dodano macierz cartier
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commit
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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": 54,
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"execution_count": 35,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -52,7 +52,7 @@
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" degrees1 = {}\n",
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" for j in range(1, m):\n",
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" for i in range(1, r):\n",
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" if (r*(m-j) - m*i >= delta): ####tu jest blad\n",
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" if (r*(m-j) - m*i >= delta): \n",
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" s = Rx(m-j)*Rx(x)*Rx(f.derivative()) - Rx(m)*Rx(i)*f\n",
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" psi = Rx(cut(s, i))\n",
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" basis += [(Fxy(psi/y^j), Fxy(m*y^(m-j)/x^i))]\n",
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@ -146,6 +146,17 @@
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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 cartier_matrix(self):\n",
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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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" 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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" M[i, :] = v\n",
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" return M \n",
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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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" Rxy.<x, y> = PolynomialRing(GF(p), 2)\n",
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@ -291,6 +302,11 @@
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" return str(g) + ' dx'\n",
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" return '('+str(g) + ') dx'\n",
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"\n",
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" def mult(self, constant):\n",
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" C = self.curve\n",
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" omega = self.form\n",
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" return superelliptic_form(C, constant*omega) \n",
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" \n",
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" def cartier(self):\n",
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" C = self.curve\n",
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" m = C.exponent\n",
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@ -312,6 +328,30 @@
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" result += superelliptic_form(C, polynomial_part(p, h)/(f^B*y^(j1)))\n",
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" return result \n",
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" \n",
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" def coordinates(self):\n",
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" C = self.curve\n",
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" p = C.characteristic\n",
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" m = C.exponent\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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" g = C.genus()\n",
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" degrees_holo = C.degree_holo\n",
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" degrees_holo_inv = {b:a for a, b in degrees_holo.items()}\n",
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" basis = C.basis_holomorphic_differentials\n",
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" \n",
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" for j in range(1, m):\n",
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" omega_j = Fx(self.jth_component(j))\n",
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" if omega_j != Fx(0):\n",
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" d = degree_of_rational_fctn(omega_j, p)\n",
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" index = degrees_holo_inv[(d, j)]\n",
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" a = coeff_of_rational_fctn(omega_j, p)\n",
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" a1 = coeff_of_rational_fctn(basis[index].jth_component(j), p)\n",
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" elt = self - basis[index].mult(a/a1)\n",
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" return elt.coordinates() + a/a1*vector([GF(p)(i == index) for i in range(0, g)])\n",
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" \n",
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" return vector(g*[0])\n",
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" \n",
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" def jth_component(self, j):\n",
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" g = self.form\n",
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" C = self.curve\n",
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@ -511,7 +551,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 55,
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"execution_count": 31,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -569,7 +609,9 @@
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" final_type[0] = 0\n",
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" for i in range(1, dim+1):\n",
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" if final_type[i] == -1:\n",
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" final_type[i] = final_type[i-1] + 1\n",
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" final_type[i] = min(final_type[i-1] + 1, dim/2)\n",
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" \n",
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" print('poprawiony ft', final_type)\n",
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" \n",
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" if is_final(final_type, dim/2):\n",
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" return final_type[1:dim/2 + 1]\n",
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@ -584,14 +626,14 @@
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" return 0\n",
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" \n",
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" for i in range(1, n):\n",
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" if final_type[i] != final_type[i - 1] or final_type[i] != final_type[i - 1] + 1:\n",
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" if final_type[i] != final_type[i - 1] and final_type[i] != final_type[i - 1] + 1:\n",
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" return 0\n",
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" return 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": 60,
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"execution_count": 18,
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"metadata": {},
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"outputs": [
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{
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@ -600,49 +642,37 @@
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"text": [
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"0 3\n",
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"test [0, -1, -1, -1, 4, -1, -1, -1, 4]\n",
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"0 3 4 error\n",
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"poprawiony ft [0, 1, 2, 3, 4, 4, 4, 4, 4]\n",
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"0 3 4 [1, 2, 3, 4]\n",
