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fix some line length and add some details to the doc
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src/sage/rings/function_field/drinfeld_modules/drinfeld_module.py

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@@ -1013,8 +1013,12 @@ def exponential(self, name='z'):
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INPUT:
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- ``name`` (string, default: ``'z'``) -- the name of the generator of
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the lazy power series ring.
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- ``name`` (string, default: ``'z'``) -- the name of the
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generator of the lazy power series ring.
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OUTPUT:
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A lazy power series over the base field.
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EXAMPLES::
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@@ -1025,8 +1029,8 @@ def exponential(self, name='z'):
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sage: exp = phi.exponential(); exp
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z + ((1/(T^2+T))*z^2) + ((1/(T^8+T^6+T^5+T^3))*z^4) + O(z^8)
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The exponential is returned as a lazy power series, meaning that any of
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its coefficients can be computed on demands::
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The exponential is returned as a lazy power series, meaning that
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any of its coefficients can be computed on demands::
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sage: exp[2^4]
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1/(T^64 + T^56 + T^52 + T^50 + T^49 + T^44 + T^42 + T^41 + T^38 + T^37 + T^35 + T^30 + T^29 + T^27 + T^23 + T^15)
@@ -1066,7 +1070,8 @@ def exponential(self, name='z'):
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REFERENCE:
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See section 4.6 of [Gos1998]_ for the definition of the exponential.
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See section 4.6 of [Gos1998]_ for the definition of the
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exponential.
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"""
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L = LazyPowerSeriesRing(self._base, name)
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return L(self._compute_coefficient_exp, valuation=1)
@@ -1267,6 +1272,15 @@ def logarithm(self, name='z'):
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By definition, the logarithm is the compositional inverse of the
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exponential (see :meth:`exponential`).
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INPUT:
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- ``name`` (string, default: ``'z'``) -- the name of the
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generator of the lazy power series ring.
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OUTPUT:
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A lazy power series over the base field.
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EXAMPLES::
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sage: A = GF(2)['T']
@@ -1275,8 +1289,8 @@ def logarithm(self, name='z'):
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sage: log = phi.logarithm(); log
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z + ((1/(T^2+T))*z^2) + ((1/(T^6+T^5+T^3+T^2))*z^4) + O(z^8)
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The logarithm is returned as a lazy power series, meaning that any of
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its coefficients can be computed on demands::
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The logarithm is returned as a lazy power series, meaning that
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any of its coefficients can be computed on demands::
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sage: log[2^4]
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1/(T^30 + T^29 + T^27 + T^26 + T^23 + T^22 + T^20 + T^19 + T^15 + T^14 + T^12 + T^11 + T^8 + T^7 + T^5 + T^4)

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