minimal_model of GradedCommutativeAlgebra misuses cache

[miguelmarco]

Is there an existing issue for this?

• I have searched the existing issues for a bug report that matches the one I want to file, without success.

Did you read the documentation and troubleshoot guide?

• I have read the documentation and troubleshoot guide

Environment

- **OS**: Debian Linux
- **Sage Version**: 9.8

Steps To Reproduce

1. Create two GradedCommutativeDifferentialAlgebras with the same names in the generators but different minimal models
2. Compute the minimal model of the first one
3. Compute the minimal model of the second one

Expected Behavior

The codomain of the minimal model of the second GCDA should be the second algebra itself

Actual Behavior

It returns the first algebra

Additional Information

Example:

sage: A.<e1,e2,e3,e4,e5,e6> = GradedCommutativeAlgebra(QQ)
sage: B1 = A.cdg_algebra({e5:e1*e2,e6:e3*e4})
sage: B2 = A.cdg_algebra({e5:e1*e2,e6:e1*e2+e3*e4})
sage: B1.minimal_model()
Commutative Differential Graded Algebra morphism:
  From: Commutative Differential Graded Algebra with generators ('x1_0', 'x1_1', 'x1_2', 'x1_3', 'y1_0', 'y1_1') in degrees (1, 1, 1, 1, 1, 1) over Rational Field with differential:
   x1_0 --> 0
   x1_1 --> 0
   x1_2 --> 0
   x1_3 --> 0
   y1_0 --> x1_0*x1_1
   y1_1 --> x1_2*x1_3
  To:   Commutative Differential Graded Algebra with generators ('e1', 'e2', 'e3', 'e4', 'e5', 'e6') in degrees (1, 1, 1, 1, 1, 1) over Rational Field with differential:
   e1 --> 0
   e2 --> 0
   e3 --> 0
   e4 --> 0
   e5 --> e1*e2
   e6 --> e3*e4
  Defn: (x1_0, x1_1, x1_2, x1_3, y1_0, y1_1) --> (e1, e2, e3, e4, e5, e6)
sage: B2.minimal_model()
Commutative Differential Graded Algebra morphism:
  From: Commutative Differential Graded Algebra with generators ('x1_0', 'x1_1', 'x1_2', 'x1_3', 'y1_0', 'y1_1') in degrees (1, 1, 1, 1, 1, 1) over Rational Field with differential:
   x1_0 --> 0
   x1_1 --> 0
   x1_2 --> 0
   x1_3 --> 0
   y1_0 --> x1_0*x1_1
   y1_1 --> x1_2*x1_3
  To:   Commutative Differential Graded Algebra with generators ('e1', 'e2', 'e3', 'e4', 'e5', 'e6') in degrees (1, 1, 1, 1, 1, 1) over Rational Field with differential:
   e1 --> 0
   e2 --> 0
   e3 --> 0
   e4 --> 0
   e5 --> e1*e2
   e6 --> e3*e4
  Defn: (x1_0, x1_1, x1_2, x1_3, y1_0, y1_1) --> (e1, e2, e3, e4, e5, -e5 + e6)

[miguelmarco]

I found the cuplrit in the fact that CachedRepresentation of CohomologyClass caches only the string representation, so it reuses them for different parents.

Solved by adding a parent to the creation of the class.