zapis w bazie dziala w polowie
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75290c6b6a
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@ -2,7 +2,7 @@
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"cells": [
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"cells": [
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{
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{
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"cell_type": "code",
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"cell_type": "code",
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"execution_count": 19,
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"execution_count": 115,
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"metadata": {},
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"metadata": {},
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"outputs": [],
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"outputs": [],
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"source": [
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"source": [
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@ -35,8 +35,8 @@
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" Fxy = FractionField(Rxy)\n",
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" Fxy = FractionField(Rxy)\n",
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" \n",
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" \n",
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" basis = {}\n",
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" basis = {}\n",
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" k = 0\n",
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" if j == 'all':\n",
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" if j == 'all':\n",
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" k = 0\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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" for i in range(1, r):\n",
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" if (r*j - m*i >= delta):\n",
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" if (r*j - m*i >= delta):\n",
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@ -44,14 +44,13 @@
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" k = k+1\n",
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" k = k+1\n",
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" return basis\n",
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" return basis\n",
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" else:\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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" for i in range(1, r):\n",
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" if (r*j - m*i >= delta):\n",
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" if (r*j - m*i >= delta):\n",
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" basis[k] = superelliptic_form(self, Fxy(x^(i-1)/y^j))\n",
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" basis[k] = superelliptic_form(self, Fxy(x^(i-1)/y^j))\n",
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" k = k+1\n",
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" k = k+1\n",
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" return basis\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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" def degree_and_basis_de_rham(self, j = 'all'):\n",
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" f = self.polynomial\n",
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" f = self.polynomial\n",
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" m = self.exponent\n",
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" m = self.exponent\n",
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" p = self.characteristic\n",
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" p = self.characteristic\n",
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@ -61,21 +60,39 @@
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" Rxy.<x, y> = PolynomialRing(GF(p), 2)\n",
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" Rxy.<x, y> = PolynomialRing(GF(p), 2)\n",
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" Fxy = FractionField(Rxy)\n",
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" Fxy = FractionField(Rxy)\n",
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" basis = {}\n",
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" basis = {}\n",
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" degrees0 = {}\n",
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" degrees1 = {}\n",
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" t = 0\n",
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" if j == 'all':\n",
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" if j == 'all':\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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" holo = C.basis_holomorphic_differentials(j)\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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" for k in range(0, len(holo)):\n",
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" basis[k] = superelliptic_cech(self, holo[k], superelliptic_function(self, Rx(0))) \n",
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" basis[t] = superelliptic_cech(self, holo[k], superelliptic_function(self, Rx(0))) \n",
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" k = len(basis)\n",
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" g = Rx(holo[k].jth_component(j))\n",
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" \n",
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" degrees0[t] = (g.degree(), j)\n",
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" t += 1\n",
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" for i in range(1, r):\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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" if (r*(m-j) - m*i >= delta):\n",
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" s = Rx(m-j)*Rx(x)*Rx(f.derivative()) - Rx(m)*Rx(i)*f\n",
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" s = Rx(m-j)*Rx(x)*Rx(f.derivative()) - Rx(m)*Rx(i)*f\n",
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" psi = Rx(cut(s, i))\n",
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" psi = Rx(cut(s, i))\n",
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" basis[k] = superelliptic_cech(self, superelliptic_form(self, Fxy(psi/y^j)), superelliptic_function(self, Fxy(m*y^j/x^i)))\n",
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" basis[t] = superelliptic_cech(self, superelliptic_form(self, Fxy(psi/y^j)), superelliptic_function(self, Fxy(m*y^j/x^i)))\n",
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" k = k+1\n",
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" degrees0[t] = (psi.degree(), j)\n",
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" return basis\n",
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" degrees1[t] = (-i, j)\n",
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" \n",
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" t += 1\n",
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" return basis, degrees0, degrees1\n",
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" \n",
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" def degree_de_rham(self, i, j='all'):\n",
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" basis, degrees0, degrees1 = self.degree_and_basis_de_rham(j)\n",
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" if i==0:\n",
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" return degrees0\n",
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" \n",
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" if i==1:\n",
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" return degrees1\n",
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" \n",
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" def basis_de_rham(self, j = 'all'): \n",
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" basis, degrees0, degrees1 = self.degree_and_basis_de_rham(j)\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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"def reduction(C, g):\n",
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" p = C.characteristic\n",
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" p = C.characteristic\n",
