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src/sage/schemes/projective/projective_subscheme.py

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@@ -1408,12 +1408,16 @@ def Chow_form(self):
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def global_height(self, prec=None):
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"""
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Return the (projective) global height of the subscheme.
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INPUT:
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- ``prec`` -- desired floating point precision (default:
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default RealField precision).
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OUTPUT:
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- a real number.
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EXAMPLES::
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sage: R.<x> = QQ[]
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sage: NF.<a> = NumberField(x^2 - 5)
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sage: P.<x,y,z> = ProjectiveSpace(NF, 2)
@@ -1433,13 +1437,17 @@ def global_height(self, prec=None):
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def local_height(self, v, prec=None):
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"""
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Return the (projective) local height of the subscheme.
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INPUT:
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- ``v`` -- a prime or prime ideal of the base ring.
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- ``prec`` -- desired floating point precision (default:
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default RealField precision).
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OUTPUT:
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- a real number.
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EXAMPLES::
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sage: R.<x> = QQ[]
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sage: NF.<a> = NumberField(x^2 - 5)
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sage: I = NF.ideal(3)
@@ -1460,13 +1468,17 @@ def local_height(self, v, prec=None):
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def local_height_arch(self, i, prec=None):
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"""
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Return the local height at the ``i``-th infinite place of the subscheme.
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INPUT:
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- ``i`` -- an integer.
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- ``prec`` -- desired floating point precision (default:
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default RealField precision).
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OUTPUT:
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- a real number.
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EXAMPLES::
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sage: R.<x> = QQ[]
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sage: NF.<a> = NumberField(x^2 - 5)
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sage: P.<x,y,z> = ProjectiveSpace(NF, 2)

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