Warn with substitution of derived classes using equality

[rws]

There is a long-standing problem with substitution in that some substitutions do not work when given as equality but do work when given as dictionary.

sage: (x*pi).subs(x*pi==e)
x*pi
sage: (x*pi).subs({x*pi:e})
e

sage: s = x.series(x,2); s
1*x + Order(x^2)
sage: (x*pi).subs(x*pi==s)
pi*x

It looks like that in some cases the conversion to dict switches lhs and rhs of the equation and this is because of such behaviour:

sage: x*pi==e
e == pi*x
sage: x == s
1*x + Order(x^2) == x

[rws]

class A(SageObject):
    def __init__(self):
        from sage.symbolic.ring import SR
        self._parent = SR
    def __eq__(a, b):
        print(a, b)
        return True
    def __repr__(self):
        return "A"

class B(A):
    def __eq__(a, b):
        print(a, b)
        return True
    def __repr__(self):
        return "B"

sage: from sage.symbolic.tests import A,B
sage: A() == B()
(B, A)
True

versus

class A():
    def __init__(self):
        from sage.symbolic.ring import SR
        self._parent = SR
    def __eq__(a, b):
        print(a, b)
        return True
    def __repr__(self):
        return "A"

class B(A):
    def __eq__(a, b):
        print(a, b)
        return True
    def __repr__(self):
        return "B"

sage: from sage.symbolic.tests import A,B
sage: A() == B()
(A, B)
True

The first has A inherit from SageObject the second not.

[rws]

Since we cannot use the @richcmp decorator on a cdef class we cannot work arond but must investigate the reason for the argument switching, which is possibly in Cython.

[rws]

Adding __eq__ does not work I get a Cython compile error reported at ​https://github.com/cython/cython/issues/2019

[jdemeyer]

Replying to rws:

class A(SageObject):
    def __init__(self):
        from sage.symbolic.ring import SR
        self._parent = SR
    def __eq__(a, b):
        print(a, b)
        return True
    def __repr__(self):
        return "A"

class B(A):
    def __eq__(a, b):
        print(a, b)
        return True
    def __repr__(self):
        return "B"

sage: from sage.symbolic.tests import A,B
sage: A() == B()
(B, A)
True

versus

class A():
    def __init__(self):
        from sage.symbolic.ring import SR
        self._parent = SR
    def __eq__(a, b):
        print(a, b)
        return True
    def __repr__(self):
        return "A"

class B(A):
    def __eq__(a, b):
        print(a, b)
        return True
    def __repr__(self):
        return "B"

sage: from sage.symbolic.tests import A,B
sage: A() == B()
(A, B)
True

I think this is just a difference between new-style and old-style classes. This has nothing to do with Cython.

[jdemeyer]

Without any Cython classes involved:

sage: class A(object):
....:     def __eq__(a, b):
....:         print(a, b)
....:         return True
....:     def __repr__(self):
....:         return "A"
....: 
....: class B(A):
....:     def __eq__(a, b):
....:         print(a, b)
....:         return True
....:     def __repr__(self):
....:         return "B"
sage: A() == B()
(B, A)
True

[rws]

Why then would class A(): not switch arguments? Anyway, this ticket either should warn if subclasses are encountered or at least add explanations to the documentation.

[rws]

Replying to rws:

Why then would class A(): not switch arguments? Anyway, this ticket either should warn if subclasses are encountered or at least add explanations to the documentation.

Okay the answer is ​https://stackoverflow.com/questions/54867/what-is-the-difference-between-old-style-and-new-style-classes-in-python and Python is a PITA.