jth_component of form; poczatek bazy de Rhama
This commit is contained in:
parent
8778f1f84b
commit
200e3a1990
@ -2,9 +2,22 @@
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 219,
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"execution_count": 87,
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"metadata": {},
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"outputs": [],
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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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"source": [
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"class superelliptic:\n",
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" def __init__(self, f, m, p):\n",
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@ -13,7 +26,6 @@
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" self.exponent = m\n",
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" self.characteristic = p\n",
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" \n",
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" \n",
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" def __repr__(self):\n",
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" f = self.polynomial\n",
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" m = self.exponent\n",
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@ -36,8 +48,8 @@
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" basis = {}\n",
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" if j == 'all':\n",
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" k = 0\n",
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" for i in range(1, r):\n",
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" for j in range(1, m):\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*j - m*i >= delta):\n",
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" basis[k] = superelliptic_form(C, x^(i-1)/y^j)\n",
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" k = k+1\n",
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@ -49,7 +61,21 @@
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" basis[k] = superelliptic_form(C, 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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" \n",
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" def basis_de_rham(self, j = 'all'):\n",
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" f = self.polynomial\n",
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" m = self.exponent\n",
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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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" 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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" \n",
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"def reduction(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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" \n",
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" while(g.degree(R(y)) >= m):\n",
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" d = g.degree(R(y))\n",
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" G = g.coefficient(R(y^d))\n",
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" G = coff(g, d)\n",
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" i = floor(d/m)\n",
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" g = g - G*y^d + f^i * y^(d%m) *G\n",
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" \n",
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" \n",
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" g = R3(g)\n",
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" for j in range(0, m):\n",
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" G = g.coefficients(sparse = false)[j]\n",
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" g1 += RR(y^(j-m)*f*G)\n",
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" \n",
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" if j==0:\n",
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" G = coff(g, 0)\n",
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" g1 += G\n",
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" else:\n",
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" G = coff(g, j)\n",
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" g1 += RR(y^(j-m)*f*G)\n",
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" return(g1)\n",
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" \n",
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"class superelliptic_function:\n",
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@ -184,55 +213,128 @@
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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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" R.<x, y> = PolynomialRing(GF(p), 2)\n",
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" g = R(g)\n",
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" return g.coefficient(y^j)"
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" R1.<x> = PolynomialRing(GF(p))\n",
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" R2 = FractionField(R1)\n",
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" R3.<y> = PolynomialRing(R2)\n",
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" R4 = FractionField(R3)\n",
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" R5.<y_inv> = PolynomialRing(R2)\n",
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" g = R4(g)\n",
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" g = g(y = 1/y_inv)\n",
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" g = R5(g)\n",
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" return coff(g, j)\n",
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" \n",
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" def is_regular_on_U0(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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" R.<x> = PolynomialRing(GF(p))\n",
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" for j in range(1, m):\n",
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" if self.jth_component(j) not in R:\n",
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" return 0\n",
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" return 1\n",
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" \n",
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" def is_regular_on_Uinfty(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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" f = C.polynomial\n",
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" r = f.degree()\n",
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" delta = GCD(m, r)\n",
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" M = m/delta\n",
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" R = r/delta\n",
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" \n",
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" for j in range(1, m):\n",
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" A = self.jth_component(j)\n",
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" d = degree_of_rational_fctn(A)\n",
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" if(-d*M + j*R -(M+1)<0):\n",
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" return 0\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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" 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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" \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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" RR = FractionField(R)\n",
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" f = RR(f)\n",
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" f1 = f.numerator()\n",
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" f2 = f.denominator()\n",
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" d1 = f1.degree()\n",
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" d2 = f2.degree()\n",
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" return(d1 - d2)\n",
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"\n",
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"def coff(f, d):\n",
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" lista = f.coefficients(sparse = false)\n",
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" if len(lista) <= d:\n",
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" return 0\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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" 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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]
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},
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{
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"cell_type": "code",
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"execution_count": 220,
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"execution_count": 80,
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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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"{0: (1/y) dx}"
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"((-2*x^3*y + x^2 + x)/y) dx"
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]
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},
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"execution_count": 220,
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"execution_count": 80,
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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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"C.basis_holomorphic_differentials()"
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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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]
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},
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{
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"cell_type": "code",
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"execution_count": 179,
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"execution_count": 81,
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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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"0"
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]
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},
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"execution_count": 179,
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"metadata": {},
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"output_type": "execute_result"
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"(1/y) dx\n",
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"1 1\n",
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"{0: (1/y) dx}\n"
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]
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}
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],
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"source": [
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"A.degree(y)"
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"licz = 0\n",
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"m = 2\n",
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"p = 5\n",
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"R1.<x> = PolynomialRing(GF(p))\n",
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"f = R1(x^3 + x + 4)\n",
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"r = f.degree()\n",
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"C = superelliptic(f, m, p)\n",
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"for i in range(0, r):\n",
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" for j in range(1, m):\n",
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" omega = superelliptic_form(C, x^i/y^j)\n",
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" if (omega.is_regular_on_U0() and omega.is_regular_on_Uinfty()):\n",
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" print(omega)\n",
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" licz += 1\n",
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"print(licz, C.genus())\n",
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"print(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": 180,
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"execution_count": 82,
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"metadata": {},
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"outputs": [],
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"source": [
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},
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{
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"cell_type": "code",
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"execution_count": 181,
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"execution_count": 83,
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"metadata": {},
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"outputs": [],
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"source": [
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},
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{
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"cell_type": "code",
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"execution_count": 183,
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"execution_count": 84,
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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^2 + 1"
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"3*x^2 + 1"
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]
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},
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"execution_count": 183,
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"execution_count": 84,
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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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{
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"cell_type": "code",
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"execution_count": 33,
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"metadata": {},
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"outputs": [
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{
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"y"
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]
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},
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"execution_count": 33,
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"execution_count": 85,
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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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{
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"cell_type": "code",
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"execution_count": 39,
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"execution_count": 86,
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"metadata": {},
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"outputs": [],
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"source": [
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},
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{
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"cell_type": "code",
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"execution_count": 213,
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"execution_count": 3,
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"metadata": {},
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"outputs": [],
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"source": [
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"p = 5\n",
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"R1.<x> = PolynomialRing(GF(p))\n",
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"R2 = FractionField(R1)\n",
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"R3.<y> = PolynomialRing(R2)\n",
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"g = y^2/x + y/(x+1) "
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"g = y^2/x + y/(x+1) \n",
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"g = 1/y+x/y^2"
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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": 218,
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"execution_count": 4,
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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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"[0, 1/(x + 1), 1/x]"
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"x*z^2 + z"
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]
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},
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"execution_count": 218,
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"execution_count": 4,
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"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"g.coefficients(sparse = false)"
|
||||
"R3.<z> = PolynomialRing(R2)\n",
|
||||
"g(y = 1/z)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 57,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"x^3 + x + 4"
|
||||
]
|
||||
},
|
||||
"execution_count": 57,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"f"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 62,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"ename": "AttributeError",
|
||||
"evalue": "'sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint' object has no attribute 'coefficient'",
|
||||
"output_type": "error",
|
||||
"traceback": [
|
||||
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
|
||||
"\u001b[0;31mAttributeError\u001b[0m Traceback (most recent call last)",
|
||||
"\u001b[0;32m<ipython-input-62-e054c182ec1a>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcoefficient\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/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.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint' object has no attribute 'coefficient'"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"f.coefficient()"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
||||
Loading…
Reference in New Issue
Block a user