lepsze nazwy cial

This commit is contained in:
jgarnek 2021-08-21 20:50:10 +02:00
parent 7abda884fa
commit 75290c6b6a

View File

@ -2,14 +2,14 @@
"cells": [ "cells": [
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 4, "execution_count": 19,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
"class superelliptic:\n", "class superelliptic:\n",
" def __init__(self, f, m, p):\n", " def __init__(self, f, m, p):\n",
" R.<x> = PolynomialRing(GF(p))\n", " Rx.<x> = PolynomialRing(GF(p))\n",
" self.polynomial = R(f)\n", " self.polynomial = Rx(f)\n",
" self.exponent = m\n", " self.exponent = m\n",
" self.characteristic = p\n", " self.characteristic = p\n",
" \n", " \n",
@ -31,8 +31,8 @@
" p = self.characteristic\n", " p = self.characteristic\n",
" r = f.degree()\n", " r = f.degree()\n",
" delta = GCD(r, m)\n", " delta = GCD(r, m)\n",
" R2.<x, y> = PolynomialRing(GF(p), 2)\n", " Rxy.<x, y> = PolynomialRing(GF(p), 2)\n",
" RR = FractionField(R2)\n", " Fxy = FractionField(Rxy)\n",
" \n", " \n",
" basis = {}\n", " basis = {}\n",
" if j == 'all':\n", " if j == 'all':\n",
@ -40,14 +40,14 @@
" for j in range(1, m):\n", " for j in range(1, m):\n",
" for i in range(1, r):\n", " for i in range(1, r):\n",
" if (r*j - m*i >= delta):\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", " k = k+1\n",
" return basis\n", " return basis\n",
" else:\n", " else:\n",
" k = 0\n", " k = 0\n",
" for i in range(1, r):\n", " for i in range(1, r):\n",
" if (r*j - m*i >= delta):\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", " k = k+1\n",
" return basis\n", " return basis\n",
" \n", " \n",
@ -57,79 +57,79 @@
" p = self.characteristic\n", " p = self.characteristic\n",
" r = f.degree()\n", " r = f.degree()\n",
" delta = GCD(r, m)\n", " delta = GCD(r, m)\n",
" R.<x> = PolynomialRing(GF(p))\n", " Rx.<x> = PolynomialRing(GF(p))\n",
" R1.<x, y> = PolynomialRing(GF(p), 2)\n", " Rxy.<x, y> = PolynomialRing(GF(p), 2)\n",
" RR = FractionField(R1)\n", " Fxy = FractionField(Rxy)\n",
" basis = {}\n", " basis = {}\n",
" if j == 'all':\n", " if j == 'all':\n",
" for j in range(1, m):\n", " for j in range(1, m):\n",
" holo = C.basis_holomorphic_differentials(j)\n", " holo = C.basis_holomorphic_differentials(j)\n",
" for k in range(0, len(holo)):\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", " k = len(basis)\n",
" \n", " \n",
" for i in range(1, r):\n", " for i in range(1, r):\n",
" if (r*(m-j) - m*i >= delta):\n", " if (r*(m-j) - m*i >= delta):\n",
" s = R(m-j)*R(x)*R(f.derivative()) - R(m)*R(i)*f\n", " s = Rx(m-j)*Rx(x)*Rx(f.derivative()) - Rx(m)*Rx(i)*f\n",
" psi = R(cut(s, i))\n", " psi = Rx(cut(s, i))\n",
" basis[k] = superelliptic_cech(self, superelliptic_form(self, psi/y^j), superelliptic_function(self, m*y^j/x^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", " k = k+1\n",
" return basis\n", " return basis\n",
" \n", " \n",
"def reduction(C, g):\n", "def reduction(C, g):\n",
" p = C.characteristic\n", " p = C.characteristic\n",
" R.<x, y> = PolynomialRing(GF(p), 2)\n", " Rxy.<x, y> = PolynomialRing(GF(p), 2)\n",
" RR = FractionField(R)\n", " Fxy = FractionField(Rxy)\n",
" f = C.polynomial\n", " f = C.polynomial\n",
" r = f.degree()\n", " r = f.degree()\n",
" m = C.exponent\n", " m = C.exponent\n",
" g = RR(g)\n", " g = Fxy(g)\n",
" g1 = g.numerator()\n", " g1 = g.numerator()\n",
" g2 = g.denominator()\n", " g2 = g.denominator()\n",
" \n", " \n",
" R1.<x> = PolynomialRing(GF(p))\n", " Rx.<x> = PolynomialRing(GF(p))\n",
" R2 = FractionField(R1)\n", " Fx = FractionField(Rx)\n",
" R3.<y> = PolynomialRing(R2) \n", " FxRy.<y> = PolynomialRing(Fx) \n",
" (A, B, C) = xgcd(R3(g2), R3(y^m - f))\n", " (A, B, C) = xgcd(FxRy(g2), FxRy(y^m - f))\n",
" g = R3(g1*B/A)\n", " g = FxRy(g1*B/A)\n",
" \n", " \n",
" while(g.degree(R(y)) >= m):\n", " while(g.degree(Rxy(y)) >= m):\n",
" d = g.degree(R(y))\n", " d = g.degree(Rxy(y))\n",
" G = coff(g, d)\n", " G = coff(g, d)\n",
" i = floor(d/m)\n", " i = floor(d/m)\n",
" g = g - G*y^d + f^i * y^(d%m) *G\n", " g = g - G*y^d + f^i * y^(d%m) *G\n",
" \n", " \n",
" return(R3(g))\n", " return(FxRy(g))\n",
"\n", "\n",
"def reduction_form(C, g):\n", "def reduction_form(C, g):\n",
" p = C.characteristic\n", " p = C.characteristic\n",
" R.<x, y> = PolynomialRing(GF(p), 2)\n", " Rxy.<x, y> = PolynomialRing(GF(p), 2)\n",
" RR = FractionField(R)\n", " Fxy = FractionField(Rxy)\n",
" f = C.polynomial\n", " f = C.polynomial\n",
" r = f.degree()\n", " r = f.degree()\n",
" m = C.exponent\n", " m = C.exponent\n",
" g = reduction(C, g)\n", " g = reduction(C, g)\n",
"\n", "\n",
" g1 = RR(0)\n", " g1 = RR(0)\n",
" R1.<x> = PolynomialRing(GF(p))\n", " Rx.<x> = PolynomialRing(GF(p))\n",
" R2 = FractionField(R1)\n", " Fx = FractionField(Rx)\n",
" R3.<y> = PolynomialRing(R2)\n", " FxRy.<y> = PolynomialRing(Fx)\n",
