Different Monoids share the same name

[tobiasdiez]

Steps To Reproduce

sage: F = FreeMonoid(3,'x')
sage: F
Free monoid on 3 generators (x0, x1, x2)
sage: F.rename("F")
sage: F
F
sage: G = FreeMonoid(3,'x')
sage: G
F

Expected Behavior

Last call should return Free monoid on 3 generators (x0, x1, x2)

Actual Behavior

Gives the name F

Additional Information

Is this the expected behavior?

Environment

Latest

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

[fchapoton]

And

sage: F is G
True

[mantepse]

I would exactly this behavior, because F and G are the same monoid.

[user202729]

Isn't this just because of the unique parent condition? In practice most people don't rename things around like this.

On the other hand… yes, this just reinforces why things with mutable states are not a particularly good idea. Maybe we can make M = RenamedParent(M, "M") and somehow elements of the new parent is a wrapper around elements of the old parent, with .parent() changed…? Would require a massive refactor though.

[tobiasdiez]

My

And

sage: F is G
True

I guess this is where my confusion came from: if they have different names, then I wouldn't consider F and G to be the same anymore.

But if it's by design, then we can close this issue.