Wrong parent when using diff_form of degree zero

[mjungmath]

sage: M = Manifold(2, 'M')
sage: X.<x,y> = M.chart()
sage: M.diff_form(0).parent()
Free module X(M) of vector fields on the 2-dimensional differentiable manifold M

This output is obviously wrong. The parent should represent the algebra of scalar fields instead. However, the element is correct:

sage: M.diff_form(0)
Scalar field on the 2-dimensional differentiable manifold M

While seeking the origin, I have encountered an issue even worse:

from sage.tensor.modules.finite_rank_free_module import FiniteRankFreeModule

sage: M = FiniteRankFreeModule(QQ, 3)
sage: M.alternating_form(0)
---------------------------------------------------------------------------
KeyError                                  Traceback (most recent call last)
...
AttributeError: 'RationalField_with_category' object has no attribute 'element_class'

This should be fixed with this ticket.

CC: @egourgoulhon @tscrim

Component: geometry

Keywords: differential_forms

Author: Michael Jung

Branch/Commit: ba3b4b9

Reviewer: Eric Gourgoulhon, Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/29570

[mjungmath]

Branch: u/gh-mjungmath/diff_form_bug

[mjungmath]

Commit: 3b36f0d

[mjungmath]

New commits:

3b36f0d

Trac #29570: alternating_form returns correct element

[tscrim]

comment:3

I am assuming this change is a mistake:

diff --git a/src/sage/tensor/modules/finite_rank_free_module.py b/src/sage/tensor/modules/finite_rank_free_module.py
index b8d048b..623454c 100644
--- a/src/sage/tensor/modules/finite_rank_free_module.py
+++ b/src/sage/tensor/modules/finite_rank_free_module.py
@@ -1084,7 +1084,7 @@ class FiniteRankFreeModule(UniqueRepresentation, Parent):
         See
         :class:`~sage.tensor.modules.ext_pow_free_module.ExtPowerDualFreeModule`
         for more documentation.
-
+def dual_exterior_power
         """
         from sage.tensor.modules.ext_pow_free_module import ExtPowerDualFreeModule
         if p == 0:

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

85e7970

Trac #29570: Typo fixed, doctest added, returned element preferably non-zero

[sagetrac-git]

Changed commit from 3b36f0d to 85e7970

[mjungmath]

comment:5

Sure. I am sorry. Yesterday was late for me...

I removed the unnecessary line and also added a doctest to show that the error had been fixed.

[egourgoulhon]

comment:6

Thanks for fixing this.
However, I don't think self._ring._an_element_() shall be used when degree is 0 in FiniteRankFreeModule.alternating_form(). Indeed, the method _an_element() returns a random element (for instance 1 in your example), whereas alternating_form() shall return a generic element, as it does for the degrees >= 1.
Maybe a try with the element_class and except with the generic constructor of the base ring shall be better.

[mjungmath]

comment:7

Replying to @egourgoulhon:

Thanks for fixing this.
However, I don't think self._ring._an_element_() shall be used when degree is 0 in FiniteRankFreeModule.alternating_form(). Indeed, the method _an_element() returns a random element (for instance 1 in your example), whereas alternating_form() shall return a generic element, as it does for the degrees >= 1.
Maybe a try with the element_class and except with the generic constructor of the base ring shall be better.

I agree, your suggestions sounds much better. Do arbitrary rings such as ZZ even provide constructors for generic elements?

However, in the first place, this issue occured due to the line

         return self.dual_exterior_power(degree).element_class(self, degree,
                                               name=name, latex_name=latex_name)

where self is definitely not the parent of the ring element. I would say, this is highly unstable since we cannot predict which arguments the element class actually takes and needs (for degree > 0 this is fine since we know which elements we deal with).

[egourgoulhon]

comment:8

Replying to @mjungmath:

I would say, this is highly unstable since we cannot predict which arguments the element class actually takes and needs (for degree > 0 this is fine since we know which elements we deal with).

Indeed! Maybe an explicit scalar field construction (inside a try block) like you did for the non-free case is preferable then:

try:
    return self._domain.scalar_field(name=name, latex_name=latex_name)
except AttributeError: 
    return self._ring.an_element() # or something better...