Maximum recursion depth error when listing points of a projective space

[videlec]

sage: P = ProjectiveSpace(2,GF(2))
sage: P.point_set().list()
Traceback (most recent call last):
...
RuntimeError: maximum recursion depth exceeded in __instancecheck__

Depends on #18290

CC: @nathanncohen

Component: algebraic geometry

Issue created by migration from https://trac.sagemath.org/ticket/18400

[videlec]

Dependencies: #18290

[videlec]

comment:2

Though, the following works

sage: P.point_set().points()
[(0 : 0 : 1),
 (0 : 1 : 0),
 (0 : 1 : 1),
 (0 : 2 : 1),
 (1 : 0 : 0),
 (1 : 0 : 1),
 (1 : 1 : 0),
 (1 : 1 : 1),
 (1 : 2 : 1),
 (2 : 0 : 1),
 (2 : 1 : 0),
 (2 : 1 : 1),
 (2 : 2 : 1)]

[nathanncohen]

comment:3

Also:

sage: len(ProjectiveSpace(2,GF(2)))
...
AttributeError: 'ProjectiveSpace_finite_field_with_category' object has no attribute 'list'

[nathanncohen]

comment:4

And

sage: len(ProjectiveSpace(2,GF(2)).point_set())
...
RuntimeError: maximum recursion depth exceeded while calling a Python object

[nathanncohen]

comment:5

apparently list() calls len, and len calls list. I do not see anything wrong with the design.

[videlec]

comment:6

The two examples in comment:3 and comment:4 are not exactly wrong in the same way. In algebraic geometry, a scheme is not a set. And indeed

sage: P = ProjectiveSapce(2,GF(2))
sage: P in Sets()
False
sage: P.point_set() in Sets()
True

I do not understand why there is a __len__ implemented there! It is inherited from Parent as

def __len__(self):
    return len(self.list())

Haaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

Vincent

[nathanncohen]

comment:7

First, what about removing the .list() function, which returns tuple(self), i.e. a tuple?

[nathanncohen]

comment:8

What about removing .list() from Parent? God knows that I hate both Parent and categories, but given that a Parent is not necessarily a finite set it is not very smart to have it return the cardinality of the set after a full enumeration.

This 'len' should be in FiniteEnumerateSet or whatever it is named nowadays.

[videlec]

comment:9

See the 3 years old ticket #12955...

[nathanncohen]

comment:10

Oh. Then it is going to be addressed. Fine.

[videlec]

comment:11

Replying to @nathanncohen:

Oh. Then it is going to be addressed.

Some people thinks that opening a ticket solves an issue... I am worried by the "it is going to" which is a date between now and never (though the bound is strict on the right hand side).

[nathanncohen]

comment:12

Yeah. And the people who think that just got millions from Europe.

[pjbruin]

comment:13

I just ran into this bug:

sage: P.<x,y> = ProjectiveSpace(1, QQ)
sage: Q = P.subscheme(x - y)
sage: S = Q.point_set()
sage: S.points()
[(1 : 1)]
sage: S.list()
Traceback (most recent call last):
...
RuntimeError: maximum recursion depth exceeded in __instancecheck__

The easiest way to solve this is to make list() an alias for points() in sage.schemes.projective.projective_homset.SchemeHomset_points_projective_field. Alternatively we could implement __iter__() in this class and make points() a wrapper around that.