factor ignores complex conjugate

[jlportner]

Steps To Reproduce

1. I run SageMath version 10.2, Release Date: 2023-12-03.
2. When I enter the following commands:

y = SR.var("y") # or y = var("y")
f = y * conjugate(y)
f.factor()

4. This returns y^2 which is clearly not true for y being complex.

Expected Behavior

The expected result for this would be to just return y * conjugate(y) as by documentation when declaring y as a variable of SR it is assumed that y is in the complex plain.

Actual Behavior

The factor function treats y as a real variable and thus returns the wrong result of y^2.

Additional Information

No response

Environment

- **OS**: Arch Linux
- **Kernel**: Linux 6.6.4-arch1-1
- **Sage Version**: 10.2
- **Python Version**: 3.11.6

Checklist

• I have searched the existing issues for a bug report that matches the one I want to file, without success.
• I have read the documentation and troubleshoot guide

[jlportner]

From my understanding the problem comes from the declaration of the var function in the SymbolicRing class.

def var(self, name, latex_name=None, n=None, domain=None):

Since no domain is assumed here in the default case this is passed on downwards and therefore complex is never assumed.
So either domain=None should be replaced with domain =CC or the documentation should be changed to reflect that by default the variables are actually not in the complex plane.

[RuchitJagodara]

@jlportner,
Can you tell me the file location where you found this var funciton as I am new to this organization and not able to find that.

[jlportner]

I found it in the file src/sage/symbolic/ring.pyx in line 751. I don't know how to properly reference such locations.

[RuchitJagodara]

I checked it and I found that the issue is with the default value only because whenever we were defining a variable without specifying any domain it was calling symbol() function with domain=None; Subsequently, it calls new_Expression_symbol() function with domain=None. In this code, I found that it was not giving any specific domain to the variable and so when we define a new variable using SR.var() function, it is passing the is_real() (Because it does not have any specific domain) test but giving the wrong answer on factor() function, where we are assuming that the variable is in complex plane by default which is correct according to the documentation.

[RuchitJagodara]

@jlportner I have created a PR, can you review it ?

[dimpase]

How about

sage: y = SR.var("y", domain="complex")
sage: factor(y*conjugate(y))
y*conjugate(y)

I'm not sure whether making domain="complex" the default is what we want.