diff --git a/superelliptic.ipynb b/superelliptic.ipynb
index d035a55..5122735 100644
--- a/superelliptic.ipynb
+++ b/superelliptic.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 55,
+   "execution_count": 1,
    "metadata": {
     "collapsed": false
    },
@@ -322,12 +322,10 @@
     "    RptW.<W> = PolynomialRing(RtQ)\n",
     "    fct = RptW(fct)\n",
     "    alpha = (fct.derivative())(W = start)\n",
-    "    w0 = Rt(1)\n",
+    "    w0 = Rt(start)\n",
     "    i = 1\n",
     "    while(i < prec):\n",
-    "        a = 0\n",
-    "        while(Rt(fct(W = w0)).valuation()) <= i:\n",
-    "            w0 = w0 - fct(W = w0)/alpha\n",
+    "        w0 = w0 - fct(W = w0)/alpha + O(t^(prec))\n",
     "        i += 1\n",
     "    return w0\n",
     "\n",