znowu dziala. Przed zmiana do Fxy(xi)
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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": 6,
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"execution_count": 5,
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"metadata": {
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"collapsed": false
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},
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@ -10,13 +10,10 @@
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],
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"source": [
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"def basis_holomorphic_differentials_degree(f, m, p):\n",
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" kxi1.<xi1> = PolynomialRing(GF(p))\n",
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" kxi = kxi1.quotient(xi1^p)\n",
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" xi = kxi(xi1)\n",
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" r = f.degree()\n",
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" delta = GCD(r, m)\n",
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" Rx.<x> = PolynomialRing(kxi)\n",
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" Rxy.<x, y> = PolynomialRing(kxi, 2)\n",
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" Rx.<x> = PolynomialRing(GF(p))\n",
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" Rxy.<x, y> = PolynomialRing(GF(p), 2)\n",
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" Fxy = FractionField(Rxy)\n",
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" #########basis of holomorphic differentials and de Rham\n",
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" \n",
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@ -44,11 +41,8 @@
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"def basis_de_rham_degrees(f, m, p):\n",
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" r = f.degree()\n",
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" delta = GCD(r, m)\n",
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" kxi1.<xi1> = PolynomialRing(GF(p))\n",
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" kxi = kxi1.quotient(xi1^p)\n",
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" xi = kxi(xi1)\n",
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" Rx.<x> = PolynomialRing(kxi)\n",
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" Rxy.<x, y> = PolynomialRing(kxi, 2)\n",
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" Rx.<x> = PolynomialRing(GF(p))\n",
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" Rxy.<x, y> = PolynomialRing(GF(p), 2)\n",
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" Fxy = FractionField(Rxy)\n",
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" basis_holo = holomorphic_differentials_basis(f, m, p)\n",
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" basis = []\n",
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@ -86,11 +80,8 @@
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"class superelliptic:\n",
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" \n",
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" def __init__(self, f, m, p):\n",
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" kxi1.<xi1> = PolynomialRing(GF(p))\n",
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" kxi = kxi1.quotient(xi1^p)\n",
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" xi = kxi(xi1)\n",
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" Rx.<x> = PolynomialRing(kxi)\n",
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" Rxy.<x, y> = PolynomialRing(kxi, 2)\n",
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" Rx.<x> = PolynomialRing(GF(p))\n",
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" Rxy.<x, y> = PolynomialRing(GF(p), 2)\n",
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" Fxy = FractionField(Rxy)\n",
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" self.polynomial = Rx(f)\n",
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" self.exponent = m\n",
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@ -162,10 +153,10 @@
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" basis = self.basis_holomorphic_differentials\n",
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" g = self.genus()\n",
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" p = self.characteristic\n",
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" kxi1.<xi1> = PolynomialRing(GF(p))\n",
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" kxi = kxi1.quotient(xi1^p)\n",
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" xi = kxi(xi1)\n",
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" M = matrix(kxi, g, g)\n",
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" \n",
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" \n",
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" \n",
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" M = matrix(GF(p), g, g)\n",
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" for i in range(0, len(basis)):\n",
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" w = basis[i]\n",
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" v = w.cartier().coordinates()\n",
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@ -183,10 +174,7 @@
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" \n",
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"def reduction(C, g):\n",
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" p = C.characteristic\n",
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" kxi1.<xi1> = PolynomialRing(GF(p))\n",
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" kxi = kxi1.quotient(xi1^p)\n",
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" xi = kxi(xi1)\n",
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" Rxy.<x, y> = PolynomialRing(kxi, 2)\n",
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" Rxy.<x, y> = PolynomialRing(GF(p), 2)\n",
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" Fxy = FractionField(Rxy)\n",
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" f = C.polynomial\n",
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" r = f.degree()\n",
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@ -211,10 +199,7 @@
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"\n",
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"def reduction_form(C, g):\n",
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" p = C.characteristic\n",
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" kxi1.<xi1> = PolynomialRing(GF(p))\n",
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" kxi = kxi1.quotient(xi1^p)\n",
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" xi = kxi(xi1)\n",
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" Rxy.<x, y> = PolynomialRing(kxi, 2)\n",
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" Rxy.<x, y> = PolynomialRing(GF(p), 2)\n",
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" Fxy = FractionField(Rxy)\n",
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" f = C.polynomial\n",
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" r = f.degree()\n",
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@ -222,7 +207,7 @@
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" g = reduction(C, g)\n",
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"\n",
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" g1 = Rxy(0)\n",
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" Rx.<x> = PolynomialRing(kxi)\n",
