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Fix some doctest warnings #37279

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Feb 13, 2024
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12 changes: 6 additions & 6 deletions src/sage/rings/finite_rings/integer_mod_ring.py
Original file line number Diff line number Diff line change
Expand Up @@ -616,14 +616,14 @@ def multiplicative_subgroups(self):

EXAMPLES::

sage: # needs sage.groups
sage: Integers(5).multiplicative_subgroups() # optional - gap_package_polycyclic
sage: # optional - gap_package_polycyclic, needs sage.groups
sage: Integers(5).multiplicative_subgroups()
((2,), (4,), ())
sage: Integers(15).multiplicative_subgroups() # optional - gap_package_polycyclic
sage: Integers(15).multiplicative_subgroups()
((11, 7), (11, 4), (2,), (11,), (14,), (7,), (4,), ())
sage: Integers(2).multiplicative_subgroups() # optional - gap_package_polycyclic
sage: Integers(2).multiplicative_subgroups()
((),)
sage: len(Integers(341).multiplicative_subgroups()) # optional - gap_package_polycyclic
sage: len(Integers(341).multiplicative_subgroups())
80

TESTS::
Expand All @@ -632,7 +632,7 @@ def multiplicative_subgroups(self):
((),)
sage: IntegerModRing(2).multiplicative_subgroups() # needs sage.groups
((),)
sage: IntegerModRing(3).multiplicative_subgroups() # needs sage.groups # optional - gap_package_polycyclic
sage: IntegerModRing(3).multiplicative_subgroups() # optional - gap_package_polycyclic, needs sage.groups
((2,), ())
"""
return tuple(tuple(g.value() for g in H.gens())
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2 changes: 1 addition & 1 deletion src/sage/rings/generic.py
Original file line number Diff line number Diff line change
Expand Up @@ -36,7 +36,7 @@ class ProductTree:
Similarly, the :meth:`interpolation` method can be used to implement
the inverse Fast Fourier Transform::

sage: tree.interpolation(zs).padded_list(len(ys)) == ys
sage: tree.interpolation(zs).padded_list(len(ys)) == ys # needs sage.rings.finite_rings
True

This class encodes the tree as *layers*: Layer `0` is just a tuple
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4 changes: 2 additions & 2 deletions src/sage/rings/polynomial/polynomial_rational_flint.pyx
Original file line number Diff line number Diff line change
Expand Up @@ -2127,11 +2127,11 @@ cdef class Polynomial_rational_flint(Polynomial):

::

sage: # needs sage.libs.pari
sage: # needs sage.groups sage.libs.pari
sage: f = x^4 - 17*x^3 - 2*x + 1
sage: G = f.galois_group(pari_group=True); G
PARI group [24, -1, 5, "S4"] of degree 4
sage: PermutationGroup(G) # needs sage.groups
sage: PermutationGroup(G)
Transitive group number 5 of degree 4

You can use KASH or GAP to compute Galois groups as well. The advantage is
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1 change: 1 addition & 0 deletions src/sage/schemes/curves/affine_curve.py
Original file line number Diff line number Diff line change
Expand Up @@ -1801,6 +1801,7 @@ def fundamental_group(self, simplified=True, puiseux=False):
to the algebraic field::

sage: # needs sage.rings.number_field
sage: x = polygen(ZZ)
sage: a = QQ[x](x^2 + 5).roots(QQbar)[0][0]
sage: F = NumberField(a.minpoly(), 'a', embedding=a)
sage: F.inject_variables()
Expand Down
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