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"0 4\n",
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"test [0, -1, -1, -1, 4, -1, -1, -1, 4]\n",
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"0 4 4 error\n",
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"poprawiony ft [0, 1, 2, 3, 4, 4, 4, 4, 4]\n",
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"0 4 4 [1, 2, 3, 4]\n",
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"1 1\n",
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"test [0, -1, -1, -1, 4, -1, -1, -1, 4]\n",
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"1 1 4 error\n",
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"1 2\n",
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"test [0, -1, -1, -1, 4, -1, -1, -1, 4]\n",
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"1 2 4 error\n",
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"1 3\n",
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"test [0, -1, -1, -1, 4, -1, -1, -1, 4]\n",
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"1 3 4 error\n",
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"2 0\n",
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"test [0, -1, -1, -1, 4, -1, -1, -1, 4]\n",
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"2 0 4 error\n",
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"2 2\n",
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"test [0, -1, -1, -1, 4, -1, -1, -1, 4]\n",
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"2 2 4 error\n",
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"2 3\n",
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"test [0, -1, -1, -1, 4, -1, -1, -1, 4]\n",
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"2 3 4 error\n",
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"3 0\n",
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"test [0, -1, -1, -1, 4, -1, -1, -1, 4]\n",
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"3 0 4 error\n",
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"3 1\n",
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"test [0, -1, -1, -1, 4, -1, -1, -1, 4]\n",
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"3 1 4 error\n",
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"3 2\n",
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"test [0, -1, -1, -1, 4, -1, -1, -1, 4]\n",
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"3 2 4 error\n",
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"3 4\n",
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"test [0, -1, -1, -1, 4, -1, -1, -1, 4]\n",
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"3 4 4 error\n",
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"4 1\n",
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"test [0, -1, -1, -1, 4, -1, -1, -1, 4]\n",
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"4 1 4 error\n",
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"4 3\n",
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"test [0, 1, 1, 2, 3, 3, 3, 4, 4]\n",
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"4 3 4 error\n",
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"4 4\n",
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"test [0, -1, -1, 3, 3, 4, -1, -1, 4]\n",
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"4 4 4 error\n"
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"poprawiony ft [0, 1, 2, 3, 4, 4, 4, 4, 4]\n",
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"1 1 4 [1, 2, 3, 4]\n",
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"1 2\n"
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]
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},
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{
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"ename": "KeyboardInterrupt",
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"evalue": "",
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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;31mKeyboardInterrupt\u001b[0m Traceback (most recent call last)",
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"\u001b[0;32m<ipython-input-18-afeec6e02e63>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m 6\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mC\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mis_smooth\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[1;32m 7\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 8\u001b[0;31m \u001b[0mV\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mC\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mverschiebung_matrix\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 9\u001b[0m \u001b[0mF\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mC\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfrobenius_matrix\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 10\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mV\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrank\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mflag\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mF\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mV\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[0;34m\u001b[0m\u001b[0m\n",
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"\u001b[0;32m<ipython-input-17-0d6574174a68>\u001b[0m in \u001b[0;36mverschiebung_matrix\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 123\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\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[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbasis\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[1;32m 124\u001b[0m \u001b[0mw\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbasis\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 125\u001b[0;31m \u001b[0mv\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mw\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mverschiebung\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcoordinates\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 126\u001b[0m \u001b[0mM\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mv\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 127\u001b[0m \u001b[0;32mreturn\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<ipython-input-17-0d6574174a68>\u001b[0m in \u001b[0;36mcoordinates\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 450\u001b[0m \u001b[0ma1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcoeff_of_rational_fctn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbasis\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0momega0\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mjth_component\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m)\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 451\u001b[0m \u001b[0melt\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mbasis\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmult\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0ma1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 452\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0melt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcoordinates\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0ma1\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mvector\u001b[0m\u001b[0;34m(\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[0mi\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mindex\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\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[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\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[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 453\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 