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" Rx.<x> = PolynomialRing(GF(p))\n",
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" Fx = FractionField(Rx)\n",
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" FxRy.<y> = PolynomialRing(Fx)\n",
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" \n",
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@ -239,10 +224,7 @@
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"class superelliptic_function:\n",
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" def __init__(self, C, g):\n",
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" p = C.characteristic\n",
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" kxi1.<xi1> = PolynomialRing(GF(p))\n",
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" kxi = kxi1.quotient(xi1^p)\n",
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" xi = kxi(xi1)\n",
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" Rxy.<x, y> = PolynomialRing(kxi, 2)\n",
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" Rxy.<x, y> = PolynomialRing(GF(p), 2)\n",
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" Fxy = FractionField(Rxy)\n",
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" f = C.polynomial\n",
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" r = f.degree()\n",
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@ -584,7 +566,7 @@
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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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"execution_count": 6,
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"metadata": {
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"collapsed": false
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},
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@ -2251,38 +2233,121 @@
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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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"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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"source": [
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"p = 5\n",
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"Rx.<x> = PolynomialRing(GF(p))\n",
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"Rxy.<x, y> = PolynomialRing(GF(p), 2)\n",
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"Fxy = FractionField(Rxy)\n",
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"kxi1.<xi1> = PolynomialRing(Fxy)\n",
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"kxi = kxi1.quotient(xi1^p)\n",
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"xi = kxi(xi1)\n",
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"\n",
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"f1 = Rx(x^3 + x + 1)\n",
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"f = Rx(f1(x^p))\n",
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"m = 2\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": 11,
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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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"omega = C.basis_holomorphic_differentials[2]"
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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": 12,
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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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"ename": "NotImplementedError",
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"evalue": "",
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"data": {
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"text/plain": [
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"x^2/y"
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]
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},
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"execution_count": 12,
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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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"omega.form"
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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": 14,
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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*xi1bar^2 + 2*x/y*xi1bar + x^2/y"
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]
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},
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"execution_count": 14,
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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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"omega.form(x = x+xi, y = y)"
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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": 15,
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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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"ename": "TypeError",
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"evalue": "cannot convert 1/y*xi1bar^2 + 2*x/y*xi1bar + x^2/y/1 to an element of Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 5",
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"output_type": "error",
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"traceback": [
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"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
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"\u001b[0;31mNotImplementedError\u001b[0m Traceback (most recent call last)",
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"\u001b[0;32m/tmp/ipykernel_968/1691347420.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0mf\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mf1\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0mm\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m \u001b[0mC\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msuperelliptic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
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"\u001b[0;32m/tmp/ipykernel_968/2781228428.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, f, m, p)\u001b[0m\n\u001b[1;32m 81\u001b[0m \u001b[0mRx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mPolynomialRing\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkxi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnames\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'x'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m;\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mRx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_first_ngens\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 82\u001b[0m \u001b[0mRxy\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mPolynomialRing\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkxi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnames\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'x'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'y'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m;\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mRxy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_first_ngens\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 83\u001b[0;31m \u001b[0mFxy\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mFractionField\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mRxy\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 84\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpolynomial\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mRx\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 85\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexponent\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
