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<title> Computing Galois groups using KASH3 doesn't work. #42520

Description

@Genya-Z

Steps To Reproduce

Here is the session:

┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 10.9, Release Date: 2026-05-04                    │
│ Using Python 3.14.6. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
sage: R.<x>=QQ[]
sage: (x^16 - x^13 + 2*x^12 - x^11 + 5*x^10 + 2*x^9 + 6*x^8 + 2*x^7 + 5*x^6 - x^5 + 2*x^4 - x^3 + 1).galois_group()
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In[2], line 1
----> 1 (x**Integer(16) - x**Integer(13) + Integer(2)*x**Integer(12) - x**Integer(11) + Integer(5)*x**Integer(10) + Integer(2)*x**Integer(9) + Integer(6)*x**Integer(8) + Integer(2)*x**Integer(7) + Integer(5)*x**Integer(6) - x**Integer(5) + Integer(2)*x**Integer(4) - x**Integer(3) + Integer(1)).galois_group()

File sage/rings/polynomial/polynomial_rational_flint.pyx:2225, in sage.rings.polynomial.polynomial_rational_flint.Polynomial_rational_flint.galois_group()
-> 2225                 d = int(kash.eval('%s.ext1' % G.name()))

ValueError: invalid literal for int() with base 10: "Error, the variable 'sage0' must have a value"

Expected Behavior

Computes the Galois group.

Actual Behavior

Throws an error.

Additional Information

No response

Environment

  • OS: Artix Linux 7.1.3.artix1-1
  • Sage Version: 10.9

Checklist

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

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