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" Rxy.<x, y> = PolynomialRing(GF(p), 2)\n",
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" Rxy.<x, y> = PolynomialRing(GF(p), 2)\n",
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@ -110,7 +127,7 @@
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" m = C.exponent\n",
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" m = C.exponent\n",
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" g = reduction(C, g)\n",
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" g = reduction(C, g)\n",
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"\n",
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"\n",
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" g1 = RR(0)\n",
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" g1 = Rxy(0)\n",
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" Rx.<x> = PolynomialRing(GF(p))\n",
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" Rx.<x> = PolynomialRing(GF(p))\n",
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" Fx = FractionField(Rx)\n",
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" Fx = FractionField(Rx)\n",
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" FxRy.<y> = PolynomialRing(Fx)\n",
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" FxRy.<y> = PolynomialRing(Fx)\n",
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@ -119,7 +136,7 @@
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" for j in range(0, m):\n",
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" for j in range(0, m):\n",
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" if j==0:\n",
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" if j==0:\n",
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" G = coff(g, 0)\n",
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" G = coff(g, 0)\n",
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" g1 += G\n",
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" g1 += FxRy(G)\n",
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" else:\n",
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" else:\n",
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" G = coff(g, j)\n",
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" G = coff(g, j)\n",
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" g1 += Fxy(y^(j-m)*f*G)\n",
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" g1 += Fxy(y^(j-m)*f*G)\n",
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@ -143,9 +160,13 @@
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" \n",
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" \n",
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" def jth_component(self, j):\n",
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" def jth_component(self, j):\n",
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" g = self.function\n",
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" g = self.function\n",
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" Rxy.<x, y> = PolynomialRing(GF(p), 2)\n",
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" C = self.curve\n",
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" g = Rxy(g)\n",
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" p = C.characteristic\n",
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" return g.coefficient(y^j)\n",
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" Rx.<x> = PolynomialRing(GF(p))\n",
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" Fx.<x> = FractionField(Rx)\n",
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" FxRy.<y> = PolynomialRing(Fx)\n",
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" g = FxRy(g)\n",
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" return coff(g, j)\n",
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" \n",
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" \n",
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" def __add__(self, other):\n",
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" def __add__(self, other):\n",
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" C = self.curve\n",
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" C = self.curve\n",
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@ -219,11 +240,13 @@
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" \n",
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" \n",
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" def jth_component(self, j):\n",
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" def jth_component(self, j):\n",
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" g = self.form\n",
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" g = self.form\n",
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" C = self.curve\n",
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" p = C.characteristic\n",
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" Rx.<x> = PolynomialRing(GF(p))\n",
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" Rx.<x> = PolynomialRing(GF(p))\n",
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" Fx = FractionField(Rx)\n",
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" Fx = FractionField(Rx)\n",
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" FxRy.<y> = PolynomialRing(Fx)\n",
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" FxRy.<y> = PolynomialRing(Fx)\n",
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" Fxy = FractionField(FxRy)\n",
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" Fxy = FractionField(FxRy)\n",
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" Ryinv = PolynomialRing(Fx)\n",
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" Ryinv.<y_inv> = PolynomialRing(Fx)\n",
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" g = Fxy(g)\n",
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" g = Fxy(g)\n",
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" g = g(y = 1/y_inv)\n",
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" g = g(y = 1/y_inv)\n",
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" g = Ryinv(g)\n",
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" g = Ryinv(g)\n",
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@ -272,8 +295,75 @@
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" C = self.curve\n",
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" C = self.curve\n",
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" return superelliptic_cech(C, self.omega0 - other.omega0, self.f - other.f)\n",
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" return superelliptic_cech(C, self.omega0 - other.omega0, self.f - other.f)\n",
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" \n",
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" \n",
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" def mult(self, constant):\n",
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" C = self.curve\n",
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" w1 = self.omega0.form\n",
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" f1 = self.f.function\n",
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" w2 = superelliptic_form(C, constant*w1)\n",
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" f2 = superelliptic_function(C, constant*f1)\n",
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" return superelliptic_cech(C, w2, f2)\n",
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" \n",
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" def __repr__(self):\n",
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" def __repr__(self):\n",
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" return \"(\" + str(self.omega0) + \", \" + str(self.f) + \", \" + str(self.omega8) + \")\" \n",
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" return \"(\" + str(self.omega0) + \", \" + str(self.f) + \", \" + str(self.omega8) + \")\" \n",
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" \n",
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" def basis_coeffs(self):\n",
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" C = self.curve\n",
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" g = self.f\n",
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" basis = C.basis_de_rham()\n",
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"\n",
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" def coordinates(self):\n",
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" print(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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" Rx.<x> = PolynomialRing(GF(p))\n",
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" Fx = FractionField(Rx)\n",
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" FxRy.<y> = PolynomialRing(Fx)\n",
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" g = C.genus()\n",
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" degrees0 = C.degree_de_rham(0)\n",
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" degrees0_inv = {b:a for a, b in degrees0.items()} \n",
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" degrees1 = C.degree_de_rham(1)\n",
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" degrees1_inv = {b:a for a, b in degrees1.items()}\n",
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" basis = C.basis_de_rham()\n",
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" \n",
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" omega = self.omega0\n",
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" fct = self.f\n",
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" \n",
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" if fct.function == Rx(0) and omega.form == Rx(0):\n",
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" for j in range(1, m):\n",
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" omega_j = Fx(omega.jth_component(j))\n",
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" if omega_j != Fx(0):\n",
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" d = d = degree_of_rational_fctn(omega_j)\n",
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" index = degrees0_inv[(d, j)]\n",
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" a = coeff_of_rational_fctn(omega_j)\n",
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" a1 = coeff_of_rational_fctn(basis[index].omega0.jth_component(j))\n",
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" elt = self - basis[index].mult(a/a1)\n",
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" return elt.coordinates() + a/a1*vector([GF(p)(i == index) for i in range(0, 2*g)])\n",
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" \n",
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" for j in range(1, m):\n",
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" fct_j = Fx(fct.jth_component(j))\n",
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" if (fct_j != Rx(0)):\n",
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" d = degree_of_rational_fctn(fct_j)\n",
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" \n",
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" if (d, j) in degrees1.values():\n",
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" index = degrees1_inv[(d, j)]\n",
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" a = coeff_of_rational_fctn(fct_j)\n",
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" a1 = coeff_of_rational_fctn(basis[index].f.jth_component(j))\n",
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" elt = self - basis[index].mult(a/a1)\n",
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" return elt.coordinates() + a/a1*vector([GF(p)(i == index) for i in range(0, 2*g)])\n",
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" \n",
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" if d<0:\n",
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" a = coeff_of_rational_fctn(fct_j)\n",
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" elt =- superelliptic_cech(C, elt.omega0, elt.f - FxRy(y^j*x^d)).mult(a)\n",
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" return elt.coordinates()\n",
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" \n",
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" if (fct_j != Rx(0)):\n",
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" G = superelliptic_function(C, y^j*x^d)\n",
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" a = coeff_of_rational_fctn(fct_j)\n",
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" elt =-superelliptic_cech(diffn(G), G).mult(a)\n",
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" return elt.coordinates()\n",
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"\n",
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" return vector(2*g*[0])\n",
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" \n",
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" \n",
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"def degree_of_rational_fctn(f):\n",
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"def degree_of_rational_fctn(f):\n",
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" Rx.<x> = PolynomialRing(GF(p))\n",
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" Rx.<x> = PolynomialRing(GF(p))\n",
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" d2 = f2.degree()\n",
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" d2 = f2.degree()\n",
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" return(d1 - d2)\n",
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" return(d1 - d2)\n",
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"\n",
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"\n",
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"def coeff_of_rational_fctn(f):\n",
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" Rx.<x> = PolynomialRing(GF(p))\n",
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" Fx = FractionField(Rx)\n",
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" f = Fx(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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" a1 = f1.coefficients(sparse = false)[d1]\n",
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" a2 = f2.coefficients(sparse = false)[d2]\n",
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" return(a1/a2)\n",
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"\n",
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"def coff(f, d):\n",
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"def coff(f, d):\n",
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" lista = f.coefficients(sparse = false)\n",
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" lista = f.coefficients(sparse = false)\n",
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" if len(lista) <= d:\n",
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" if len(lista) <= d:\n",
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@ -299,30 +401,86 @@
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},
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},
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{
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{
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"cell_type": "code",
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"cell_type": "code",
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"execution_count": 20,
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"execution_count": 116,
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"metadata": {},
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"metadata": {},
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"outputs": [
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"outputs": [
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{
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{
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"ename": "TypeError",
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"data": {
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"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'",
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"text/plain": [
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"{0: ((x/y) dx, 2/x*y, ((x^3*y^5 - x^3 + x - 1)/(x^2*y^6)) dx),\n",
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" 1: (((-1)/y) dx, 2/x^2*y, ((-x^3*y^5 + x^3 - 2*x - 2)/(x^3*y^6)) dx),\n",
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" 2: (((-2*x)/y^2) dx, 2/x*y^2, ((-2*x^3*y^3 + x^3 - 1)/(x^2*y^5)) dx),\n",
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" 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",
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" 4: ((1/y^3) dx, 0, (1/y^3) dx),\n",
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" 5: (0 dx, 2/x*y^3, ((-2*x^3 - x - 1)/(x^2*y^4)) dx),\n",
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" 6: ((1/y^4) dx, 0, (1/y^4) dx),\n",
