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Improve NotImplementedError for sqrt(Mod(a,n), all=True) #39856

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Improve NotImplementedError for sqrt(Mod(a,n), all=True) #39856

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15 changes: 14 additions & 1 deletion src/sage/rings/finite_rings/integer_mod.pyx
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Original file line number Diff line number Diff line change
Expand Up @@ -1174,6 +1174,19 @@ cdef class IntegerMod_abstract(FiniteRingElement):
sage: Mod(1/25, next_prime(2^90)).sqrt()^(-2)
25

Error message as requested in :issue:`38802`::

sage: sqrt(Mod(2, 101010), all=True)
Traceback (most recent call last):
...
NotImplementedError: Finding all square roots in extensions is not implemented; try extend=False to find only roots in the base ring Zmod(n).

Using the suggested ``extend=False`` works and returns an empty list
as expected::

sage: sqrt(Mod(2, 101010), all=True, extend=False)
[]

::

sage: a = Mod(3, 5); a
Expand Down Expand Up @@ -1260,7 +1273,7 @@ cdef class IntegerMod_abstract(FiniteRingElement):
z = Q.gen()
if all:
# TODO
raise NotImplementedError
raise NotImplementedError("Finding all square roots in extensions is not implemented; try extend=False to find only roots in the base ring Zmod(n).")
return z
if all:
return []
Expand Down