454\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mj\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm\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<ipython-input-17-0d6574174a68>\u001b[0m in \u001b[0;36mcoordinates\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 450\u001b[0m \u001b[0ma1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcoeff_of_rational_fctn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbasis\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0momega0\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mjth_component\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m)\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 451\u001b[0m \u001b[0melt\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mbasis\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmult\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0ma1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 452\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0melt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcoordinates\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0ma1\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mvector\u001b[0m\u001b[0;34m(\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[0mi\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mindex\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\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[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\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[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 453\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 454\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mj\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm\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<ipython-input-17-0d6574174a68>\u001b[0m in \u001b[0;36mcoordinates\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 447\u001b[0m \u001b[0md\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdegree_of_rational_fctn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0momega_j\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 448\u001b[0m \u001b[0mindex\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdegrees_holo_inv\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mj\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--> 449\u001b[0;31m \u001b[0ma\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcoeff_of_rational_fctn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0momega_j\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\u001b[1;32m 450\u001b[0m \u001b[0ma1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcoeff_of_rational_fctn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbasis\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0momega0\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mjth_component\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m)\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 451\u001b[0m \u001b[0melt\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mbasis\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmult\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0ma1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||
"\u001b[0;32m<ipython-input-17-0d6574174a68>\u001b[0m in \u001b[0;36mcoeff_of_rational_fctn\u001b[0;34m(f, p)\u001b[0m\n\u001b[1;32m 502\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 503\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mcoeff_of_rational_fctn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf\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[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 504\u001b[0;31m \u001b[0mRx\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[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[0m\u001b[1;32m 505\u001b[0m \u001b[0mFx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mFractionField\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mRx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 506\u001b[0m \u001b[0mf\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mFx\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[0;32m/opt/sagemath-9.1/local/lib/python3.7/site-packages/sage/rings/polynomial/polynomial_ring_constructor.py\u001b[0m in \u001b[0;36mPolynomialRing\u001b[0;34m(base_ring, *args, **kwds)\u001b[0m\n\u001b[1;32m 631\u001b[0m \u001b[0;32mraise\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"you must specify the names of the variables\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 632\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 633\u001b[0;31m \u001b[0mnames\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnormalize_names\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnames\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 634\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 635\u001b[0m \u001b[0;31m# At this point, we have only handled the \"names\" keyword if it was\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||
"\u001b[0;32m/opt/sagemath-9.1/local/lib/python3.7/site-packages/sage/structure/category_object.pyx\u001b[0m in \u001b[0;36msage.structure.category_object.normalize_names (build/cythonized/sage/structure/category_object.c:8424)\u001b[0;34m()\u001b[0m\n\u001b[1;32m 922\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 923\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 924\u001b[0;31m \u001b[0mcpdef\u001b[0m \u001b[0mnormalize_names\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mPy_ssize_t\u001b[0m \u001b[0mngens\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnames\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 925\u001b[0m r\"\"\"\n\u001b[1;32m 926\u001b[0m \u001b[0mReturn\u001b[0m \u001b[0ma\u001b[0m \u001b[0mtuple\u001b[0m \u001b[0mof\u001b[0m \u001b[0mstrings\u001b[0m \u001b[0mof\u001b[0m \u001b[0mvariable\u001b[0m \u001b[0mnames\u001b[0m \u001b[0mof\u001b[0m \u001b[0mlength\u001b[0m \u001b[0mngens\u001b[0m \u001b[0mgiven\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||
"\u001b[0;32m/opt/sagemath-9.1/local/lib/python3.7/site-packages/sage/structure/category_object.pyx\u001b[0m in \u001b[0;36msage.structure.category_object.normalize_names (build/cythonized/sage/structure/category_object.c:7828)\u001b[0;34m()\u001b[0m\n\u001b[1;32m 1019\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnames\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mtuple\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlist\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[1;32m 1020\u001b[0m \u001b[0;31m# Convert names to strings and strip whitespace\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1021\u001b[0;31m \u001b[0mnames\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstrip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mnames\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 1022\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 1023\u001b[0m \u001b[0;31m# Interpret names as string and convert to tuple of strings\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||
"\u001b[0;32msrc/cysignals/signals.pyx\u001b[0m in \u001b[0;36mcysignals.signals.python_check_interrupt\u001b[0;34m()\u001b[0m\n",
|
||||
"\u001b[0;31mKeyboardInterrupt\u001b[0m: "
|
||||
]
|
||||
}
|
||||
],
|
||||
|
|
@ -681,7 +711,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 56,
|
||||
"execution_count": 34,
|
||||
"metadata": {
|
||||
"scrolled": true
|
||||
},
|
||||
|
|
@ -690,53 +720,69 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"[0 0 0 0 0 0 0 0]\n",
|
||||
"[0 0 0 0 0 0 0 0]\n",
|
||||
"[0 0 0 0 0 0 0 0]\n",
|
||||
"[0 0 0 0 0 0 0 0]\n",
|
||||
"[0 0 0 0 0 0 0 0]\n",
|
||||
"[0 0 0 0 0 0 0 0]\n",
|
||||
"[0 0 0 0 0 0 0 0]\n",
|
||||
"[0 0 0 0 0 0 0 0]\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"Rx.<x> = PolynomialRing(GF(5))\n",
|
||||
