.julialang.org/u/chakravala)
#### Post date: [August 5, 2020, 8:25pm UTC](https://discourse.julialang.org/t/strange-inconsistent-in-complex-algebra/36851/46 "2020-08-05T20:25:28Z")
> [@gangchern](#):
>
> I suggest Julia devloper to add a True zero in the core math packgage.
Maybe you can define a single root choice for this zero
> **[GitHub - eschnett/ZeroRing.jl: A number type that has only a single value...](https://github.com/eschnett/ZeroRing.jl)**
>
> A number type that has only a single value (zero) and needs no storage - GitHub - eschnett/ZeroRing.jl: A number type that has only a single value (zero) and needs no storage
In history it took a long time to invent a number zero.
Maybe zero should be its own thing, like `I` for matrices.
---
### Author:  [@schnetter](https://discourse.julialang.org/u/schnetter)
#### Post date: [August 5, 2020, 8:50pm UTC](https://discourse.julialang.org/t/strange-inconsistent-in-complex-algebra/36851/47 "2020-08-05T20:50:39Z")
The “zero ring” is unfortunately not integral. (I was very disappointed when I found out.) For example, there is `0 / 0 = 0`, or `0 * x = x`. Thus `ZeroElem` is a subtype of `Number`, but not a subtype of `Integer`.
One could define a type `Int0`, and integer type with 0 bits, similar to how Julia interprets `Bool` very similar to `Int`. But that would be very similar to defining a constant `trueZero` that gets promoted to the various zeros in the various Number types. I don’t think that would be useful as part of the language standard.
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