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" 7: ((2*x/y^4) dx, 2/x*y^4, ((2*x^3 - 2*x*y - y)/(x^2*y^4)) dx),\n",
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" 8: ((1/y^5) dx, 0, (1/y^5) dx),\n",
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" 9: ((x/y^5) dx, 0, (x/y^5) dx),\n",
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" 10: ((1/y^6) dx, 0, (1/y^6) dx),\n",
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" 11: ((x/y^6) dx, 0, (x/y^6) dx)}"
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]
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},
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"execution_count": 116,
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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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"p = 5\n",
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"C = superelliptic(x^3 + x + 2, 7, p)\n",
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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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},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 113,
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [],
|
||||||
|
"source": [
|
||||||
|
"RxRy.<x, y> = PolynomialRing(GF(p), 2)\n",
|
||||||
|
"w1 = superelliptic_cech(C, superelliptic_form(C, (1/y^5)), superelliptic_function(C, 0))\n",
|
||||||
|
"w2 = superelliptic_cech(C, superelliptic_form(C,2*x/y^4), superelliptic_function(C, 2/x*y^4))\n",
|
||||||
|
"w = w1+w2+w2"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 114,
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [
|
||||||
|
{
|
||||||
|
"name": "stdout",
|
||||||
|
"output_type": "stream",
|
||||||
|
"text": [
|
||||||
|
"(((-x*y + 1)/y^5) dx, 4/x*y^4, ((-x^3*y + x*y^2 + x^2 - 2*y^2)/(x^2*y^5)) dx)\n"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"ename": "AttributeError",
|
||||||
|
"evalue": "'superelliptic_function' object has no attribute 'jth_coordinate'",
|
||||||
"output_type": "error",
|
"output_type": "error",
|
||||||
"traceback": [
|
"traceback": [
|
||||||
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
|
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
|
||||||
"\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)",
|
"\u001b[0;31mAttributeError\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-114-c2988137dec9>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mw\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[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",
|
"\u001b[0;32m<ipython-input-111-0f546555b2f0>\u001b[0m in \u001b[0;36mcoordinates\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 341\u001b[0m \u001b[0mindex\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdegrees1_inv\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md\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[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 342\u001b[0m \u001b[0ma\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcoeff_of_rational_fctn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfct_j\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 343\u001b[0;31m \u001b[0ma1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcoeff_of_rational_fctn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbasis\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mjth_coordinate\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[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 344\u001b[0m \u001b[0melt\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mbasis\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmult\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0ma1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 345\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0melt\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[0ma\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0ma1\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mvector\u001b[0m\u001b[0;34m(\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[0mi\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mindex\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\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[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mg\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[0;32m<ipython-input-19-a65119f7de4f>\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, C, g)\u001b[0m\n\u001b[1;32m 186\u001b[0m \u001b[0mRxy\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[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\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'y'\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[0my\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mRxy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_first_ngens\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 187\u001b[0m \u001b[0mFxy\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mFractionField\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mRxy\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 188\u001b[0;31m \u001b[0mg\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mFxy\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mreduction_form\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mC\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mg\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 189\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mform\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mg\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 190\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcurve\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mC\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
"\u001b[0;31mAttributeError\u001b[0m: 'superelliptic_function' object has no attribute 'jth_coordinate'"
|
||||||
"\u001b[0;32m<ipython-input-19-a65119f7de4f>\u001b[0m in \u001b[0;36mreduction_form\u001b[0;34m(C, g)\u001b[0m\n\u001b[1;32m 112\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mj\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[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 113\u001b[0m \u001b[0mG\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcoff\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mg\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[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 114\u001b[0;31m \u001b[0mg1\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0mG\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 115\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 116\u001b[0m \u001b[0mG\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcoff\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mg\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[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.__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'"
|
|
||||||
]
|
]
|
||||||
}
|
}
|
||||||
],
|
],
|
||||||
"source": [
|
"source": [
|
||||||
"C = superelliptic(x^3 + x + 2, 7, 5)\n",
|
"w.coordinates()"
|
||||||
"C.basis_de_rham()\n",
|
]
|
||||||
"#C.basis_holomorphic_differentials()"
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 65,
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [],
|
||||||
|
"source": [
|
||||||
|
"a, b, c = C.degree_and_basis_de_rham()"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
|
|
@ -653,6 +811,46 @@
|
||||||
"A.derivative(x)"
|
"A.derivative(x)"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 42,
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [],
|
||||||
|
"source": [
|
||||||
|
"dict1 = {}\n",
|
||||||
|
"dict1[3] = 5\n",
|
||||||
|
"dict1[6] = 121"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 46,
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [],
|
||||||
|
"source": [
|
||||||
|
"degrees1_inv = {b:a for a, b in dict1.items()}"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 47,
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [
|
||||||
|
{
|
||||||
|
"data": {
|
||||||
|
"text/plain": [
|
||||||
|
"{5: 3, 121: 6}"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"execution_count": 47,
|
||||||
|
"metadata": {},
|
||||||
|
"output_type": "execute_result"
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"source": [
|
||||||
|
"degrees1_inv"
|
||||||
|
]
|
||||||
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": null,
|
"execution_count": null,
|
||||||
|
|
|
||||||
Loading…
Reference in New Issue