From 8f2ce9796b2f8ae0c1109d42c0bdc07fd80de3cf Mon Sep 17 00:00:00 2001 From: "Johan S. R. Nielsen" Date: Tue, 23 Feb 2016 17:21:33 +0100 Subject: [PATCH] Reflow doc-string --- .../coding/guruswami_sudan/rootfinding.py | 21 ++++++++++--------- 1 file changed, 11 insertions(+), 10 deletions(-) diff --git a/src/sage/coding/guruswami_sudan/rootfinding.py b/src/sage/coding/guruswami_sudan/rootfinding.py index 637d35b5f95..ff3b14adcdc 100644 --- a/src/sage/coding/guruswami_sudan/rootfinding.py +++ b/src/sage/coding/guruswami_sudan/rootfinding.py @@ -306,20 +306,21 @@ def rootfind_roth_ruckenstein(Q, maxd=None, precision=None): r""" Returns the list of roots of a bivariate polynomial ``Q``. - Uses the Roth-Ruckenstein algorithm to find roots or roots - modulo-up-to-some-precision of a `Q \in \mathbb{F}[x][y]` where `\mathbb{F}` is a field. + Uses the Roth-Ruckenstein algorithm to find roots or modular roots of a `Q + \in \mathbb{F}[x][y]` where `\mathbb{F}` is a field. - If ``precision = None`` then actual roots will be found, i.e. all `f \in \mathbb{F}[x]` - such that `Q(f) = 0`. This will be returned as a list of `\mathbb{F}[x]` elements. + If ``precision = None`` then actual roots will be found, i.e. all `f \in + \mathbb{F}[x]` such that `Q(f) = 0`. This will be returned as a list of + `\mathbb{F}[x]` elements. - If ``precision = k`` for some integer ``k``, then all `f \in \mathbb{F}[x]` such that - `Q(f) \equiv 0 \mod x^k` will be returned. This set is infinite, and so it - will be returned as a list of pairs in `\mathbb{F}[x] \times \mathbb{Z}_+`, where - `(f, d)` denotes that `Q(f + x^d h) \equiv 0 \mod x^k` for any `h \in - \mathbb{F}[x]`. + If ``precision = d`` for some integer ``d``, then all `f \in \mathbb{F}[x]` + such that `Q(f) \equiv 0 \mod x^d` will be returned. This set is infinite, + and so it will be returned as a list of pairs in `\mathbb{F}[x] \times + \mathbb{Z}_+`, where `(f, d)` denotes that `Q(f + x^d h) \equiv 0 \mod x^d` + for any `h \in \mathbb{F}[x]`. If ``maxd`` is given, then find only `f` with `deg f \leq maxd`. In case - `precision=k` setting `maxd` means to only find the roots up to precision + `precision=d` setting `maxd` means to only find the roots up to precision `maxd`; otherwise, the precision will be `precision-1`. INPUT: