symbolic constant e reverses relations

[tmonteil]

As discussed on ​this ask question:

sage: x == e
e == x
sage: x > e
e < x
sage: x <= e
e >= x

Note that it only happens with e, this constant is handled in the dedicated SAGE_ROOT/src/sage/symbolic/constants_c.pyx.

This does not happen with the symbolic expression e:

sage: x == e*1
x == e
sage: x > e*1
x > e
sage: x <= e*1
x <= e

[jdemeyer]

The reason is that constant_E is a subclass. When Python sees a < b where type(b) is a strict subclass of type(a), it instead evaluates b > a.

So this gives us basically the following options:

1. Consider this not a bug and move on.

2. Ensure that type(e) is the same as type(x).

3. Ensure that type(e) and type(x) are both subtypes of a common subclass.

[tmonteil]

Replying to jdemeyer:

The reason is that constant_E is a subclass. When Python sees a < b where type(b) is a strict subclass of type(a), it instead evaluates b > a.

Aha, so it is at the Python level, thanks for the hint, i could not find the explanation within Sage source code.

So this gives us basically the following options:

1. Consider this not a bug and move on.

The problem comes from #26490, so in this case, we should do more parsing to replace lines such as tempic=tempic+","+(dvar==ics[1])._maxima_().str() to something that hardcodes maxima's "=" symbol. Also, from a user perspective, one could program something with rhs and lhs and get confused when such unexpected case appears.

2. Ensure that type(e) is the same as type(x).

Would replacing

e = E()

with

e = E() * 1

in SAGE_ROOT/src/sage/symbolic/constants.py be considered as a correct fix ?

3. Ensure that type(e) and type(x) are both subtypes of a common subclass.

[jdemeyer]

Replying to tmonteil:

Would replacing

e = E()

with

e = E() * 1

in SAGE_ROOT/src/sage/symbolic/constants.py be considered as a correct fix ?

If you want to do that, then why do we need the constant_E class in the first place? My guess is that it's mainly for documentation, such that e? gives information about e as opposed to generic expressions.

[jdemeyer]

Replying to tmonteil:

Aha, so it is at the Python level, thanks for the hint, i could not find the explanation within Sage source code.

To elaborate on this: for arithmetic operators like __add__, there is a reversed version like __radd__. But the reversed version of __le__ is just __gt__. So user code cannot make a difference between a < b and b > a.