chyba dziala baza dR
This commit is contained in:
parent
200e3a1990
commit
8e234d2c21
@ -2,22 +2,9 @@
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 87,
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"execution_count": 48,
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"metadata": {},
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"outputs": [
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{
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"ename": "NameError",
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"evalue": "name 'holo' is not defined",
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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;31mNameError\u001b[0m Traceback (most recent call last)",
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"\u001b[0;32m<ipython-input-87-fb238ae380ad>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;32mclass\u001b[0m \u001b[0msuperelliptic\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 2\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m__init__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\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[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0mR\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[0mR\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 4\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpolynomial\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mR\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 5\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<ipython-input-87-fb238ae380ad>\u001b[0m in \u001b[0;36msuperelliptic\u001b[0;34m()\u001b[0m\n\u001b[1;32m 53\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[1;32m 54\u001b[0m \u001b[0mholo\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbaza_holo\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mj\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---> 55\u001b[0;31m \u001b[0;32mfor\u001b[0m \u001b[0mk\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[0mholo\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 56\u001b[0m \u001b[0mbaza\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mholo\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 57\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
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"\u001b[0;31mNameError\u001b[0m: name 'holo' is not defined"
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]
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}
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],
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"outputs": [],
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"source": [
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"class superelliptic:\n",
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" def __init__(self, f, m, p):\n",
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@ -44,6 +31,8 @@
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" p = self.characteristic\n",
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" r = f.degree()\n",
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" delta = GCD(r, m)\n",
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" R2.<x, y> = PolynomialRing(GF(p), 2)\n",
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" RR = FractionField(R2)\n",
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" \n",
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" basis = {}\n",
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" if j == 'all':\n",
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@ -51,14 +40,14 @@
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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*j - m*i >= delta):\n",
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" basis[k] = superelliptic_form(C, x^(i-1)/y^j)\n",
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" basis[k] = superelliptic_form(self, RR(x^(i-1)/y^j))\n",
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" k = k+1\n",
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" return basis\n",
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" else:\n",
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" k = 0\n",
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" for i in range(1, r):\n",
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" if (r*j - m*i >= delta):\n",
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" basis[k] = superelliptic_form(C, x^(i-1)/y^j)\n",
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" basis[k] = superelliptic_form(self, RR(x^(i-1)/y^j))\n",
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" k = k+1\n",
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" return basis\n",
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" \n",
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@ -68,13 +57,24 @@
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" p = self.characteristic\n",
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" r = f.degree()\n",
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" delta = GCD(r, m)\n",
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" #?????\n",
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" R.<x> = PolynomialRing(GF(p))\n",
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" R1.<x, y> = PolynomialRing(GF(p), 2)\n",
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" RR = FractionField(R1)\n",
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" basis = {}\n",
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" if j == 'all':\n",
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" for j in range(1, m):\n",
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" holo = baza_holo(m, f, j, p)\n",
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" for k in range(0, len(holo)):\n",
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" baza[k] = holo[k]\n",
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" holo = C.basis_holomorphic_differentials(j)\n",
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" for k in range(0, len(holo)):\n",
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" basis[k] = superelliptic_cech(self, holo[k], superelliptic_function(self, R(0))) \n",
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" k = len(basis)\n",
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" \n",
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" for i in range(1, r):\n",
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" if (r*(m-j) - m*i >= delta):\n",
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" s = R(m-j)*R(x)*R(f.derivative()) - R(m)*R(i)*f\n",
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" psi = R(cut(s, i))\n",
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" basis[k] = superelliptic_cech(self, superelliptic_form(self, psi/y^j), superelliptic_function(self, m*y^j/x^i))\n",
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" k = k+1\n",
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" return basis\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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" \n",
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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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" R.<x, y> = PolynomialRing(GF(p), 2)\n",
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" RR = FractionField(R)\n",
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" f = C.polynomial\n",
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" C = self.curve\n",
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" f = C.polynomial\n",
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" m = C.exponent\n",
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" p = C.characteristic\n",
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" g = self.function\n",
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" R.<x, y> = PolynomialRing(GF(p), 2)\n",
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" RR = FractionField(R)\n",
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" g = RR(g)\n",
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" A = g.derivative(x)\n",
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" B = g.derivative(y)*f.derivative(x)/(m*y^(m-1))\n",
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" return superelliptic_form(C, A+B)\n",
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" \n",
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"class superelliptic_form:\n",
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" def __init__(self, C, g):\n",
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" p = C.characteristic\n",
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" R.<x, y> = PolynomialRing(GF(p), 2)\n",
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" RR = FractionField(R)\n",
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" g = RR(reduction_form(C, g))\n",
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" return 1\n",
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" \n",
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"class superelliptic_cech:\n",
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" def __init__(self, omega, fct):\n",
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" def __init__(self, C, omega, fct):\n",
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" self.omega0 = omega\n",
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" self.omega8 = omega - diffn(fct)\n",
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" self.f = fct\n",
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" self.curve = C\n",
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" \n",
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"def degree_of_rational_fctn(f):\n",
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" R.<x> = PolynomialRing(GF(p))\n",
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" return lista[d]\n",
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"\n",
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"def cut(f, i):\n",
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" R = f.parent()\n",
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" coeff = f.coefficients(sparse = false)\n",
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" return sum(x^(j-i-1) * coeff[j] for j in range(i+1, f.degree() + 1))"
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" return sum(R(x^(j-i-1)) * coeff[j] for j in range(i+1, f.degree() + 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": 80,
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"execution_count": 49,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"((-2*x^3*y + x^2 + x)/y) dx"
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"{0: <__main__.superelliptic_cech object at 0x6fdcefeaf60>,\n",
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" 1: <__main__.superelliptic_cech object at 0x6fdcefea8d0>}"
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]
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},
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"execution_count": 80,
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"execution_count": 49,
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"metadata": {},
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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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"C = superelliptic(x^3 + x + 2, 2, 5)\n",
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"omega = superelliptic_form(C, (x^2+x)/y + 3*x^3)\n",
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"omega"
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"C.basis_de_rham()\n",
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"#C.basis_holomorphic_differentials()"
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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": 81,
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"execution_count": 50,
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"metadata": {},
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"outputs": [
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{
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@ -334,7 +343,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 82,
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -536,6 +545,95 @@
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"f.coefficient()"
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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": 35,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"x^3 + x + 1"
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]
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},
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"execution_count": 35,
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"metadata": {},
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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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"x^3+x+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": 36,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"Symbolic Ring"
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]
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},
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"execution_count": 36,
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"metadata": {},
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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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"parent(x)"
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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": 37,
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"metadata": {},
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"outputs": [],
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"source": [
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"R.<x> = PolynomialRing(GF(5))"
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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": 39,
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"metadata": {},
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"outputs": [],
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"source": [
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"R = (x^3+x).parent()"
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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": 44,
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"metadata": {},
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"outputs": [],
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"source": [
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"R.<x, y> = PolynomialRing(GF(5))\n",
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"RR = FractionField(R)\n",
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"A = RR(1/(x*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": 45,
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"metadata": {},
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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)/(x^2*y)"
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]
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},
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"execution_count": 45,
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"metadata": {},
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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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"A.derivative(x)"
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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": null,
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Block a user