Eq versus == behavior following Float "integer" is_integer changes

[cbm755]

Float("2", 32) == Float("2", 64) is now False after #25875.

But Eq(Float("2", 32), Float("2", 64)) is still True. IIRC, we want structural equality to imply mathematical equality (in many perhaps most cases). But of course not the other way around.

@smichr do you think that Eq(Float2, 32), Float(2, 64)) should also be non-truthy?

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In seems this would also be consistent with this behaviour:

>>> n = Symbol('n', integer=True)
>>> Eq(n, Float("3", 32))
False

[oscarbenjamin]

What == should do is clear because it is for structural equality. Eq is a whole other can of worms though.

[asmeurer]

In seems this would also be consistent with this behaviour:

That incorrect behavior has been fixed:

>>> n = Symbol('n', integer=True)
>>> Eq(n, Float("3", 32))
Eq(n, 3.0)

[asmeurer]

I'm not sure what the behavior here should be. Whatever it does, the behavior for Eq(Rational, Float) should work the same as Eq(Float, Float) for floats of different precision. My initial feeling is that they should return True, as they currently do. Returning False would be bad, but staying unevaluated is an option.

[asmeurer]

That incorrect behavior has been fixed:

The discussions around that fix are also relevant here #23731 #25856 #25875 #25865 #25864