diff --git a/script/research/ec/valuation.ipynb b/script/research/ec/valuation.ipynb index 2f11f3ea1..bbcbef553 100644 --- a/script/research/ec/valuation.ipynb +++ b/script/research/ec/valuation.ipynb @@ -689,6 +689,51 @@ "d = [i for i in range(1, 10) if f in M^i]\n", "max(d)" ] + }, + { + "cell_type": "markdown", + "id": "3b1b13e9", + "metadata": {}, + "source": [ + "# Simple Method by Parameterizing\n", + "\n", + "We parameterize our line $f$ so that $(x(0), y(0)) = P$" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "02ae75dc", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "10*t^3 + 9*t^2" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "K. = GF(11)[]\n", + "x = t + 2\n", + "# y - 2x = 0\n", + "# => y = 2x\n", + "y = 2*x\n", + "# Now just write equation in terms of parameterized x(t) and y(t)\n", + "y^2 - x^3 - 4*x" + ] + }, + { + "cell_type": "markdown", + "id": "7381d05b", + "metadata": {}, + "source": [ + "As observed we have a uniformizer $t$ with $k = 2$." + ] } ], "metadata": {