Symbolic functions break the __hash__ contract

[vbraun]

Equal objects must have the same hash if they are hashable (http://docs.python.org/2/reference/datamodel.html#object.__hash__):

sage: my_func = function('func',nargs=1)
sage: f = my_func(0)
sage: bool(f == f.simplify())
True
sage: hash(f) == hash(f.simplify())
False

As reported on http://ask.sagemath.org/question/2587/simplify-shenanigans, hash lookup errors then leads to undesirable behavior:

sage: ex = my_func(0) + my_func(1)
sage: ex.subs(my_func(0)==1)
func(1) + 1
sage: ex.simplify().subs(my_func(0)==1)
func(0) + func(1)

Component: symbolics

Issue created by migration from https://trac.sagemath.org/ticket/14608

[videlec]

comment:1

Within Sage it is impossible to satisfy "equal objects must have the same hash if they are hashable" because equality is too laxist.

sage: RIF(2) == 2
True
sage: hash(RIF(2))
6400019251
sage: hash(2)
2

Or

sage: bool(pi == RR(pi))
True
sage: hash(pi)
2650685528
sage: hash(RR(pi))
1826823505

You can not hope to solve this problem with one ticket (because the Symbolic ring contains all Sage objects) !

[videlec]

comment:2

see also http://wiki.sagemath.org/EqualityCoercion.

[nathanncohen]

comment:3

(cc me)