@@ -371,18 +371,20 @@ def NumberField(polynomial, name=None, check=True, names=None, embedding=None,
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One can embed into any other field::
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- sage: K.<a> = NumberField(x^3- 2, embedding=CC.gen()- 0.6)
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+ sage: K.<a> = NumberField(x^3 - 2, embedding=CC.gen() - 0.6)
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sage: CC(a)
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-0.629960524947436 + 1.09112363597172*I
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- sage: L = Qp(5) # needs sage.rings.padics
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+
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+ sage: # needs sage.rings.padics
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+ sage: L = Qp(5)
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sage: f = polygen(L)^3 - 2
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- sage: K.<a> = NumberField(x^3- 2, embedding=f.roots()[0][0])
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+ sage: K.<a> = NumberField(x^3 - 2, embedding=f.roots()[0][0])
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sage: a + L(1)
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4 + 2*5^2 + 2*5^3 + 3*5^4 + 5^5 + 4*5^6 + 2*5^8 + 3*5^9 + 4*5^12
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+ 4*5^14 + 4*5^15 + 3*5^16 + 5^17 + 5^18 + 2*5^19 + O(5^20)
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- sage: L.<b> = NumberField(x^6- x^2+ 1/10, embedding=1)
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- sage: K.<a> = NumberField(x^3-x+ 1/10, embedding=b^2)
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- sage: a+ b
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+ sage: L.<b> = NumberField(x^6 - x^2 + 1/10, embedding=1)
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+ sage: K.<a> = NumberField(x^3 - x + 1/10, embedding=b^2)
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+ sage: a + b
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b^2 + b
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sage: CC(a) == CC(b)^2
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True
@@ -409,7 +411,7 @@ def NumberField(polynomial, name=None, check=True, names=None, embedding=None,
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Note that the codomain of the embedding must be ``QQbar`` or ``AA`` for this to work
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(see :trac:`20184`)::
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- sage: N.<g> = NumberField(x^3 + 2,embedding=1)
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+ sage: N.<g> = NumberField(x^3 + 2, embedding=1)
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sage: 1 < g
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False
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sage: g > 1
@@ -493,7 +495,7 @@ def NumberField(polynomial, name=None, check=True, names=None, embedding=None,
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The following has been fixed in :trac:`8800`::
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sage: P.<x> = QQ[]
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- sage: K.<a> = NumberField(x^3 - 5,embedding=0)
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+ sage: K.<a> = NumberField(x^3 - 5, embedding=0)
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sage: L.<b> = K.extension(x^2 + a)
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sage: F, R = L.construction()
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sage: F(R) == L # indirect doctest
@@ -1561,7 +1563,7 @@ def construction(self):
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::
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sage: P.<x> = QQ[]
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- sage: K.<a> = NumberField(x^3-5,embedding=0)
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+ sage: K.<a> = NumberField(x^3-5, embedding=0)
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sage: L.<b> = K.extension(x^2+a)
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sage: a*b
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a*b
@@ -8224,7 +8226,7 @@ def _coerce_from_other_number_field(self, x):
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The following was fixed in :trac:`8800`::
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sage: P.<x> = QQ[]
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- sage: K.<a> = NumberField(x^3 - 5,embedding=0)
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+ sage: K.<a> = NumberField(x^3 - 5, embedding=0)
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sage: L.<b> = K.extension(x^2 + a)
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sage: F,R = L.construction()
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sage: F(R) == L #indirect doctest
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