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| sage: dd | But gathered from Python 2.7 documentation:: object.__hash__(self) Called by built-in function hash() and for operations on members of hashed collections including set, frozenset, and dict. __hash__() should return an integer. The only required property is that objects which compare equal have the same hash value; As a first consequence of the above behavior:: sage: {3.1415926535897932: 'approx', pi: 'exact'} |
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| as a consequence:: | And also:: |
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More strange consequences when using UniqueRepresentation --------------------------------------------------------- :: sage: F1 = FiniteEnumeratedSet([0.000000]) sage: F2 = FiniteEnumeratedSet([0]) sage: F1 is F2 True sage: F2.list() [0.000000000000000] sage: Sage's current specifications clashes with Python's specifications ------------------------------------------------------------------ :: sage: S = SymmetricFunctions(QQ) sage: x = S.s()[5] sage: y = S.p()(x) sage: x == y True sage: hash(x), hash(y) (-1840429907820881728, 5178019317311573726) It's surely syntactically nice to have x == y evaluate True after a coercion. However enforcing that the two hash functions be the same would be simply impossible: this would force to systematically coerce any symmetric function to some fixed base for computing the hash function, and we just can't afford that. |
Equality and Coercion could be harmful
The goal of this page is to gather all problems due to equality accepting coercion in borderline cases:
sage: bool(pi == 3.14159265358979323) True sage: hash(pi) 2943215493 sage: hash(3.14159265358979323) 1826823505
But gathered from Python 2.7 documentation:
object.__hash__(self) Called by built-in function hash() and for operations on members of hashed collections including set, frozenset, and dict. __hash__() should return an integer. The only required property is that objects which compare equal have the same hash value;
As a first consequence of the above behavior:
sage: {3.1415926535897932: 'approx', pi: 'exact'}
{3.1415926535897932: 'approx', pi: 'exact'}
sage: {0:"exact", 0.0000000000000000000:"approx"}
{0: 'approx'}And also:
sage: pii = 3.14159265358979323
sage: bool(pii == pi)
True
sage: dd = {pi: "exact"}
sage: pi in dd
True
sage: pii in dd
False
sage: pii in dd.keys()
TrueMore strange consequences when using UniqueRepresentation
sage: F1 = FiniteEnumeratedSet([0.000000]) sage: F2 = FiniteEnumeratedSet([0]) sage: F1 is F2 True sage: F2.list() [0.000000000000000] sage:
Sage's current specifications clashes with Python's specifications
sage: S = SymmetricFunctions(QQ) sage: x = S.s()[5] sage: y = S.p()(x) sage: x == y True sage: hash(x), hash(y) (-1840429907820881728, 5178019317311573726)
It's surely syntactically nice to have x == y evaluate True after a coercion. However enforcing that the two hash functions be the same would be simply impossible: this would force to systematically coerce any symmetric function to some fixed base for computing the hash function, and we just can't afford that.