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Test radical on a field without squarefree_decomposition()
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src/sage/rings/polynomial/polynomial_element.pyx

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@@ -10534,6 +10534,8 @@ cdef class Polynomial(CommutativePolynomial):
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Traceback (most recent call last):
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...
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NotImplementedError: square-free decomposition not implemented for this polynomial
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sage: f.radical()
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y^2 + ((x^2 + x + 1)/(x + 1))*y + x/(x + 1)
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"""
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P = self._parent
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R = P.base_ring()

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