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support all= keyword argument in AlgebraicClosureFiniteFieldElement.sqrt() #35280

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Apr 1, 2023
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support all= keyword argument in AlgebraicClosureFiniteFieldElement.sqrt() #35280

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21 changes: 15 additions & 6 deletions src/sage/rings/algebraic_closure_finite_field.py
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Original file line number Diff line number Diff line change
Expand Up @@ -340,25 +340,34 @@ def is_square(self):
"""
return True

def sqrt(self):
def sqrt(self, all=False):
"""
Return a square root of ``self``.

If the optional keyword argument ``all`` is set to ``True``,
return a list of all square roots of ``self`` instead.

EXAMPLES::

sage: F = GF(3).algebraic_closure()
sage: F.gen(2).sqrt()
z4^3 + z4 + 1

sage: F.gen(2).sqrt(all=True)
[z4^3 + z4 + 1, 2*z4^3 + 2*z4 + 2]
sage: (F.gen(2)^2).sqrt()
z2
sage: (F.gen(2)^2).sqrt(all=True)
[z2, 2*z2]
"""
F = self.parent()
x = self._value
if x.is_square():
return self.__class__(F, x.sqrt(extend=False))
else:
if not x.is_square():
l = self._level
x = F.inclusion(l, 2*l)(x)
return self.__class__(F, x.sqrt(extend=False))
sqrt = x.sqrt(extend=False, all=all)
if all:
return [self.__class__(F, y) for y in sqrt]
return self.__class__(F, sqrt)

def nth_root(self, n):
"""
Expand Down