@@ -1013,8 +1013,12 @@ def exponential(self, name='z'):
10131013
10141014 INPUT:
10151015
1016- - ``name`` (string, default: ``'z'``) -- the name of the generator of
1017- the lazy power series ring.
1016+ - ``name`` (string, default: ``'z'``) -- the name of the
1017+ generator of the lazy power series ring.
1018+
1019+ OUTPUT:
1020+
1021+ A lazy power series over the base field.
10181022
10191023 EXAMPLES::
10201024
@@ -1025,8 +1029,8 @@ def exponential(self, name='z'):
10251029 sage: exp = phi.exponential(); exp
10261030 z + ((1/(T^2+T))*z^2) + ((1/(T^8+T^6+T^5+T^3))*z^4) + O(z^8)
10271031
1028- The exponential is returned as a lazy power series, meaning that any of
1029- its coefficients can be computed on demands::
1032+ The exponential is returned as a lazy power series, meaning that
1033+ any of its coefficients can be computed on demands::
10301034
10311035 sage: exp[2^4]
10321036 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'):
10661070
10671071 REFERENCE:
10681072
1069- See section 4.6 of [Gos1998]_ for the definition of the exponential.
1073+ See section 4.6 of [Gos1998]_ for the definition of the
1074+ exponential.
10701075 """
10711076 L = LazyPowerSeriesRing (self ._base , name )
10721077 return L (self ._compute_coefficient_exp , valuation = 1 )
@@ -1267,6 +1272,15 @@ def logarithm(self, name='z'):
12671272 By definition, the logarithm is the compositional inverse of the
12681273 exponential (see :meth:`exponential`).
12691274
1275+ INPUT:
1276+
1277+ - ``name`` (string, default: ``'z'``) -- the name of the
1278+ generator of the lazy power series ring.
1279+
1280+ OUTPUT:
1281+
1282+ A lazy power series over the base field.
1283+
12701284 EXAMPLES::
12711285
12721286 sage: A = GF(2)['T']
@@ -1275,8 +1289,8 @@ def logarithm(self, name='z'):
12751289 sage: log = phi.logarithm(); log
12761290 z + ((1/(T^2+T))*z^2) + ((1/(T^6+T^5+T^3+T^2))*z^4) + O(z^8)
12771291
1278- The logarithm is returned as a lazy power series, meaning that any of
1279- its coefficients can be computed on demands::
1292+ The logarithm is returned as a lazy power series, meaning that
1293+ any of its coefficients can be computed on demands::
12801294
12811295 sage: log[2^4]
12821296 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)
0 commit comments