" \n", " \n",
" g = R3(g)\n", " g = FxRy(g)\n",
" for j in range(0, m):\n", " for j in range(0, m):\n",
" if j==0:\n", " if j==0:\n",
" G = coff(g, 0)\n", " G = coff(g, 0)\n",
" g1 += G\n", " g1 += G\n",
" else:\n", " else:\n",
" G = coff(g, j)\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", " return(g1)\n",
" \n", " \n",
"class superelliptic_function:\n", "class superelliptic_function:\n",
" def __init__(self, C, g):\n", " def __init__(self, C, g):\n",
" p = C.characteristic\n", " p = C.characteristic\n",
" R.<x, y> = PolynomialRing(GF(p), 2)\n", " Rxy.<x, y> = PolynomialRing(GF(p), 2)\n",
" RR = FractionField(R)\n", " Fxy = FractionField(Rxy)\n",
" f = C.polynomial\n", " f = C.polynomial\n",
" r = f.degree()\n", " r = f.degree()\n",
" m = C.exponent\n", " m = C.exponent\n",
@ -143,8 +143,8 @@
" \n", " \n",
" def jth_component(self, j):\n", " def jth_component(self, j):\n",
" g = self.function\n", " g = self.function\n",
" R.<x, y> = PolynomialRing(GF(p), 2)\n", " Rxy.<x, y> = PolynomialRing(GF(p), 2)\n",
" g = R(g)\n", " g = Rxy(g)\n",
" return g.coefficient(y^j)\n", " return g.coefficient(y^j)\n",
" \n", " \n",
" def __add__(self, other):\n", " def __add__(self, other):\n",
@ -181,9 +181,9 @@
" m = C.exponent\n", " m = C.exponent\n",
" p = C.characteristic\n", " p = C.characteristic\n",
" g = self.function\n", " g = self.function\n",
" R.<x, y> = PolynomialRing(GF(p), 2)\n", " Rxy.<x, y> = PolynomialRing(GF(p), 2)\n",
" RR = FractionField(R)\n", " Fxy = FractionField(Rxy)\n",
" g = RR(g)\n", " g = Fxy(g)\n",
" A = g.derivative(x)\n", " A = g.derivative(x)\n",
" B = g.derivative(y)*f.derivative(x)/(m*y^(m-1))\n", " B = g.derivative(y)*f.derivative(x)/(m*y^(m-1))\n",
" return superelliptic_form(C, A+B)\n", " return superelliptic_form(C, A+B)\n",
@ -191,9 +191,9 @@
"class superelliptic_form:\n", "class superelliptic_form:\n",
" def __init__(self, C, g):\n", " def __init__(self, C, g):\n",
" p = C.characteristic\n", " p = C.characteristic\n",
" R.<x, y> = PolynomialRing(GF(p), 2)\n", " Rxy.<x, y> = PolynomialRing(GF(p), 2)\n",
" RR = FractionField(R)\n", " Fxy = FractionField(Rxy)\n",
" g = RR(reduction_form(C, g))\n", " g = Fxy(reduction_form(C, g))\n",
" self.form = g\n", " self.form = g\n",
" self.curve = C \n", " self.curve = C \n",
" \n", " \n",
@ -219,23 +219,23 @@
" \n", " \n",
" def jth_component(self, j):\n", " def jth_component(self, j):\n",
" g = self.form\n", " g = self.form\n",
" R1.<x> = PolynomialRing(GF(p))\n", " Rx.<x> = PolynomialRing(GF(p))\n",
" R2 = FractionField(R1)\n", " Fx = FractionField(Rx)\n",
" R3.<y> = PolynomialRing(R2)\n", " FxRy.<y> = PolynomialRing(Fx)\n",
" R4 = FractionField(R3)\n", " Fxy = FractionField(FxRy)\n",
" R5.<y_inv> = PolynomialRing(R2)\n", " Ryinv = PolynomialRing(Fx)\n",
" g = R4(g)\n", " g = Fxy(g)\n",
" g = g(y = 1/y_inv)\n", " g = g(y = 1/y_inv)\n",
" g = R5(g)\n", " g = Ryinv(g)\n",
" return coff(g, j)\n", " return coff(g, j)\n",
" \n", " \n",
" def is_regular_on_U0(self):\n", " def is_regular_on_U0(self):\n",
" C = self.curve\n", " C = self.curve\n",
" p = C.characteristic\n", " p = C.characteristic\n",
" m = C.exponent\n", " m = C.exponent\n",
" R.<x> = PolynomialRing(GF(p))\n", " Rx.<x> = PolynomialRing(GF(p))\n",
" for j in range(1, m):\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 0\n",
" return 1\n", " return 1\n",
" \n", " \n",
@ -276,9 +276,9 @@
" return \"(\" + str(self.omega0) + \", \" + str(self.f) + \", \" + str(self.omega8) + \")\" \n", " return \"(\" + str(self.omega0) + \", \" + str(self.f) + \", \" + str(self.omega8) + \")\" \n",
" \n", " \n",
"def degree_of_rational_fctn(f):\n", "def degree_of_rational_fctn(f):\n",
" R.<x> = PolynomialRing(GF(p))\n", " Rx.<x> = PolynomialRing(GF(p))\n",
" RR = FractionField(R)\n", " Fx = FractionField(Rx)\n",
" f = RR(f)\n", " f = Fx(f)\n",
" f1 = f.numerator()\n", " f1 = f.numerator()\n",
" f2 = f.denominator()\n", " f2 = f.denominator()\n",
" d1 = f1.degree()\n", " d1 = f1.degree()\n",
@ -299,38 +299,46 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 5, "execution_count": 20,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
"data": { "ename": "TypeError",
"text/plain": [ "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'",
