@@ -792,25 +792,24 @@ def scale_by(self, t):
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def normalize_coordinates (self , ** kwds ):
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"""
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- Ensures that this morphism has integral coefficients, and,
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- if the coordinate ring has a GCD, then it ensures that the
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+ Ensures that this morphism has integral coefficients.
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+ If the coordinate ring has a GCD, then it ensures that the
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coefficients have no common factor.
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- Also, makes the leading coefficients of the first polynomial
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+ It also makes the leading coefficients of the first polynomial
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positive (if positive has meaning in the coordinate ring).
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This is done in place.
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- When ``ideal`` or ``valuation`` is specified,
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- normalization occurs with respect to the absolute value
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- defined by the ``ideal`` or ``valuation``. That is, the
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- coefficients are scaled such that one coefficient has
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- absolute value 1 while the others have absolute value
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- less than or equal to 1. Only supported when the base
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- ring is a number field.
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+ When ``ideal`` or ``valuation`` is specified, normalization occurs
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+ with respect to the absolute value defined by the ``ideal`` or
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+ ``valuation``. That is, the coefficients are scaled such that
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+ one coefficient has absolute value 1 while the others have
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+ absolute value less than or equal to 1.
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+ Only supported when the base ring is a number field.
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INPUT:
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- keywords :
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+ kwds :
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- ``ideal`` -- (optional) a prime ideal of the base ring of this
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morphism.
@@ -926,7 +925,7 @@ def normalize_coordinates(self, **kwds):
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Dynamical System of Projective Space of dimension 1 over
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Number Field in a with defining polynomial 3*x^2 + 1
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Defn: Defined on coordinates by sending (z : w) to
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- ((-3/2*a + 1/2)*z^2 + (-3/2*a + 1/2)*w^2 : (-3/2*a - 3/2)*z*w)
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+ ((-3/2*a + 1/2)*z^2 + (-3/2*a + 1/2)*w^2 : (-3/2*a - 3/2)*z*w)
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::
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@@ -1027,7 +1026,7 @@ def normalize_coordinates(self, **kwds):
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if GCD != 1 :
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self .scale_by (R (1 ) / GCD )
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- # scales by 1/gcd of the coefficients.
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+ # Scale by 1/GCD of the coefficients.
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if R in _NumberFields :
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O = R .maximal_order ()
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elif isinstance (R , FiniteField ):
@@ -1042,8 +1041,9 @@ def normalize_coordinates(self, **kwds):
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if GCD != 1 :
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self .scale_by (1 / GCD )
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+
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+ # If R is not p-adic, we make the first coordinate positive
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from sage .rings .padics .padic_base_generic import pAdicGeneric
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- # if R is not padic, we make the first coordinate positive
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if not isinstance (R , pAdicGeneric ):
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if self [0 ].lc () < 0 :
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self .scale_by (- 1 )
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