diff --git a/src/sage/rings/laurent_series_ring_element.pyx b/src/sage/rings/laurent_series_ring_element.pyx index 405752c6191..bdc2cdea53e 100644 --- a/src/sage/rings/laurent_series_ring_element.pyx +++ b/src/sage/rings/laurent_series_ring_element.pyx @@ -1,6 +1,12 @@ -""" +r""" Laurent Series +Laurent series in Sage are represented internally as a power of the variable +times the power series part. If a Laurent series `f` is represented as +`f = t^n \cdot u` where `t` is the variable and `u` has nonzero constant term, +`u` can be accessed through :meth:`~LaurentSeries.valuation_zero_part` and `n` +can be accessed through :meth:`~LaurentSeries.valuation`. + EXAMPLES:: sage: R. = LaurentSeriesRing(GF(7), 't'); R @@ -35,11 +41,6 @@ Saving and loading. sage: loads(K.dumps()) == K # needs sage.rings.real_mpfr True -IMPLEMENTATION: Laurent series in Sage are represented internally -as a power of the variable times the unit part (which need not be a -unit - it's a polynomial with nonzero constant term). The zero -Laurent series has unit part 0. - AUTHORS: - William Stein: original version @@ -89,8 +90,8 @@ cdef class LaurentSeries(AlgebraElement): r""" A Laurent Series. - We consider a Laurent series of the form `t^n \cdot f` where `f` is a - power series. + We consider a Laurent series of the form `f = t^n \cdot u` where `u` is a + power series with nonzero constant term. INPUT: @@ -1301,7 +1302,7 @@ cdef class LaurentSeries(AlgebraElement): sage: g.valuation() 0 - Note that the valuation of an element undistinguishable from + Note that the valuation of an element indistinguishable from zero is infinite:: sage: h = f - f; h