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"\u001b[0;32m/ext/sage/9.5/local/var/lib/sage/venv-python3.9.9/lib/python3.9/site-packages/sage/rings/fraction_field.py\u001b[0m in \u001b[0;36mFractionField\u001b[0;34m(R, names)\u001b[0m\n\u001b[1;32m 129\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mring\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mis_Ring\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mR\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 130\u001b[0m \u001b[0;32mraise\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"R must be a ring\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 131\u001b[0;31m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mR\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mis_integral_domain\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 132\u001b[0m \u001b[0;32mraise\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"R must be an integral domain.\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 133\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mR\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfraction_field\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
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"\u001b[0;32m/ext/sage/9.5/local/var/lib/sage/venv-python3.9.9/lib/python3.9/site-packages/sage/rings/polynomial/multi_polynomial_ring_base.pyx\u001b[0m in \u001b[0;36msage.rings.polynomial.multi_polynomial_ring_base.MPolynomialRing_base.is_integral_domain (build/cythonized/sage/rings/polynomial/multi_polynomial_ring_base.c:4294)\u001b[0;34m()\u001b[0m\n\u001b[1;32m 107\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 108\u001b[0m \"\"\"\n\u001b[0;32m--> 109\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbase_ring\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mis_integral_domain\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mproof\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 110\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 111\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mis_noetherian\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||
"\u001b[0;32m/ext/sage/9.5/local/var/lib/sage/venv-python3.9.9/lib/python3.9/site-packages/sage/rings/ring.pyx\u001b[0m in \u001b[0;36msage.rings.ring.Ring.is_integral_domain (build/cythonized/sage/rings/ring.c:8605)\u001b[0;34m()\u001b[0m\n\u001b[1;32m 999\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1000\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mproof\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1001\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mNotImplementedError\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 1002\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1003\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||
"\u001b[0;31mNotImplementedError\u001b[0m: "
|
||||
"\u001b[0;31mAttributeError\u001b[0m Traceback (most recent call last)",
|
||||
"\u001b[0;32m/ext/sage/9.5/local/var/lib/sage/venv-python3.9.9/lib/python3.9/site-packages/sage/rings/fraction_field.py\u001b[0m in \u001b[0;36m_element_constructor_\u001b[0;34m(self, x, y, coerce)\u001b[0m\n\u001b[1;32m 695\u001b[0m \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 696\u001b[0;31m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mresolve_fractions\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 697\u001b[0m \u001b[0;32mexcept\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mAttributeError\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||
"\u001b[0;32m/ext/sage/9.5/local/var/lib/sage/venv-python3.9.9/lib/python3.9/site-packages/sage/rings/fraction_field.py\u001b[0m in \u001b[0;36mresolve_fractions\u001b[0;34m(x, y)\u001b[0m\n\u001b[1;32m 672\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mresolve_fractions\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 673\u001b[0;31m \u001b[0mxn\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnumerator\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 674\u001b[0m \u001b[0mxd\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdenominator\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||
"\u001b[0;32m/ext/sage/9.5/local/var/lib/sage/venv-python3.9.9/lib/python3.9/site-packages/sage/structure/element.pyx\u001b[0m in \u001b[0;36msage.structure.element.Element.__getattr__ (build/cythonized/sage/structure/element.c:4754)\u001b[0;34m()\u001b[0m\n\u001b[1;32m 493\u001b[0m \"\"\"\n\u001b[0;32m--> 494\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgetattr_from_category\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 495\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||
"\u001b[0;32m/ext/sage/9.5/local/var/lib/sage/venv-python3.9.9/lib/python3.9/site-packages/sage/structure/element.pyx\u001b[0m in \u001b[0;36msage.structure.element.Element.getattr_from_category (build/cythonized/sage/structure/element.c:4866)\u001b[0;34m()\u001b[0m\n\u001b[1;32m 506\u001b[0m \u001b[0mcls\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mP\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_abstract_element_class\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 507\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mgetattr_from_other_class\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcls\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 508\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||
"\u001b[0;32m/ext/sage/9.5/local/var/lib/sage/venv-python3.9.9/lib/python3.9/site-packages/sage/cpython/getattr.pyx\u001b[0m in \u001b[0;36msage.cpython.getattr.getattr_from_other_class (build/cythonized/sage/cpython/getattr.c:2566)\u001b[0;34m()\u001b[0m\n\u001b[1;32m 355\u001b[0m \u001b[0mdummy_error_message\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mname\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 356\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mAttributeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdummy_error_message\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 357\u001b[0m \u001b[0mcdef\u001b[0m \u001b[0mPyObject\u001b[0m\u001b[0;34m*\u001b[0m \u001b[0mattr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0minstance_getattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcls\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||
"\u001b[0;31mAttributeError\u001b[0m: 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular' object has no attribute '__custom_name'",
|
||||
"\nDuring handling of the above exception, another exception occurred:\n",
|
||||
"\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)",
|
||||
"\u001b[0;32m/tmp/ipykernel_1899/916120484.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0momega1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msuperelliptic_form\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mC\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0momega\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mform\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mxi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
|
||||
