From 75290c6b6a7b5af6023535192d4123198c0c5be0 Mon Sep 17 00:00:00 2001 From: jgarnek Date: Sat, 21 Aug 2021 20:50:10 +0200 Subject: [PATCH] lepsze nazwy cial --- superelliptic.ipynb | 150 +++++++++++++++++++++++--------------------- 1 file changed, 79 insertions(+), 71 deletions(-) diff --git a/superelliptic.ipynb b/superelliptic.ipynb index 8b065a5..8a8f046 100644 --- a/superelliptic.ipynb +++ b/superelliptic.ipynb @@ -2,14 +2,14 @@ "cells": [ { "cell_type": "code", - "execution_count": 4, + "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "class superelliptic:\n", " def __init__(self, f, m, p):\n", - " R. = PolynomialRing(GF(p))\n", - " self.polynomial = R(f)\n", + " Rx. = PolynomialRing(GF(p))\n", + " self.polynomial = Rx(f)\n", " self.exponent = m\n", " self.characteristic = p\n", " \n", @@ -31,8 +31,8 @@ " p = self.characteristic\n", " r = f.degree()\n", " delta = GCD(r, m)\n", - " R2. = PolynomialRing(GF(p), 2)\n", - " RR = FractionField(R2)\n", + " Rxy. = PolynomialRing(GF(p), 2)\n", + " Fxy = FractionField(Rxy)\n", " \n", " basis = {}\n", " if j == 'all':\n", @@ -40,14 +40,14 @@ " for j in range(1, m):\n", " for i in range(1, r):\n", " if (r*j - m*i >= delta):\n", - " basis[k] = superelliptic_form(self, RR(x^(i-1)/y^j))\n", + " basis[k] = superelliptic_form(self, Fxy(x^(i-1)/y^j))\n", " k = k+1\n", " return basis\n", " else:\n", " k = 0\n", " for i in range(1, r):\n", " if (r*j - m*i >= delta):\n", - " basis[k] = superelliptic_form(self, RR(x^(i-1)/y^j))\n", + " basis[k] = superelliptic_form(self, Fxy(x^(i-1)/y^j))\n", " k = k+1\n", " return basis\n", " \n", @@ -57,79 +57,79 @@ " p = self.characteristic\n", " r = f.degree()\n", " delta = GCD(r, m)\n", - " R. = PolynomialRing(GF(p))\n", - " R1. = PolynomialRing(GF(p), 2)\n", - " RR = FractionField(R1)\n", + " Rx. = PolynomialRing(GF(p))\n", + " Rxy. = PolynomialRing(GF(p), 2)\n", + " Fxy = FractionField(Rxy)\n", " basis = {}\n", " if j == 'all':\n", " for j in range(1, m):\n", " holo = C.basis_holomorphic_differentials(j)\n", " for k in range(0, len(holo)):\n", - " basis[k] = superelliptic_cech(self, holo[k], superelliptic_function(self, R(0))) \n", + " basis[k] = superelliptic_cech(self, holo[k], superelliptic_function(self, Rx(0))) \n", " k = len(basis)\n", " \n", " for i in range(1, r):\n", " if (r*(m-j) - m*i >= delta):\n", - " s = R(m-j)*R(x)*R(f.derivative()) - R(m)*R(i)*f\n", - " psi = R(cut(s, i))\n", - " basis[k] = superelliptic_cech(self, superelliptic_form(self, psi/y^j), superelliptic_function(self, m*y^j/x^i))\n", + " s = Rx(m-j)*Rx(x)*Rx(f.derivative()) - Rx(m)*Rx(i)*f\n", + " psi = Rx(cut(s, i))\n", + " basis[k] = superelliptic_cech(self, superelliptic_form(self, Fxy(psi/y^j)), superelliptic_function(self, Fxy(m*y^j/x^i)))\n", " k = k+1\n", " return basis\n", " \n", "def reduction(C, g):\n", " p = C.characteristic\n", - " R. = PolynomialRing(GF(p), 2)\n", - " RR = FractionField(R)\n", + " Rxy. = PolynomialRing(GF(p), 2)\n", + " Fxy = FractionField(Rxy)\n", " f = C.polynomial\n", " r = f.degree()\n", " m = C.exponent\n", - " g = RR(g)\n", + " g = Fxy(g)\n", " g1 = g.numerator()\n", " g2 = g.denominator()\n", " \n", - " R1. = PolynomialRing(GF(p))\n", - " R2 = FractionField(R1)\n", - " R3. = PolynomialRing(R2) \n", - " (A, B, C) = xgcd(R3(g2), R3(y^m - f))\n", - " g = R3(g1*B/A)\n", + " Rx. = PolynomialRing(GF(p))\n", + " Fx = FractionField(Rx)\n", + " FxRy. = PolynomialRing(Fx) \n", + " (A, B, C) = xgcd(FxRy(g2), FxRy(y^m - f))\n", + " g = FxRy(g1*B/A)\n", " \n", - " while(g.degree(R(y)) >= m):\n", - " d = g.degree(R(y))\n", + " while(g.degree(Rxy(y)) >= m):\n", + " d = g.degree(Rxy(y))\n", " G = coff(g, d)\n", " i = floor(d/m)\n", " g = g - G*y^d + f^i * y^(d%m) *G\n", " \n", - " return(R3(g))\n", + " return(FxRy(g))\n", "\n", "def reduction_form(C, g):\n", " p = C.characteristic\n", - " R. = PolynomialRing(GF(p), 2)\n", - " RR = FractionField(R)\n", + " Rxy. = PolynomialRing(GF(p), 2)\n", + " Fxy = FractionField(Rxy)\n", " f = C.polynomial\n", " r = f.degree()\n", " m = C.exponent\n", " g = reduction(C, g)\n", "\n", " g1 = RR(0)\n", - " R1. = PolynomialRing(GF(p))\n", - " R2 = FractionField(R1)\n", - " R3. = PolynomialRing(R2)\n", + " Rx. = PolynomialRing(GF(p))\n", + " Fx = FractionField(Rx)\n", + " FxRy. = PolynomialRing(Fx)\n", " \n", - " g = R3(g)\n", + " g = FxRy(g)\n", " for j in range(0, m):\n", " if j==0:\n", " G = coff(g, 0)\n", " g1 += G\n", " else:\n", " G = coff(g, j)\n", - " g1 += RR(y^(j-m)*f*G)\n", + " g1 += Fxy(y^(j-m)*f*G)\n", " return(g1)\n", " \n", "class superelliptic_function:\n", " def __init__(self, C, g):\n", " p = C.characteristic\n", - " R. = PolynomialRing(GF(p), 2)\n", - " RR = FractionField(R)\n", + " Rxy. = PolynomialRing(GF(p), 2)\n", + " Fxy = FractionField(Rxy)\n", " f = C.polynomial\n", " r = f.degree()\n", " m = C.exponent\n", @@ -143,8 +143,8 @@ " \n", " def jth_component(self, j):\n", " g = self.function\n", - " R. = PolynomialRing(GF(p), 2)\n", - " g = R(g)\n", + " Rxy. = PolynomialRing(GF(p), 2)\n", + " g = Rxy(g)\n", " return g.coefficient(y^j)\n", " \n", " def __add__(self, other):\n", @@ -181,9 +181,9 @@ " m = C.exponent\n", " p = C.characteristic\n", " g = self.function\n", - " R. = PolynomialRing(GF(p), 2)\n", - " RR = FractionField(R)\n", - " g = RR(g)\n", + " Rxy. = PolynomialRing(GF(p), 2)\n", + " Fxy = FractionField(Rxy)\n", + " g = Fxy(g)\n", " A = g.derivative(x)\n", " B = g.derivative(y)*f.derivative(x)/(m*y^(m-1))\n", " return superelliptic_form(C, A+B)\n", @@ -191,9 +191,9 @@ "class superelliptic_form:\n", " def __init__(self, C, g):\n", " p = C.characteristic\n", - " R. = PolynomialRing(GF(p), 2)\n", - " RR = FractionField(R)\n", - " g = RR(reduction_form(C, g))\n", + " Rxy. = PolynomialRing(GF(p), 2)\n", + " Fxy = FractionField(Rxy)\n", + " g = Fxy(reduction_form(C, g))\n", " self.form = g\n", " self.curve = C \n", " \n", @@ -219,23 +219,23 @@ " \n", " def jth_component(self, j):\n", " g = self.form\n", - " R1. = PolynomialRing(GF(p))\n", - " R2 = FractionField(R1)\n", - " R3. = PolynomialRing(R2)\n", - " R4 = FractionField(R3)\n", - " R5. = PolynomialRing(R2)\n", - " g = R4(g)\n", + " Rx. = PolynomialRing(GF(p))\n", + " Fx = FractionField(Rx)\n", + " FxRy. = PolynomialRing(Fx)\n", + " Fxy = FractionField(FxRy)\n", + " Ryinv = PolynomialRing(Fx)\n", + " g = Fxy(g)\n", " g = g(y = 1/y_inv)\n", - " g = R5(g)\n", + " g = Ryinv(g)\n", " return coff(g, j)\n", " \n", " def is_regular_on_U0(self):\n", " C = self.curve\n", " p = C.characteristic\n", " m = C.exponent\n", - " R. = PolynomialRing(GF(p))\n", + " Rx. = PolynomialRing(GF(p))\n", " for j in range(1, m):\n", - " if self.jth_component(j) not in R:\n", + " if self.jth_component(j) not in Rx:\n", " return 0\n", " return 1\n", " \n", @@ -276,9 +276,9 @@ " return \"(\" + str(self.omega0) + \", \" + str(self.f) + \", \" + str(self.omega8) + \")\" \n", " \n", "def degree_of_rational_fctn(f):\n", - " R. = PolynomialRing(GF(p))\n", - " RR = FractionField(R)\n", - " f = RR(f)\n", + " Rx. = PolynomialRing(GF(p))\n", + " Fx = FractionField(Rx)\n", + " f = Fx(f)\n", " f1 = f.numerator()\n", " f2 = f.denominator()\n", " d1 = f1.degree()\n", @@ -299,38 +299,46 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 20, "metadata": {}, "outputs": [ { - "data": { - "text/plain": [ - "{0: ((1/y) dx, 0, (1/y) dx), 1: ((x/y) dx, 2/x*y, ((x - 1)/(x^2*y)) dx)}" - ] - }, - "execution_count": 5, - "metadata": {}, - "output_type": "execute_result" + "ename": "TypeError", + "evalue": "unsupported operand parent(s) for +: 'Real Field with 53 bits of precision' and 'Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 5'", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in 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"\u001b[0;31mTypeError\u001b[0m: unsupported operand parent(s) for +: 'Real Field with 53 bits of precision' and 'Fraction Field of Univariate Polynomial Ring in x over Finite Field of size 5'" + ] } ], "source": [ - "C = superelliptic(x^3 + x + 2, 2, 5)\n", + "C = superelliptic(x^3 + x + 2, 7, 5)\n", "C.basis_de_rham()\n", "#C.basis_holomorphic_differentials()" ] }, { "cell_type": "code", - "execution_count": 50, + "execution_count": 7, "metadata": {}, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "(1/y) dx\n", - "1 1\n", - "{0: (1/y) dx}\n" + "ename": "NameError", + "evalue": "name 'y' is not defined", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m 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