przed powrotem obliczania bazy do srodka klasy
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parent
15036ab49f
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4277b74355
@ -2,7 +2,7 @@
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 110,
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"execution_count": 1,
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"metadata": {
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"collapsed": false
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},
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@ -79,7 +79,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 99,
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"execution_count": 2,
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"metadata": {
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"collapsed": false
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},
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@ -203,22 +203,20 @@
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" C = self.curve\n",
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" g1 = self.function\n",
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" g2 = other.function\n",
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" g = reduction(C, g1 + g2)\n",
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" return superelliptic_function(C, g)\n",
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" return superelliptic_function(C, g1+g2)\n",
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" \n",
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" def __sub__(self, other):\n",
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" C = self.curve\n",
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" g1 = self.function\n",
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" g2 = other.function\n",
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" g = reduction(C, g1 - g2)\n",
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" return superelliptic_function(C, g)\n",
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" return superelliptic_function(C, g1 - g2)\n",
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" \n",
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" def __mul__(self, other):\n",
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" C = self.curve\n",
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" g1 = self.function\n",
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" g2 = other.function\n",
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" g = reduction(C, g1 * g2)\n",
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" return superelliptic_function(C, g)\n",
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" #g = reduction(C, g1 * g2)\n",
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" return superelliptic_function(C, g1*g2)\n",
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" \n",
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" def __truediv__(self, other):\n",
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" C = self.curve\n",
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@ -232,13 +230,14 @@
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" m = C.exponent\n",
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" p = C.characteristic\n",
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" g = self.function\n",
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" RXy.<X, y> = PolynomialRing(QQ, 2)\n",
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" FXy = FractionField(RXy)\n",
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" g = RXy(g)\n",
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" RxXy.<x, X, y> = PolynomialRing(QQ, 3)\n",
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" FxXy = FractionField(RXy)\n",
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" g = RxXy(g)\n",
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" A = g.derivative(X)*X^(-(p-1))/p\n",
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" t = teichmuller(f)\n",
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" B = g.derivative(y)*t.derivative()/(m*y^(m-1))*X^(-(p-1))/p\n",
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" return superelliptic_form(C, A+B)\n",
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" A1 = 0\n",
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" return superelliptic_form(C, A+A1+B)\n",
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" \n",
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"class superelliptic_form:\n",
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" def __init__(self, C, g):\n",
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@ -484,25 +483,18 @@
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},
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{
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"cell_type": "code",
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"execution_count": 109,
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"execution_count": 4,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"-720*X^9 - 15312*X^7 - 107160*X^5 + x^3 - 249984*X^3 - x\n"
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]
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},
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{
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"data": {
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"text/plain": [
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"6*X^7 + 3*X^5 + x^3 + 8*x"
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"6*X^2 + x + 3*X + 8"
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]
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},
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"execution_count": 109,
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"execution_count": 4,
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"metadata": {
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},
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"output_type": "execute_result"
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@ -510,7 +502,7 @@
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],
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"source": [
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"Rx.<x> = PolynomialRing(QQ)\n",
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"f = Rx(x^3 - x)\n",
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"f = Rx(x - 1)\n",
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"teichmuller(f)"
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]
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},
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@ -2,7 +2,7 @@
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"execution_count": 8,
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"metadata": {
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"collapsed": false
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},
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@ -160,8 +160,12 @@
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" M[i, :] = v\n",
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" return M \n",
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" \n",
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" def p_rank(self):\n",
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" return self.cartier_matrix().rank()\n",
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"# def p_rank(self):\n",
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"# return self.cartier_matrix().rank()\n",
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" \n",
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" def a_number(self):\n",
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" g = C.genus()\n",
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" return g - self.cartier_matrix().rank()\n",
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" \n",
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" def final_type(self, test = 0):\n",
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" F = self.frobenius_matrix()\n",
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@ -2496,6 +2500,161 @@
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"o4"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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],
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"source": [
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"m = 2\n",
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"p = 3\n",
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"R.<x> = PolynomialRing(GF(p))\n",
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"f = x^3 - x\n",
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"C = superelliptic(f, m, p)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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],
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"source": [
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"g = f(x^3 - x)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"x^9 + x^3 + x"
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]
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},
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"execution_count": 7,
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"metadata": {
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},
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"output_type": "execute_result"
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}
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],
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"source": [
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"g"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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],
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"source": [
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"C1 = superelliptic(g, m, p)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"Superelliptic curve with the equation y^2 = x^9 + x^3 + x over finite field with 3 elements."
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]
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},
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"execution_count": 9,
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"metadata": {
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},
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"output_type": "execute_result"
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}
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],
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"source": [
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"C1"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"[((1/y) dx, 0, (1/y) dx),\n",
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" ((x/y) dx, 0, (x/y) dx),\n",
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" ((x^2/y) dx, 0, (x^2/y) dx),\n",
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" ((x^3/y) dx, 0, (x^3/y) dx),\n",
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" (((x^7 + x)/y) dx, 2/x*y, (1/(x*y)) dx),\n",
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" (((-x^6 - 1)/y) dx, 2/x^2*y, 0 dx),\n",
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" (0 dx, 2/x^3*y, ((-1)/(x^3*y)) dx),\n",
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" ((x^4/y) dx, 2/x^4*y, ((-x^2 + 1)/(x^4*y)) dx)]"
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]
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},
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"execution_count": 10,
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"metadata": {
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},
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"output_type": "execute_result"
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}
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],
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"source": [
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"C1.basis_de_rham"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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],
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"source": [
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"p = 5\n",
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"R.<x> = PolynomialRing(GF(p))\n",
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"m = 3\n",
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"f = x^4 + x + 1\n",
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"C = superelliptic(f, m, p)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"1"
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]
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},
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"execution_count": 10,
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"metadata": {
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},
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"output_type": "execute_result"
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}
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],
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"source": [
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"C.a_number()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 0,
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@ -2515,7 +2674,7 @@
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"metadata": {
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"cocalc": {
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"description": "Open-source mathematical software system",
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"priority": 10,
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"priority": 1,
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"url": "https://www.sagemath.org/"
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}
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},
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@ -1116,6 +1116,35 @@
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"E = EllipticCurve(GF(3), [1,1])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"[2 0]\n",
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"[2 0]"
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]
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},
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"execution_count": 2,
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"metadata": {
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},
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"output_type": "execute_result"
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}
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],
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"source": [
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"p = 5\n",
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"R.<x> = PolynomialRing(GF(p))\n",
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"f = x^3 + x + 1\n",
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"m = 2\n",
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"C = superelliptic(f, m, p)\n",
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"C.verschiebung_matrix()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 0,
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@ -1135,7 +1164,7 @@
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"metadata": {
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"cocalc": {
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"description": "Open-source mathematical software system",
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"priority": 10,
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"priority": 1,
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"url": "https://www.sagemath.org/"
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}
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},
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