@@ -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)
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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)
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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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