przed powrotem obliczania bazy do srodka klasy

crystalline_p2.ipynb

@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 110,
+   "execution_count": 1,
    "metadata": {
     "collapsed": false
    },
@@ -79,7 +79,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 99,
+   "execution_count": 2,
    "metadata": {
     "collapsed": false
    },
@@ -203,22 +203,20 @@
     "        C = self.curve\n",
     "        g1 = self.function\n",
     "        g2 = other.function\n",
-    "        g = reduction(C, g1 + g2)\n",
+    "        return superelliptic_function(C, g1+g2)\n",
-    "        return superelliptic_function(C, g)\n",
     "    \n",
     "    def __sub__(self, other):\n",
     "        C = self.curve\n",
     "        g1 = self.function\n",
     "        g2 = other.function\n",
-    "        g = reduction(C, g1 - g2)\n",
+    "        return superelliptic_function(C, g1 - g2)\n",
-    "        return superelliptic_function(C, g)\n",
     "    \n",
     "    def __mul__(self, other):\n",
     "        C = self.curve\n",
     "        g1 = self.function\n",
     "        g2 = other.function\n",
-    "        g = reduction(C, g1 * g2)\n",
+    "        #g = reduction(C, g1 * g2)\n",
-    "        return superelliptic_function(C, g)\n",
+    "        return superelliptic_function(C, g1*g2)\n",
     "    \n",
     "    def __truediv__(self, other):\n",
     "        C = self.curve\n",
@@ -232,13 +230,14 @@
     "    m = C.exponent\n",
     "    p = C.characteristic\n",
     "    g = self.function\n",
-    "    RXy.<X, y> = PolynomialRing(QQ, 2)\n",
+    "    RxXy.<x, X, y> = PolynomialRing(QQ, 3)\n",
-    "    FXy = FractionField(RXy)\n",
+    "    FxXy = FractionField(RXy)\n",
-    "    g = RXy(g)\n",
+    "    g = RxXy(g)\n",
     "    A = g.derivative(X)*X^(-(p-1))/p\n",
     "    t = teichmuller(f)\n",
     "    B = g.derivative(y)*t.derivative()/(m*y^(m-1))*X^(-(p-1))/p\n",
-    "    return superelliptic_form(C, A+B)\n",
+    "    A1 = 0\n",
+    "    return superelliptic_form(C, A+A1+B)\n",
     "        \n",
     "class superelliptic_form:\n",
     "    def __init__(self, C, g):\n",
@@ -484,25 +483,18 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 109,
+   "execution_count": 4,
    "metadata": {
     "collapsed": false
    },
    "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "-720*X^9 - 15312*X^7 - 107160*X^5 + x^3 - 249984*X^3 - x\n"
-     ]
-    },
     {
      "data": {
       "text/plain": [
-       "6*X^7 + 3*X^5 + x^3 + 8*x"
+       "6*X^2 + x + 3*X + 8"
       ]
      },
-     "execution_count": 109,
+     "execution_count": 4,
      "metadata": {
      },
      "output_type": "execute_result"
@@ -510,7 +502,7 @@
    ],
    "source": [
     "Rx.<x> = PolynomialRing(QQ)\n",
-    "f = Rx(x^3 - x)\n",
+    "f = Rx(x - 1)\n",
     "teichmuller(f)"
    ]
   },

superelliptic.ipynb

@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 8,
    "metadata": {
     "collapsed": false
    },
@@ -160,8 +160,12 @@
     "            M[i, :] = v\n",
     "        return M     \n",
     "    \n",
-    "    def p_rank(self):\n",
+    "#    def p_rank(self):\n",
-    "        return self.cartier_matrix().rank()\n",
+    "#        return self.cartier_matrix().rank()\n",
+    "    \n",
+    "    def a_number(self):\n",
+    "        g = C.genus()\n",
+    "        return g - self.cartier_matrix().rank()\n",
     "    \n",
     "    def final_type(self, test = 0):\n",
     "        F = self.frobenius_matrix()\n",
@@ -2496,6 +2500,161 @@
     "o4"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+   ],
+   "source": [
+    "m = 2\n",
+    "p = 3\n",
+    "R.<x> = PolynomialRing(GF(p))\n",
+    "f = x^3 - x\n",
+    "C = superelliptic(f, m, p)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+   ],
+   "source": [
+    "g = f(x^3 - x)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "x^9 + x^3 + x"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {
+     },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "g"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+   ],
+   "source": [
+    "C1 = superelliptic(g, m, p)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Superelliptic curve with the equation y^2 = x^9 + x^3 + x over finite field with 3 elements."
+      ]
+     },
+     "execution_count": 9,
+     "metadata": {
+     },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "C1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[((1/y) dx, 0, (1/y) dx),\n",
+       " ((x/y) dx, 0, (x/y) dx),\n",
+       " ((x^2/y) dx, 0, (x^2/y) dx),\n",
+       " ((x^3/y) dx, 0, (x^3/y) dx),\n",
+       " (((x^7 + x)/y) dx, 2/x*y, (1/(x*y)) dx),\n",
+       " (((-x^6 - 1)/y) dx, 2/x^2*y, 0 dx),\n",
+       " (0 dx, 2/x^3*y, ((-1)/(x^3*y)) dx),\n",
+       " ((x^4/y) dx, 2/x^4*y, ((-x^2 + 1)/(x^4*y)) dx)]"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {
+     },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "C1.basis_de_rham"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+   ],
+   "source": [
+    "p = 5\n",
+    "R.<x> = PolynomialRing(GF(p))\n",
+    "m = 3\n",
+    "f = x^4 + x + 1\n",
+    "C = superelliptic(f, m, p)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "1"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {
+     },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "C.a_number()"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 0,
@@ -2515,7 +2674,7 @@
    "metadata": {
     "cocalc": {
      "description": "Open-source mathematical software system",
-     "priority": 10,
+     "priority": 1,
      "url": "https://www.sagemath.org/"
     }
    },

superelliptic_alpha.ipynb

@@ -1116,6 +1116,35 @@
     "E = EllipticCurve(GF(3), [1,1])"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[2 0]\n",
+       "[2 0]"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {
+     },
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "p = 5\n",
+    "R.<x> = PolynomialRing(GF(p))\n",
+    "f = x^3 + x + 1\n",
+    "m = 2\n",
+    "C = superelliptic(f, m, p)\n",
+    "C.verschiebung_matrix()"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 0,
@@ -1135,7 +1164,7 @@
    "metadata": {
     "cocalc": {
      "description": "Open-source mathematical software system",
-     "priority": 10,
+     "priority": 1,
      "url": "https://www.sagemath.org/"
     }
    },