remove dead code in categories/rings

[mantepse]

The removed line was marked as dead by codecov in #38821. For safety, we remove it in a separate pull request.

Dependencies: #38821

[fchapoton]

I am not quite sure this is "dead code". Untested code for sure, ja.

[github-actions]

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[mantepse]

Indeed, you are right. Should we make this a doctest?

from sage.structure.element import Element

class MyRingElement(Element):
    """
    sage: R = MyRing()
    sage: R.ideal(R(1))
    """
    def __init__(self, parent, x):
        Element.__init__(self, parent)
        self._x = parent._K(x)

    def _add_(self, other):
        P = self.parent()
        return P.element_class(P, self._x + other._x)

    def _mul_(self, other):
        return P.element_class(P, self._x * other._x)

class MyRing(Parent):
    def __init__(self):
        R.<x,y> = PolynomialRing(QQ)
        Q = R.quotient(x^2+y^2+1)
        self._K = Q
        category = PrincipalIdealDomains()
        Parent.__init__(self, base=QQ, category=category)

    Element = MyRingElement

[mantepse]

Should we (i.e., I) add this as a test to categories.rings?

[fchapoton]

I am not so sure. Maybe we can think about that again once the big changes are merged ?

[mantepse]

I am not so sure. Maybe we can think about that again once the big changes are merged ?

Yes, of course! Note that the tests show that the code is not so useful for principal ideal domains without gcd.

[tscrim]

#38821 has now been merged I believe.

[tscrim]

There are doctest failures.