@@ -127,10 +127,10 @@ def _test_metric_function(self, **options):
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EXAMPLES::
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- sage: UHP = HyperbolicPlane().UHP()
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- sage: UHP._test_metric_function()
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- sage: elts = [UHP.random_element() for i in range(5)]
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- sage: UHP._test_metric_function(some_elements=elts)
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+ sage: UHP = HyperbolicPlane().UHP() # optional - sage.symbolic
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+ sage: UHP._test_metric_function() # optional - sage.symbolic
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+ sage: elts = [UHP.random_element() for i in range(5)] # optional - sage.symbolic
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+ sage: UHP._test_metric_function(some_elements=elts) # optional - sage.symbolic
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"""
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tester = self ._tester (** options )
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S = tester .some_elements ()
@@ -149,11 +149,11 @@ def metric_function(self):
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EXAMPLES::
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- sage: UHP = HyperbolicPlane().UHP()
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- sage: m = UHP.metric_function()
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- sage: p1 = UHP.get_point(5 + 7*I)
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- sage: p2 = UHP.get_point(1.0 + I)
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- sage: m(p1, p2)
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+ sage: UHP = HyperbolicPlane().UHP() # optional - sage.symbolic
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+ sage: m = UHP.metric_function() # optional - sage.symbolic
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+ sage: p1 = UHP.get_point(5 + 7*I) # optional - sage.symbolic
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+ sage: p2 = UHP.get_point(1.0 + I) # optional - sage.symbolic
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+ sage: m(p1, p2) # optional - sage.symbolic
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2.23230104635820
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"""
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return lambda a ,b : a .dist (b )
@@ -166,14 +166,14 @@ def dist(self, a, b):
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EXAMPLES::
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- sage: UHP = HyperbolicPlane().UHP()
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- sage: p1 = UHP.get_point(5 + 7*I)
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- sage: p2 = UHP.get_point(1.0 + I)
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- sage: UHP.dist(p1, p2)
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+ sage: UHP = HyperbolicPlane().UHP() # optional - sage.symbolic
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+ sage: p1 = UHP.get_point(5 + 7*I) # optional - sage.symbolic
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+ sage: p2 = UHP.get_point(1.0 + I) # optional - sage.symbolic
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+ sage: UHP.dist(p1, p2) # optional - sage.symbolic
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2.23230104635820
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- sage: PD = HyperbolicPlane().PD()
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- sage: PD.dist(PD.get_point(0), PD.get_point(I/2))
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+ sage: PD = HyperbolicPlane().PD() # optional - sage.symbolic
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+ sage: PD.dist(PD.get_point(0), PD.get_point(I/2)) # optional - sage.symbolic
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arccosh(5/3)
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TESTS::
@@ -210,10 +210,10 @@ def dist(self, b):
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EXAMPLES::
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- sage: UHP = HyperbolicPlane().UHP()
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- sage: p1 = UHP.get_point(5 + 7*I)
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- sage: p2 = UHP.get_point(1 + I)
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- sage: p1.dist(p2)
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+ sage: UHP = HyperbolicPlane().UHP() # optional - sage.symbolic
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+ sage: p1 = UHP.get_point(5 + 7*I) # optional - sage.symbolic
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+ sage: p2 = UHP.get_point(1 + I) # optional - sage.symbolic
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+ sage: p1.dist(p2) # optional - sage.symbolic
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arccosh(33/7)
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"""
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return self .parent ().dist (self , b )
@@ -266,11 +266,11 @@ def dist(self, a, b):
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EXAMPLES::
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- sage: H = HyperbolicPlane()
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- sage: PD = H.PD()
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- sage: p1 = PD.get_point(0)
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- sage: p2 = PD.get_point(I/2)
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- sage: H.dist(p1, p2)
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+ sage: H = HyperbolicPlane() # optional - sage.symbolic
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+ sage: PD = H.PD() # optional - sage.symbolic
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+ sage: p1 = PD.get_point(0) # optional - sage.symbolic
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+ sage: p2 = PD.get_point(I/2) # optional - sage.symbolic
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+ sage: H.dist(p1, p2) # optional - sage.symbolic
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arccosh(5/3)
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"""
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R = self .a_realization ()
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