"{0: ((1/y) dx, 0, (1/y) dx), 1: ((x/y) dx, 2/x*y, ((x - 1)/(x^2*y)) dx)}" "output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m<ipython-input-20-d63657cf06e3>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0mC\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msuperelliptic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m7\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m5\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----> 2\u001b[0;31m \u001b[0mC\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbasis_de_rham\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 3\u001b[0m \u001b[0;31m#C.basis_holomorphic_differentials()\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m<ipython-input-19-a65119f7de4f>\u001b[0m in \u001b[0;36mbasis_de_rham\u001b[0;34m(self, j)\u001b[0m\n\u001b[1;32m 65\u001b[0m \u001b[0ms\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mRx\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mm\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mRx\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mRx\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mderivative\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mRx\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mm\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mRx\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 66\u001b[0m \u001b[0mpsi\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mRx\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcut\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms\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[0m\n\u001b[0;32m---> 67\u001b[0;31m \u001b[0mbasis\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msuperelliptic_cech\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msuperelliptic_form\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mFxy\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpsi\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msuperelliptic_function\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mFxy\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mm\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mx\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[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 68\u001b[0m \u001b[0mk\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mk\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[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 69\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mbasis\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/structure/element.pyx\u001b[0m in \u001b[0;36msage.structure.element.Element.__add__ (build/cythonized/sage/structure/element.c:10839)\u001b[0;34m()\u001b[0m\n\u001b[1;32m 1232\u001b[0m \u001b[0;31m# Left and right are Sage elements => use coercion model\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1233\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mBOTH_ARE_ELEMENT\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcl\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-> 1234\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mcoercion_model\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbin_op\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mleft\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mright\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0madd\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 1235\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1236\u001b[0m \u001b[0mcdef\u001b[0m \u001b[0mlong\u001b[0m \u001b[0mvalue\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/coerce.pyx\u001b[0m in \u001b[0;36msage.structure.coerce.CoercionModel.bin_op (build/cythonized/sage/structure/coerce.c:11180)\u001b[0;34m()\u001b[0m\n\u001b[1;32m 1253\u001b[0m \u001b[0;31m# We should really include the underlying error.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1254\u001b[0m \u001b[0;31m# This causes so much headache.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1255\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mbin_op_exception\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mop\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\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 1256\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1257\u001b[0m \u001b[0mcpdef\u001b[0m \u001b[0mcanonical_coercion\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\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;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'"
] ]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
} }
], ],
"source": [ "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_de_rham()\n",
"#C.basis_holomorphic_differentials()" "#C.basis_holomorphic_differentials()"
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 50, "execution_count": 7,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
"name": "stdout", "ename": "NameError",
"output_type": "stream", "evalue": "name 'y' is not defined",
"text": [ "output_type": "error",
"(1/y) dx\n", "traceback": [
"1 1\n", "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"{0: (1/y) dx}\n" "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)",
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"\u001b[0;31mNameError\u001b[0m: name 'y' is not defined"
] ]
} }
], ],