From 891996e1af6ce4a7a7178b9cd467ac615da95e02 Mon Sep 17 00:00:00 2001 From: jgarnek Date: Mon, 23 Aug 2021 15:14:55 +0200 Subject: [PATCH] macierz froba chyba dziala --- superelliptic.ipynb | 552 +++++++++++++++++++++++++++++++++++--------- 1 file changed, 442 insertions(+), 110 deletions(-) diff --git a/superelliptic.ipynb b/superelliptic.ipynb index cf5fcb9..6aa15df 100644 --- a/superelliptic.ipynb +++ b/superelliptic.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 118, + "execution_count": 132, "metadata": {}, "outputs": [], "source": [ @@ -77,7 +77,7 @@ " psi = Rx(cut(s, i))\n", " basis[t] = superelliptic_cech(self, superelliptic_form(self, Fxy(psi/y^j)), superelliptic_function(self, Fxy(m*y^(m-j)/x^i)))\n", " degrees0[t] = (psi.degree(), j)\n", - " degrees1[t] = (-i, j)\n", + " degrees1[t] = (-i, m-j)\n", " t += 1\n", " return basis, degrees0, degrees1\n", " \n", @@ -395,29 +395,23 @@ " return elt.coordinates() + a/a1*vector([GF(p)(i == index) for i in range(0, 2*g)])\n", " \n", " for j in range(1, m):\n", - " print('c2')\n", " fct_j = Fx(fct.jth_component(j))\n", " if (fct_j != Rx(0)):\n", " d = degree_of_rational_fctn(fct_j)\n", " \n", " if (d, j) in degrees1.values():\n", - " print('c2a')\n", " index = degrees1_inv[(d, j)]\n", " a = coeff_of_rational_fctn(fct_j)\n", - " a1 = coeff_of_rational_fctn(basis[index].f.jth_component(j))\n", - " print(a, a1, index, basis[index].is_cocycle())\n", - " elt = self - basis[index].mult(a/a1)\n", - " return elt.coordinates() + a/a1*vector([GF(p)(i == index) for i in range(0, 2*g)])\n", + " elt = self - basis[index].mult(a/m)\n", + " return elt.coordinates() + a/m*vector([GF(p)(i == index) for i in range(0, 2*g)])\n", " \n", " if d<0:\n", - " print('c2b')\n", " a = coeff_of_rational_fctn(fct_j)\n", " h = superelliptic_function(C, FxRy(a*y^j*x^d))\n", " elt = superelliptic_cech(C, self.omega0, self.f - h)\n", " return elt.coordinates()\n", " \n", " if (fct_j != Rx(0)):\n", - " print('c2c')\n", " G = superelliptic_function(C, y^j*x^d)\n", " a = coeff_of_rational_fctn(fct_j)\n", " elt =self - superelliptic_cech(C, diffn(G), G).mult(a)\n", @@ -450,7 +444,6 @@ " return(d1 - d2)\n", "\n", "def coeff_of_rational_fctn(f):\n", - " print('coeff', f)\n", " Rx. = PolynomialRing(GF(p))\n", " Fx = FractionField(Rx)\n", " f = Fx(f)\n", @@ -488,7 +481,7 @@ }, { "cell_type": "code", - "execution_count": 119, + "execution_count": 133, "metadata": {}, "outputs": [], "source": [ @@ -500,80 +493,7 @@ }, { "cell_type": "code", - "execution_count": 120, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "((x/y) dx, 2/x*y^6, ((x - 1)/(x^2*y)) dx) 1\n", - "(((-1)/y) dx, 2/x^2*y^6, ((-2*x - 2)/(x^3*y)) dx) 1\n", - "(((-2*x)/y^2) dx, 2/x*y^5, ((2*x - 1)/(x^2*y^2)) dx) 