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34212: fix doc
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src/sage/rings/number_field/number_field.py

+36-36
Original file line numberDiff line numberDiff line change
@@ -9303,32 +9303,32 @@ def logarithmic_embedding(self, prec=53):
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INPUT:
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- ``prec`` -- desired floating point precision.
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- ``prec`` -- desired floating point precision.
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OUTPUT:
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OUTPUT:
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- a tuple of real numbers.
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- a tuple of real numbers.
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EXAMPLES::
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EXAMPLES::
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sage: CF.<a> = CyclotomicField(97)
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sage: hom = Hom(CF, EuclideanSpace(1), Sets())
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sage: f = hom(logarithmic_embedding(CF(0)))
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sage: f(0)
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(-1)
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sage: f(7)
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(1.94591014905531)
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sage: CF.<a> = CyclotomicField(97)
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sage: hom = Hom(CF, EuclideanSpace(1), Sets())
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sage: f = hom(logarithmic_embedding(CF(0)))
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sage: f(0)
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(-1)
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sage: f(7)
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(1.94591014905531)
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::
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sage: F.<a> = NumberField(x^3 + 5)
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sage: K.<b> = F.extension(x^2 + 2)
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sage: hom = Hom(K, EuclideanSpace(2), Sets())
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sage: f = hom(logarithmic_embedding(K(0)))
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sage: f(0)
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(-1, -1)
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sage: f(7)
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(1.94591014905531, 3.89182029811063)
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sage: F.<a> = NumberField(x^3 + 5)
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sage: K.<b> = F.extension(x^2 + 2)
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sage: hom = Hom(K, EuclideanSpace(2), Sets())
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sage: f = hom(logarithmic_embedding(K(0)))
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sage: f(0)
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(-1, -1)
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sage: f(7)
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(1.94591014905531, 3.89182029811063)
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"""
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log_map = self._logarithmic_embedding_helper(prec)
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log_hom = Hom(self.base_ring(), EuclideanSpace(len(log_map(0))), Sets())
@@ -9344,30 +9344,30 @@ def _logarithmic_embedding_helper(self, prec=53):
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INPUT:
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- ``prec`` -- desired floating point precision.
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- ``prec`` -- desired floating point precision.
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OUTPUT:
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OUTPUT:
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- a tuple of real numbers.
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- a tuple of real numbers.
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EXAMPLES::
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EXAMPLES::
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sage: CF.<a> = CyclotomicField(97)
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sage: log_map = CF.logarithmic_embedding()
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sage: log_map(0)
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(-1)
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sage: log_map(7)
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(1.94591014905531)
9355+
sage: CF.<a> = CyclotomicField(97)
9356+
sage: log_map = CF.logarithmic_embedding()
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sage: log_map(0)
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(-1)
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sage: log_map(7)
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(1.94591014905531)
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::
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sage: F.<a> = NumberField(x^3 + 5)
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sage: K.<b> = F.extension(x^2 + 2)
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sage: log_map = K.logarithmic_embedding()
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sage: log_map(0)
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(-1, -1)
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sage: log_map(7)
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(1.94591014905531, 3.89182029811063)
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sage: F.<a> = NumberField(x^3 + 5)
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sage: K.<b> = F.extension(x^2 + 2)
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sage: log_map = K.logarithmic_embedding()
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sage: log_map(0)
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(-1, -1)
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sage: log_map(7)
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(1.94591014905531, 3.89182029811063)
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"""
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def closure_map(x):
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"""

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