BooleanMonomial 1 is not equal to Integer(1)

[rburing]

Demonstration:

sage: P.<x> = BooleanPolynomialRing()
sage: list(P(1))
[1]
sage: list(P(1))[0]
1
sage: list(P(1))[0] == 1
False
sage: type(list(P(1))[0])
<type 'sage.rings.polynomial.pbori.BooleanMonomial'>

Note that this behavior is inconsistent with the behavior for polynomial rings over finite fields:

sage: R.<y> = PolynomialRing(GF(2))
sage: list(R(1))[0] == 1
True

In the context of converting polynomials to lists, this has ​understandably caused confusion for at least one user on Ask SageMath.

[jdemeyer]

Part of the problem is that BooleanMonomialMonoid is a monoid and not a ring.

So there cannot be a coercion from ZZ to the BooleanMonomialMonoid. There could be a coercion to the common parent P but that requires a pushout construction...

[embray]

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[embray]

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