1\n", - "((1/y^2) dx, 2/x^2*y^5, ((-x - 2)/(x^3*y^2)) dx) 1\n", - "((1/y^3) dx, 0, (1/y^3) dx) 1\n", - "(0 dx, 2/x*y^4, ((-2*x - 1)/(x^2*y^3)) dx) 1\n", - "((1/y^4) dx, 0, (1/y^4) dx) 1\n", - "((2*x/y^4) dx, 2/x*y^3, ((-x - 1)/(x^2*y^4)) dx) 1\n", - "((1/y^5) dx, 0, (1/y^5) dx) 1\n", - "((x/y^5) dx, 0, (x/y^5) dx) 1\n", - "((1/y^6) dx, 0, (1/y^6) dx) 1\n", - "((x/y^6) dx, 0, (x/y^6) dx) 1\n" - ] - } - ], - "source": [ - "for w in baza.values():\n", - " print(w, w.is_cocycle())" - ] - }, - { - "cell_type": "code", - "execution_count": 75, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "({0: ((x/y) dx, 2/x*y, ((x^3*y^5 - x^3 + x - 1)/(x^2*y^6)) dx),\n", - " 1: (((-1)/y) dx, 2/x^2*y, ((-x^3*y^5 + x^3 - 2*x - 2)/(x^3*y^6)) dx),\n", - " 2: (((-2*x)/y^2) dx, 2/x*y^2, ((-2*x^3*y^3 + x^3 - 1)/(x^2*y^5)) dx),\n", - " 3: ((1/y^2) dx, 2/x^2*y^2, ((x^3*y^3 - 2*x^3 + 2*x - 2)/(x^3*y^5)) dx),\n", - " 4: ((1/y^3) dx, 0, (1/y^3) dx),\n", - " 5: (0 dx, 2/x*y^3, ((-2*x^3 - x - 1)/(x^2*y^4)) dx),\n", - " 6: ((1/y^4) dx, 0, (1/y^4) dx),\n", - " 7: ((2*x/y^4) dx, 2/x*y^4, ((2*x^3 - 2*x*y - y)/(x^2*y^4)) dx),\n", - " 8: ((1/y^5) dx, 0, (1/y^5) dx),\n", - " 9: ((x/y^5) dx, 0, (x/y^5) dx),\n", - " 10: ((1/y^6) dx, 0, (1/y^6) dx),\n", - " 11: ((x/y^6) dx, 0, (x/y^6) dx)},\n", - " {0: (1, 1),\n", - " 1: (0, 1),\n", - " 2: (1, 2),\n", - " 3: (0, 2),\n", - " 4: (0, 3),\n", - " 5: (-1, 3),\n", - " 6: (0, 4),\n", - " 7: (1, 4),\n", - " 8: (0, 5),\n", - " 9: (1, 5),\n", - " 10: (0, 6),\n", - " 11: (1, 6)},\n", - " {0: (-1, 1), 1: (-2, 1), 2: (-1, 2), 3: (-2, 2), 5: (-1, 3), 7: (-1, 4)})" - ] - }, - "execution_count": 75, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "C.degree_and_basis_de_rham()" - ] - }, - { - "cell_type": "code", - "execution_count": 121, + "execution_count": 134, "metadata": { "scrolled": false }, @@ -621,35 +541,447 @@ "((x/y^5) dx, ((3*x^4 + 3*x^2 + 4*x + 2)/x^5)*y^2, 0 dx) 1\n", "c2\n", "c2\n", - "c2a\n", + "c2b\n", "coeff (3*x^4 + 3*x^2 + 4*x + 2)/x^5\n", - "coeff 0\n", - "3 0 2 1\n" + "((x/y^5) dx, ((3*x^2 + 4*x + 2)/x^5)*y^2, ((x^3 - 1)/(x^2*y^5)) dx) 1\n", + "c2\n", + "c2\n", + "c2b\n", + "coeff (3*x^2 + 4*x + 2)/x^5\n", + "((x/y^5) dx, ((4*x + 2)/x^5)*y^2, ((x^5 - x^2 - x + 2)/(x^4*y^5)) dx) 1\n", + "c2\n", + "c2\n", + "c2b\n", + "coeff (4*x + 2)/x^5\n", + "((x/y^5) dx, 2/x^5*y^2, ((x^6 - x^2 - 2)/(x^5*y^5)) dx) 1\n", + "c2\n", + "c2\n", + "c2b\n", + "coeff 2/x^5\n", + "((x/y^5) dx, 0, (x/y^5) dx) 1\n", + "c1\n", + "baza ((x/y^5) dx, 0, (x/y^5) dx)\n", + "coeff x\n", + "coeff x\n", + "(0 dx, 0, 0 dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "w (((-1)/y) dx, 2/x^2*y^6, ((-2*x - 2)/(x^3*y)) dx)\n", + "(0 dx, ((2*x^12 + 3*x^10 + x^9 + 2*x^8 + 3*x^7 + x^6 + 3*x^5 + 3*x^4 + 3*x^2 + 4*x + 2)/x^10)*y^2, 