"C = superelliptic(x^9+3*x^3+x^2+x+1, 2, 5)\n",
|
||||
"F = C.frobenius_matrix()\n",
|
||||
"V = C.verschiebung_matrix()\n",
|
||||
"print(V*F)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 58,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"test [0, -1, -1, -1, 4, -1, -1, -1, 4]\n"
|
||||
"type w <class '__main__.superelliptic_form'>\n",
|
||||
"type self <class '__main__.superelliptic_form'>\n",
|
||||
"type self <class '__main__.superelliptic_form'>\n",
|
||||
"type self <class '__main__.superelliptic_form'>\n",
|
||||
"type w <class '__main__.superelliptic_form'>\n",
|
||||
"type self <class '__main__.superelliptic_form'>\n",
|
||||
"type self <class '__main__.superelliptic_form'>\n",
|
||||
"type self <class '__main__.superelliptic_form'>\n",
|
||||
"type w <class '__main__.superelliptic_form'>\n",
|
||||
"type self <class '__main__.superelliptic_form'>\n",
|
||||
"type self <class '__main__.superelliptic_form'>\n",
|
||||
"type self <class '__main__.superelliptic_form'>\n",
|
||||
"type w <class '__main__.superelliptic_form'>\n",
|
||||
"type self <class '__main__.superelliptic_form'>\n",
|
||||
"type self <class '__main__.superelliptic_form'>\n",
|
||||
"type self <class '__main__.superelliptic_form'>\n",
|
||||
"type self <class '__main__.superelliptic_form'>\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"'error'"
|
||||
"[2 2 0 0]\n",
|
||||
"[3 0 0 1]\n",
|
||||
"[3 0 1 0]\n",
|
||||
"[2 4 2 0]"
|
||||
]
|
||||
},
|
||||
"execution_count": 58,
|
||||
"execution_count": 34,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"p = 5\n",
|
||||
"flag(F, V, p)"
|
||||
"Rx.<x> = PolynomialRing(GF(5))\n",
|
||||
"C = superelliptic(x^9+3*x^3+x^2+x+1, 2, 5)\n",
|
||||
"C.cartier_matrix()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 26,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"ename": "AttributeError",
|
||||
"evalue": "'sage.rings.fraction_field_element.FractionFieldElement' object has no attribute 'jth_component'",
|
||||
"output_type": "error",
|
||||
"traceback": [
|
||||
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
|
||||
"\u001b[0;31mAttributeError\u001b[0m Traceback (most recent call last)",
|
||||
"\u001b[0;32m<ipython-input-26-59595845bc9b>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mC\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcartier_matrix\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<ipython-input-17-0d6574174a68>\u001b[0m in \u001b[0;36mcartier_matrix\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 146\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\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[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbasis\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[1;32m 147\u001b[0m \u001b[0mw\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbasis\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 148\u001b[0;31m \u001b[0mv\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mw\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcartier\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcoordinates\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 149\u001b[0m \u001b[0mM\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mv\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 150\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mM\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||
"\u001b[0;32m<ipython-input-24-b26f83164022>\u001b[0m in \u001b[0;36mcoordinates\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 335\u001b[0m \u001b[0mindex\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdegrees_holo_inv\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mj\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 336\u001b[0m \u001b[0ma\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcoeff_of_rational_fctn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0momega_j\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[0;32m--> 337\u001b[0;31m \u001b[0ma1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcoeff_of_rational_fctn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbasis\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mform\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mjth_component\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m)\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\u001b[1;32m 338\u001b[0m \u001b[0melt\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mbasis\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmult\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0ma1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 339\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0melt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcoordinates\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0ma1\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mvector\u001b[0m\u001b[0;34m(\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[0mi\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mindex\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\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[0mg\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/opt/sagemath-9.1/local/lib/python3.7/site-packages/sage/structure/element.pyx\u001b[0m in \u001b[0;36msage.structure.element.Element.__getattr__ (build/cythonized/sage/structure/element.c:4614)\u001b[0;34m()\u001b[0m\n\u001b[1;32m 485\u001b[0m \u001b[0mAttributeError\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;34m'LeftZeroSemigroup_with_category.element_class'\u001b[0m \u001b[0mobject\u001b[0m \u001b[0mhas\u001b[0m \u001b[0mno\u001b[0m \u001b[0mattribute\u001b[0m \u001b[0;34m'blah_blah'\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 486\u001b[0m \"\"\"\n\u001b[0;32m--> 487\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 488\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 489\u001b[0m \u001b[0mcdef\u001b[0m \u001b[0mgetattr_from_category\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\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[0;34m\u001b[0m\u001b[0m\n",
|
||||
"\u001b[0;32m/opt/sagemath-9.1/local/lib/python3.7/site-packages/sage/structure/element.pyx\u001b[0m in \u001b[0;36msage.structure.element.Element.getattr_from_category (build/cythonized/sage/structure/element.c:4723)\u001b[0;34m()\u001b[0m\n\u001b[1;32m 498\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 499\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--> 500\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 501\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 502\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m__dir__\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/opt/sagemath-9.1/local/lib/python3.7/site-packages/sage/cpython/getattr.pyx\u001b[0m in \u001b[0;36msage.cpython.getattr.getattr_from_other_class (build/cythonized/sage/cpython/getattr.c:2614)\u001b[0;34m()\u001b[0m\n\u001b[1;32m 392\u001b[0m \u001b[0mdummy_error_message\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcls\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtype\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[0m\n\u001b[1;32m 393\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--> 394\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 395\u001b[0m \u001b[0mattribute\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m<\u001b[0m\u001b[0mobject\u001b[0m\u001b[0;34m>\u001b[0m\u001b[0mattr\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 396\u001b[0m \u001b[0;31m# Check for a descriptor (__get__ in Python)\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.fraction_field_element.FractionFieldElement' object has no attribute 'jth_component'"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": []
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 59,
|
||||
|
|
|
|||
Loading…
Reference in New Issue