"\u001b[0;32m/tmp/ipykernel_1899/3188561669.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, C, g)\u001b[0m\n\u001b[1;32m 283\u001b[0m \u001b[0mRxy\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mPolynomialRing\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mGF\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnames\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'x'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'y'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m;\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mRxy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_first_ngens\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 284\u001b[0m \u001b[0mFxy\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mFractionField\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mRxy\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 285\u001b[0;31m \u001b[0mg\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mFxy\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mreduction_form\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mC\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 286\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mform\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mg\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 287\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcurve\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mC\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||
"\u001b[0;32m/tmp/ipykernel_1899/3188561669.py\u001b[0m in \u001b[0;36mreduction_form\u001b[0;34m(C, g)\u001b[0m\n\u001b[1;32m 194\u001b[0m \u001b[0mr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdegree\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 195\u001b[0m \u001b[0mm\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mC\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexponent\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 196\u001b[0;31m \u001b[0mg\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mreduction\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mC\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 197\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 198\u001b[0m \u001b[0mg1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mRxy\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||
"\u001b[0;32m/tmp/ipykernel_1899/3188561669.py\u001b[0m in \u001b[0;36mreduction\u001b[0;34m(C, g)\u001b[0m\n\u001b[1;32m 169\u001b[0m \u001b[0mr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdegree\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 170\u001b[0m \u001b[0mm\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mC\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexponent\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 171\u001b[0;31m \u001b[0mg\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mFxy\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 172\u001b[0m \u001b[0mg1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnumerator\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 173\u001b[0m \u001b[0mg2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdenominator\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||
"\u001b[0;32m/ext/sage/9.5/local/var/lib/sage/venv-python3.9.9/lib/python3.9/site-packages/sage/structure/parent.pyx\u001b[0m in \u001b[0;36msage.structure.parent.Parent.__call__ (build/cythonized/sage/structure/parent.c:9388)\u001b[0;34m()\u001b[0m\n\u001b[1;32m 896\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mmor\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 897\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mno_extra_args\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 898\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mmor\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_call_\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 899\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 900\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mmor\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_call_with_args\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkwds\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||
"\u001b[0;32m/ext/sage/9.5/local/var/lib/sage/venv-python3.9.9/lib/python3.9/site-packages/sage/structure/coerce_maps.pyx\u001b[0m in \u001b[0;36msage.structure.coerce_maps.DefaultConvertMap_unique._call_ (build/cythonized/sage/structure/coerce_maps.c:4665)\u001b[0;34m()\u001b[0m\n\u001b[1;32m 159\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mC\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mC\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 160\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mC\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_element_constructor\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mC\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_element_constructor\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 161\u001b[0;31m \u001b[0;32mraise\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 162\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 163\u001b[0m \u001b[0mcpdef\u001b[0m \u001b[0mElement\u001b[0m \u001b[0m_call_with_args\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkwds\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m{\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||
"\u001b[0;32m/ext/sage/9.5/local/var/lib/sage/venv-python3.9.9/lib/python3.9/site-packages/sage/structure/coerce_maps.pyx\u001b[0m in \u001b[0;36msage.structure.coerce_maps.DefaultConvertMap_unique._call_ (build/cythonized/sage/structure/coerce_maps.c:4557)\u001b[0;34m()\u001b[0m\n\u001b[1;32m 154\u001b[0m \u001b[0mcdef\u001b[0m \u001b[0mParent\u001b[0m \u001b[0mC\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_codomain\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 155\u001b[0m \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 156\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mC\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_element_constructor\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 157\u001b[0m \u001b[0;32mexcept\u001b[0m \u001b[0mException\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 158\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mprint_warnings\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||
"\u001b[0;32m/ext/sage/9.5/local/var/lib/sage/venv-python3.9.9/lib/python3.9/site-packages/sage/rings/fraction_field.py\u001b[0m in \u001b[0;36m_element_constructor_\u001b[0;34m(self, x, y, coerce)\u001b[0m\n\u001b[1;32m 696\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mresolve_fractions\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 697\u001b[0m \u001b[0;32mexcept\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mAttributeError\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 698\u001b[0;31m raise TypeError(\"cannot convert {!r}/{!r} to an element of {}\".format(\n\u001b[0m\u001b[1;32m 699\u001b[0m x0, y0, self))\n\u001b[1;32m 700\u001b[0m \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||
"\u001b[0;31mTypeError\u001b[0m: cannot convert 1/y*xi1bar^2 + 2*x/y*xi1bar + x^2/y/1 to an element of Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 5"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"p = 5\n",
|
||||
"kxi1.<xi1> = PolynomialRing(GF(p))\n",
|
||||
"kxi = kxi1.quotient(xi1^p)\n",
|
||||
"xi = kxi(xi1)\n",
|
||||
"Rx.<x> = PolynomialRing(kxi)\n",
|
||||
"\n",
|
||||
"f1 = x^3 + x + 1\n",
|
||||
"f = f1(x^p)\n",
|
||||
"m = 2\n",
|
||||
"C = superelliptic(f, m, p)"
|
||||
"omega1 = superelliptic_form(C, omega.form(x = x+xi, y = y))"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
|
|||
Loading…
Reference in New Issue