0 dx) 1\n", + "c2\n", + "c2\n", + "c2c\n", + "coeff (2*x^12 + 3*x^10 + x^9 + 2*x^8 + 3*x^7 + x^6 + 3*x^5 + 3*x^4 + 3*x^2 + 4*x + 2)/x^10\n", + "(((-x^2 + 2*x)/y^5) dx, ((3*x^10 + x^9 + 2*x^8 + 3*x^7 + x^6 + 3*x^5 + 3*x^4 + 3*x^2 + 4*x + 2)/x^10)*y^2, 0 dx) 1\n", + "c2\n", + "c2\n", + "c2c\n", + "coeff (3*x^10 + x^9 + 2*x^8 + 3*x^7 + x^6 + 3*x^5 + 3*x^4 + 3*x^2 + 4*x + 2)/x^10\n", + "(((2*x + 2)/y^5) dx, ((x^9 + 2*x^8 + 3*x^7 + x^6 + 3*x^5 + 3*x^4 + 3*x^2 + 4*x + 2)/x^10)*y^2, 0 dx) 1\n", + "c2\n", + "c2\n", + "c2b\n", + "coeff (x^9 + 2*x^8 + 3*x^7 + x^6 + 3*x^5 + 3*x^4 + 3*x^2 + 4*x + 2)/x^10\n", + "(((2*x + 2)/y^5) dx, ((2*x^8 + 3*x^7 + x^6 + 3*x^5 + 3*x^4 + 3*x^2 + 4*x + 2)/x^10)*y^2, ((2*x^3 - 2)/(x^2*y^5)) dx) 1\n", + "c2\n", + "c2\n", + "c2b\n", + "coeff (2*x^8 + 3*x^7 + x^6 + 3*x^5 + 3*x^4 + 3*x^2 + 4*x + 2)/x^10\n", + "(((2*x + 2)/y^5) dx, ((3*x^7 + x^6 + 3*x^5 + 3*x^4 + 3*x^2 + 4*x + 2)/x^10)*y^2, ((2*x^4 + 2*x^3 + x + 2)/(x^3*y^5)) dx) 1\n", + "c2\n", + "c2\n", + "c2b\n", + "coeff (3*x^7 + x^6 + 3*x^5 + 3*x^4 + 3*x^2 + 4*x + 2)/x^10\n", + "(((2*x + 2)/y^5) dx, ((x^6 + 3*x^5 + 3*x^4 + 3*x^2 + 4*x + 2)/x^10)*y^2, ((2*x^5 + 2*x^4 + x^2 + x + 2)/(x^4*y^5)) dx) 1\n", + "c2\n", + "c2\n", + "c2b\n", + "coeff (x^6 + 3*x^5 + 3*x^4 + 3*x^2 + 4*x + 2)/x^10\n", + "(((2*x + 2)/y^5) dx, ((3*x^5 + 3*x^4 + 3*x^2 + 4*x + 2)/x^10)*y^2, ((2*x^6 + 2*x^5 + x^2 - x + 2)/(x^5*y^5)) dx) 1\n", + "c2\n", + "c2\n", + "c2b\n", + "coeff (3*x^5 + 3*x^4 + 3*x^2 + 4*x + 2)/x^10\n", + "(((2*x + 2)/y^5) dx, ((3*x^4 + 3*x^2 + 4*x + 2)/x^10)*y^2, ((2*x^5 + 2*x^4 - 1)/(x^4*y^5)) dx) 1\n", + "c2\n", + "c2\n", + "c2b\n", + "coeff (3*x^4 + 3*x^2 + 4*x + 2)/x^10\n", + "(((2*x + 2)/y^5) dx, ((3*x^2 + 4*x + 2)/x^10)*y^2, ((2*x^8 + 2*x^7 - 1)/(x^7*y^5)) dx) 1\n", + "c2\n", + "c2\n", + "c2b\n", + "coeff (3*x^2 + 4*x + 2)/x^10\n", + "(((2*x + 2)/y^5) dx, ((4*x + 2)/x^10)*y^2, ((2*x^10 + 2*x^9 - x^2 - x + 2)/(x^9*y^5)) dx) 1\n", + "c2\n", + "c2\n", + "c2b\n", + "coeff (4*x + 2)/x^10\n", + "(((2*x + 2)/y^5) dx, 2/x^10*y^2, ((2*x^11 + 2*x^10 - x^2 - 2)/(x^10*y^5)) dx) 1\n", + "c2\n", + "c2\n", + "c2b\n", + "coeff 2/x^10\n", + "(((2*x + 2)/y^5) dx, 0, ((2*x + 2)/y^5) dx) 1\n", + "c1\n", + "baza ((x/y^5) dx, 0, (x/y^5) dx)\n", + "coeff 2*x + 2\n", + "coeff x\n", + "((2/y^5) dx, 0, (2/y^5) dx) 1\n", + "c1\n", + "baza ((1/y^5) dx, 0, (1/y^5) dx)\n", + "coeff 2\n", + "coeff 1\n", + "(0 dx, 0, 0 dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "w (((-2*x)/y^2) dx, 2/x*y^5, ((2*x - 1)/(x^2*y^2)) dx)\n", + "(0 dx, ((2*x^9 + x^7 + 2*x^6 + x^5 + 4*x^4 + x^3 + 2*x^2 + 4*x + 1)/x^5)*y^4, 0 dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2c\n", + "coeff (2*x^9 + x^7 + 2*x^6 + x^5 + 4*x^4 + x^3 + 2*x^2 + 4*x + 1)/x^5\n", + "(((-2*x^4 - x^3)/y^3) dx, ((x^7 + 2*x^6 + x^5 + 4*x^4 + x^3 + 2*x^2 + 4*x + 1)/x^5)*y^4, 0 dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2c\n", + "coeff (x^7 + 2*x^6 + x^5 + 4*x^4 + x^3 + 2*x^2 + 4*x + 1)/x^5\n", + "(((-x^3 + x^2 + x)/y^3) dx, ((2*x^6 + x^5 + 4*x^4 + x^3 + 2*x^2 + 4*x + 1)/x^5)*y^4, 0 dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2c\n", + "coeff (2*x^6 + x^5 + 4*x^4 + x^3 + 2*x^2 + 4*x + 1)/x^5\n", + "(((x^2 + 1)/y^3) dx, ((x^5 + 4*x^4 + x^3 + 2*x^2 + 4*x + 1)/x^5)*y^4, 0 dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2c\n", + "coeff (x^5 + 4*x^4 + x^3 + 2*x^2 + 4*x + 1)/x^5\n", + "(((-1)/y^3) dx, ((4*x^4 + x^3 + 2*x^2 + 4*x + 1)/x^5)*y^4, 0 dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2a\n", + "coeff (4*x^4 + x^3 + 2*x^2 + 4*x + 1)/x^5\n", + "2 5 (0 dx, 2/x*y^4, ((-2*x - 1)/(x^2*y^3)) dx)\n", + "przed d -1 j 4 (((-1)/y^3) dx, ((4*x^4 + x^3 + 2*x^2 + 4*x + 1)/x^5)*y^4, 0 dx) (0 dx, 4/x*y^4, ((x - 2)/(x^2*y^3)) dx)\n", + "po (((-1)/y^3) dx, ((x^3 + 2*x^2 + 4*x + 1)/x^5)*y^4, ((-x + 2)/(x^2*y^3)) dx)\n", + "(((-1)/y^3) dx, ((x^3 + 2*x^2 + 4*x + 1)/x^5)*y^4, ((-x + 2)/(x^2*y^3)) dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2b\n", + "coeff (x^3 + 2*x^2 + 4*x + 1)/x^5\n", + "(((-1)/y^3) dx, ((2*x^2 + 4*x + 1)/x^5)*y^4, ((-x^3 - x^2 + 2*x + 1)/(x^3*y^3)) dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2b\n", + "coeff (2*x^2 + 4*x + 1)/x^5\n", + "(((-1)/y^3) dx, ((4*x + 1)/x^5)*y^4, ((-x^4 + 2*x^2 - x - 2)/(x^4*y^3)) dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2b\n", + "coeff (4*x + 1)/x^5\n", + "(((-1)/y^3) dx, 1/x^5*y^4, ((-x^5 - x^2 - 2)/(x^5*y^3)) dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2b\n", + "coeff 1/x^5\n", + "(((-1)/y^3) dx, 0, ((-1)/y^3) dx) 1\n", + "c1\n", + "baza ((1/y^3) dx, 0, (1/y^3) dx)\n", + "coeff 4\n", + "coeff 1\n", + "(0 dx, 0, 0 dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "w ((1/y^2) dx, 2/x^2*y^5, ((-x - 2)/(x^3*y^2)) dx)\n", + "(0 dx, ((2*x^9 + x^7 + 2*x^6 + x^5 + 4*x^4 + x^3 + 2*x^2 + 4*x + 1)/x^10)*y^4, 0 dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2a\n", + "coeff (2*x^9 + x^7 + 2*x^6 + x^5 + 4*x^4 + x^3 + 2*x^2 + 4*x + 1)/x^10\n", + "1 5 (0 dx, 2/x*y^4, ((-2*x - 1)/(x^2*y^3)) dx)\n", + "przed d -1 j 4 (0 dx, ((2*x^9 + x^7 + 2*x^6 + x^5 + 4*x^4 + x^3 + 2*x^2 + 4*x + 1)/x^10)*y^4, 0 dx) (0 dx, 2/x*y^4, ((-2*x - 1)/(x^2*y^3)) dx)\n", + "po (0 dx, ((x^7 + 2*x^6 + x^5 + 4*x^4 + x^3 + 2*x^2 + 4*x + 1)/x^10)*y^4, ((2*x + 1)/(x^2*y^3)) dx)\n", + "(0 dx, ((x^7 + 2*x^6 + x^5 + 4*x^4 + x^3 + 2*x^2 + 4*x + 1)/x^10)*y^4, ((2*x + 1)/(x^2*y^3)) dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2b\n", + "coeff (x^7 + 2*x^6 + x^5 + 4*x^4 + x^3 + 2*x^2 + 4*x + 1)/x^10\n", + "(0 dx, ((2*x^6 + x^5 + 4*x^4 + x^3 + 2*x^2 + 4*x + 1)/x^10)*y^4, ((x^2 - x - 1)/(x^4*y^3)) dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2b\n", + "coeff (2*x^6 + x^5 + 4*x^4 + x^3 + 2*x^2 + 4*x + 1)/x^10\n", + "(0 dx, ((x^5 + 4*x^4 + x^3 + 2*x^2 + 4*x + 1)/x^10)*y^4, ((-x^2 - 1)/(x^5*y^3)) dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2b\n", + "coeff (x^5 + 4*x^4 + x^3 + 2*x^2 + 4*x + 1)/x^10\n", + "(0 dx, ((4*x^4 + x^3 + 2*x^2 + 4*x + 1)/x^10)*y^4, (1/(x^5*y^3)) dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2b\n", + "coeff (4*x^4 + x^3 + 2*x^2 + 4*x + 1)/x^10\n", + "(0 dx, ((x^3 + 2*x^2 + 4*x + 1)/x^10)*y^4, ((x^2 - x + 2)/(x^7*y^3)) dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2b\n", + "coeff (x^3 + 2*x^2 + 4*x + 1)/x^10\n", + "(0 dx, ((2*x^2 + 4*x + 1)/x^10)*y^4, ((-x^2 + 2*x + 1)/(x^8*y^3)) dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2b\n", + "coeff (2*x^2 + 4*x + 1)/x^10\n", + "(0 dx, ((4*x + 1)/x^10)*y^4, ((2*x^2 - x - 2)/(x^9*y^3)) dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2b\n", + "coeff (4*x + 1)/x^10\n", + "(0 dx, 1/x^10*y^4, ((-x^2 - 2)/(x^10*y^3)) dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2b\n", + "coeff 1/x^10\n", + "(0 dx, 0, 0 dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "w ((1/y^3) dx, 0, (1/y^3) dx)\n", + "(0 dx, 0, 0 dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "w (0 dx, 2/x*y^4, ((-2*x - 1)/(x^2*y^3)) dx)\n", + "(0 dx, ((2*x^6 + 4*x^4 + 3*x^3 + 2*x^2 + 3*x + 3)/x^5)*y^6, 0 dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2c\n", + "coeff (2*x^6 + 4*x^4 + 3*x^3 + 2*x^2 + 3*x + 3)/x^5\n", + "(((2*x + 1)/y) dx, ((4*x^4 + 3*x^3 + 2*x^2 + 3*x + 3)/x^5)*y^6, 0 dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2a\n", + "coeff (4*x^4 + 3*x^3 + 2*x^2 + 3*x + 3)/x^5\n", + "2 0 ((x/y) dx, 2/x*y^6, ((x - 1)/(x^2*y)) dx)\n", + "przed d -1 j 6 (((2*x + 1)/y) dx, ((4*x^4 + 3*x^3 + 2*x^2 + 3*x + 3)/x^5)*y^6, 0 dx) ((2*x/y) dx, 4/x*y^6, ((2*x - 2)/(x^2*y)) dx)\n", + "po ((1/y) dx, ((3*x^3 + 2*x^2 + 3*x + 3)/x^5)*y^6, ((-2*x + 2)/(x^2*y)) dx)\n", + "((1/y) dx, ((3*x^3 + 2*x^2 + 3*x + 3)/x^5)*y^6, ((-2*x + 2)/(x^2*y)) dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2a\n", + "coeff (3*x^3 + 2*x^2 + 3*x + 3)/x^5\n", + "4 1 (((-1)/y) dx, 2/x^2*y^6, ((-2*x - 2)/(x^3*y)) dx)\n", + "przed d -2 j 6 ((1/y) dx, ((3*x^3 + 2*x^2 + 3*x + 3)/x^5)*y^6, ((-2*x + 2)/(x^2*y)) dx) ((1/y) dx, 3/x^2*y^6, ((2*x + 2)/(x^3*y)) dx)\n", + "po (0 dx, ((2*x^2 + 3*x + 3)/x^5)*y^6, ((-2*x^2 - 2)/(x^3*y)) dx)\n", + "(0 dx, ((2*x^2 + 3*x + 3)/x^5)*y^6, ((-2*x^2 - 2)/(x^3*y)) dx) 1\n" ] }, { - "ename": "ZeroDivisionError", - "evalue": "inverse of Mod(0, 5) does not exist", - "output_type": "error", - "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mZeroDivisionError\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 \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[0m", - "\u001b[0;32m\u001b[0m in \u001b[0;36mfrobenius_matrix\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 103\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mw\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mbasis\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\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 104\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'w'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mw\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 105\u001b[0;31m \u001b[0mv\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mw\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfrobenius\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 106\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 107\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/opt/sagemath-9.1/local/lib/python3.7/site-packages/sage/rings/finite_rings/integer_mod.pyx\u001b[0m in \u001b[0;36msage.rings.finite_rings.integer_mod.IntegerMod_int._div_ (build/cythonized/sage/rings/finite_rings/integer_mod.c:27689)\u001b[0;34m()\u001b[0m\n\u001b[1;32m 2540\u001b[0m \u001b[0mright_inverse\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__modulus\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minverses\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m<\u001b[0m\u001b[0mIntegerMod_int\u001b[0m\u001b[0;34m>\u001b[0m\u001b[0mright\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mivalue\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2541\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mright_inverse\u001b[0m \u001b[0;32mis\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[0;32m-> 2542\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mZeroDivisionError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mf\"inverse of Mod({right}, {self.__modulus.sageInteger}) does not exist\"\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 2543\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 2544\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_new_c\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mivalue\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;34m<\u001b[0m\u001b[0mIntegerMod_int\u001b[0m\u001b[0;34m>\u001b[0m\u001b[0mright_inverse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mivalue\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__modulus\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mint32\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;31mZeroDivisionError\u001b[0m: inverse of Mod(0, 5) does not exist" + "name": "stdout", + "output_type": "stream", + "text": [ + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2b\n", + "coeff (2*x^2 + 3*x + 3)/x^5\n", + "(0 dx, ((3*x + 3)/x^5)*y^6, ((-2*x - 2)/(x^4*y)) dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2b\n", + "coeff (3*x + 3)/x^5\n", + "(0 dx, 3/x^5*y^6, ((-2*x^2 + 1)/(x^5*y)) dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2b\n", + "coeff 3/x^5\n", + "(0 dx, 0, 0 dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "w ((1/y^4) dx, 0, (1/y^4) dx)\n", + "(0 dx, 0, 0 dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "w ((2*x/y^4) dx, 2/x*y^3, ((-x - 1)/(x^2*y^4)) dx)\n", + "(0 dx, ((2*x^6 + 4*x^4 + 3*x^3 + 2*x^2 + 3*x + 3)/x^5)*y, 0 dx) 1\n", + "c2\n", + "c2c\n", + "coeff (2*x^6 + 4*x^4 + 3*x^3 + 2*x^2 + 3*x + 3)/x^5\n", + "(((2*x + 1)/y^6) dx, ((4*x^4 + 3*x^3 + 2*x^2 + 3*x + 3)/x^5)*y, 0 dx) 1\n", + "c2\n", + "c2b\n", + "coeff (4*x^4 + 3*x^3 + 2*x^2 + 3*x + 3)/x^5\n", + "(((2*x + 1)/y^6) dx, ((3*x^3 + 2*x^2 + 3*x + 3)/x^5)*y, ((2*x^3 - 2*x + 2)/(x^2*y^6)) dx) 1\n", + "c2\n", + "c2b\n", + "coeff (3*x^3 + 2*x^2 + 3*x + 3)/x^5\n", + "(((2*x + 1)/y^6) dx, ((2*x^2 + 3*x + 3)/x^5)*y, ((2*x^4 + x^3 - 2*x^2 - 2)/(x^3*y^6)) dx) 1\n", + "c2\n", + "c2b\n", + "coeff (2*x^2 + 3*x + 3)/x^5\n", + "(((2*x + 1)/y^6) dx, ((3*x + 3)/x^5)*y, ((2*x^5 + x^4 - 2*x - 2)/(x^4*y^6)) dx) 1\n", + "c2\n", + "c2b\n", + "coeff (3*x + 3)/x^5\n", + "(((2*x + 1)/y^6) dx, 3/x^5*y, ((2*x^6 + x^5 - 2*x^2 + 1)/(x^5*y^6)) dx) 1\n", + "c2\n", + "c2b\n", + "coeff 3/x^5\n", + "(((2*x + 1)/y^6) dx, 0, ((2*x + 1)/y^6) dx) 1\n", + "c1\n", + "baza ((x/y^6) dx, 0, (x/y^6) dx)\n", + "coeff 2*x + 1\n", + "coeff x\n", + "((1/y^6) dx, 0, (1/y^6) dx) 1\n", + "c1\n", + "baza ((1/y^6) dx, 0, (1/y^6) dx)\n", + "coeff 1\n", + "coeff 1\n", + "(0 dx, 0, 0 dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "w ((1/y^5) dx, 0, (1/y^5) dx)\n", + "(0 dx, 0, 0 dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "w ((x/y^5) dx, 0, (x/y^5) dx)\n", + "(0 dx, 0, 0 dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "w ((1/y^6) dx, 0, (1/y^6) dx)\n", + "(0 dx, 0, 0 dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "w ((x/y^6) dx, 0, (x/y^6) dx)\n", + "(0 dx, 0, 0 dx) 1\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n", + "c2\n" ] + }, + { + "data": { + "text/plain": [ + "[0 0 0 0 0 0 0 0 0 1 0 0]\n", + "[0 0 0 0 0 0 0 0 2 2 0 0]\n", + "[0 0 0 0 4 2 0 0 0 0 0 0]\n", + "[0 0 0 0 0 1 0 0 0 0 0 0]\n", + "[0 0 0 0 0 0 0 0 0 0 0 0]\n", + "[2 4 0 0 0 0 0 0 0 0 0 0]\n", + "[0 0 0 0 0 0 0 0 0 0 0 0]\n", + "[0 0 0 0 0 0 0 0 0 0 1 2]\n", + "[0 0 0 0 0 0 0 0 0 0 0 0]\n", + "[0 0 0 0 0 0 0 0 0 0 0 0]\n", + "[0 0 0 0 0 0 0 0 0 0 0 0]\n", + "[0 0 0 0 0 0 0 0 0 0 0 0]" + ] + }, + "execution_count": 134, + "metadata": {}, + "output_type": "execute_result" } ], "source": [