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#31345: removed the additions Deprecation Warnings introduced in the previous commit, and added two SEEALSO blocks
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src/sage/rings/number_field/number_field.py

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@@ -107,7 +107,9 @@
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from sage.misc.cachefunc import cached_method
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from sage.misc.superseded import deprecation
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from sage.misc.superseded import (deprecation,
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deprecated_function_alias)
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import sage.libs.ntl.all as ntl
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import sage.interfaces.gap
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from sage.misc.fast_methods import WithEqualityById
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from sage.misc.functional import is_odd, lift
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from sage.misc.superseded import deprecated_function_alias
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from sage.misc.misc_c import prod
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from sage.rings.all import Infinity
@@ -4869,14 +4870,13 @@ def selmer_generators(self, S, m, proof=True, orders=False):
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outside of `S`, but may contain it properly when not all
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primes dividing `m` are in `S`.
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.. NOTE::
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.. SEEALSO::
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When `m=p` is prime, see also the method
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:meth:`NumberField_generic.selmer_space` which gives
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additional output: as well as generators, it gives an
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abstract vector space over `GF(p)` isomorphic to `K(S,p)`
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and maps implementing the isomorphism between this space
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and `K(S,p)` as a subgroup of `K^*/(K^*)^p`.
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:meth:`NumberField_generic.selmer_space`, which gives
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additional output when `m=p` is prime: as well as generators,
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it gives an abstract vector space over `GF(p)` isomorphic to
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`K(S,p)` and maps implementing the isomorphism between this
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space and `K(S,p)` as a subgroup of `K^*/(K^*)^p`.
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EXAMPLES::
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src/sage/rings/rational_field.py

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@@ -1295,6 +1295,14 @@ def selmer_generators(self, S, m, proof=True, orders=False):
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all primes of `\QQ` outside of `S`, but may contain it
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properly when not all primes dividing `m` are in `S`.
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.. SEEALSO::
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:meth:`RationalField.selmer_space`, which gives additional
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output when `m=p` is prime: as well as generators, it gives an
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abstract vector space over `GF(p)` isomorphic to `\QQ(S,p)`
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and maps implementing the isomorphism between this space and
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`\QQ(S,p)` as a subgroup of `\QQ^*/(\QQ^*)^p`.
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EXAMPLES::
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sage: QQ.selmer_generators((), 2)
@@ -1314,6 +1322,7 @@ def selmer_generators(self, S, m, proof=True, orders=False):
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([-1, 2, 3, 5, 7], [2, 2, 2, 2, 2])
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sage: QQ.selmer_generators((2,3,5,7,), 3, orders=True)
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([2, 3, 5, 7], [3, 3, 3, 3])
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"""
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gens = list(S)
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ords = [ZZ(m)] * len(S)

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