diff --git a/superelliptic.ipynb b/superelliptic.ipynb index f252872..8c0d83e 100644 --- a/superelliptic.ipynb +++ b/superelliptic.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 54, + "execution_count": 35, "metadata": {}, "outputs": [], "source": [ @@ -52,7 +52,7 @@ " degrees1 = {}\n", " for j in range(1, m):\n", " for i in range(1, r):\n", - " if (r*(m-j) - m*i >= delta): ####tu jest blad\n", + " if (r*(m-j) - m*i >= delta): \n", " s = Rx(m-j)*Rx(x)*Rx(f.derivative()) - Rx(m)*Rx(i)*f\n", " psi = Rx(cut(s, i))\n", " basis += [(Fxy(psi/y^j), Fxy(m*y^(m-j)/x^i))]\n", @@ -145,7 +145,18 @@ " v = w.frobenius().coordinates()\n", " M[i, :] = v\n", " return M\n", - " \n", + "\n", + " def cartier_matrix(self):\n", + " basis = self.basis_holomorphic_differentials\n", + " g = self.genus()\n", + " p = self.characteristic\n", + " M = matrix(GF(p), g, g)\n", + " for i in range(0, len(basis)):\n", + " w = basis[i]\n", + " v = w.cartier().coordinates()\n", + " M[i, :] = v\n", + " return M \n", + " \n", "def reduction(C, g):\n", " p = C.characteristic\n", " Rxy. = PolynomialRing(GF(p), 2)\n", @@ -290,6 +301,11 @@ " if len(str(g)) == 1:\n", " return str(g) + ' dx'\n", " return '('+str(g) + ') dx'\n", + "\n", + " def mult(self, constant):\n", + " C = self.curve\n", + " omega = self.form\n", + " return superelliptic_form(C, constant*omega) \n", " \n", " def cartier(self):\n", " C = self.curve\n", @@ -310,7 +326,31 @@ " j1 = (p^(mult_order-1)*j)%m\n", " B = floor(p^(mult_order-1)*j/m)\n", " result += superelliptic_form(C, polynomial_part(p, h)/(f^B*y^(j1)))\n", - " return result\n", + " return result \n", + " \n", + " def coordinates(self):\n", + " C = self.curve\n", + " p = C.characteristic\n", + " m = C.exponent\n", + " Rx. = PolynomialRing(GF(p))\n", + " Fx = FractionField(Rx)\n", + " FxRy. = PolynomialRing(Fx)\n", + " g = C.genus()\n", + " degrees_holo = C.degree_holo\n", + " degrees_holo_inv = {b:a for a, b in degrees_holo.items()}\n", + " basis = C.basis_holomorphic_differentials\n", + " \n", + " for j in range(1, m):\n", + " omega_j = Fx(self.jth_component(j))\n", + " if omega_j != Fx(0):\n", + " d = degree_of_rational_fctn(omega_j, p)\n", + " index = degrees_holo_inv[(d, j)]\n", + " a = coeff_of_rational_fctn(omega_j, p)\n", + " a1 = coeff_of_rational_fctn(basis[index].jth_component(j), p)\n", + " elt = self - basis[index].mult(a/a1)\n", + " return elt.coordinates() + a/a1*vector([GF(p)(i == index) for i in range(0, g)])\n", + " \n", + " return vector(g*[0])\n", " \n", " def jth_component(self, j):\n", " g = self.form\n", @@ -511,7 +551,7 @@ }, { "cell_type": "code", - "execution_count": 55, + "execution_count": 31, "metadata": {}, "outputs": [], "source": [ @@ -569,7 +609,9 @@ " final_type[0] = 0\n", " for i in range(1, dim+1):\n", " if final_type[i] == -1:\n", - " final_type[i] = final_type[i-1] + 1\n", + " final_type[i] = min(final_type[i-1] + 1, dim/2)\n", + " \n", + " print('poprawiony ft', final_type)\n", " \n", " if is_final(final_type, dim/2):\n", " return final_type[1:dim/2 + 1]\n", @@ -584,14 +626,14 @@ " return 0\n", " \n", " for i in range(1, n):\n", - " if final_type[i] != final_type[i - 1] or final_type[i] != final_type[i - 1] + 1:\n", + " if final_type[i] != final_type[i - 1] and final_type[i] != final_type[i - 1] + 1:\n", " return 0\n", " return 1" ] }, { "cell_type": "code", - "execution_count": 60, + "execution_count": 18, "metadata": {}, "outputs": [ { @@ -600,49 +642,37 @@ "text": [ "0 3\n", "test [0, -1, -1, -1, 4, -1, -1, -1, 4]\n", - "0 3 4 error\n", + "poprawiony ft [0, 1, 2, 3, 4, 4, 4, 4, 4]\n", + "0 3 4 [1, 2, 3, 4]\n", "0 4\n", "test [0, -1, -1, -1, 4, -1, -1, -1, 4]\n", - "0 4 4 error\n", + "poprawiony ft [0, 1, 2, 3, 4, 4, 4, 4, 4]\n", + "0 4 4 [1, 2, 3, 4]\n", "1 1\n", "test [0, -1, -1, -1, 4, -1, -1, -1, 4]\n", - "1 1 4 error\n", - "1 2\n", - "test [0, -1, -1, -1, 4, -1, -1, -1, 4]\n", - "1 2 4 error\n", - "1 3\n", - "test [0, -1, -1, -1, 4, -1, -1, -1, 4]\n", - "1 3 4 error\n", - "2 0\n", - "test [0, -1, -1, -1, 4, -1, -1, -1, 4]\n", - "2 0 4 error\n", - "2 2\n", - "test [0, -1, -1, -1, 4, -1, -1, -1, 4]\n", - "2 2 4 error\n", - "2 3\n", - "test [0, -1, -1, -1, 4, -1, -1, -1, 4]\n", - "2 3 4 error\n", - "3 0\n", - "test [0, -1, -1, -1, 4, -1, -1, -1, 4]\n", - "3 0 4 error\n", - "3 1\n", - "test [0, -1, -1, -1, 4, -1, -1, -1, 4]\n", - "3 1 4 error\n", - "3 2\n", - "test [0, -1, -1, -1, 4, -1, -1, -1, 4]\n", - "3 2 4 error\n", - "3 4\n", - "test [0, -1, -1, -1, 4, -1, -1, -1, 4]\n", - "3 4 4 error\n", - "4 1\n", - "test [0, -1, -1, -1, 4, -1, -1, -1, 4]\n", - "4 1 4 error\n", - "4 3\n", - "test [0, 1, 1, 2, 3, 3, 3, 4, 4]\n", - "4 3 4 error\n", - "4 4\n", - "test [0, -1, -1, 3, 3, 4, -1, -1, 4]\n", - "4 4 4 error\n" + "poprawiony ft [0, 1, 2, 3, 4, 4, 4, 4, 4]\n", + "1 1 4 [1, 2, 3, 4]\n", + "1 2\n" + ] + }, + { + "ename": "KeyboardInterrupt", + "evalue": "", + "output_type": "error", + "traceback": [ + 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"\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 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"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. = 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 \n", + "type self \n", + "type self \n", + "type self \n", + "type w \n", + "type self \n", + "type self \n", + "type self \n", + "type w \n", + "type self \n", + "type self \n", + "type self \n", + "type w \n", + "type self \n", + "type self \n", + "type self \n", + "type self \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. = 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\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m 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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,