From fb60056eba2fc22e4bb52342035b0e20f454cf56 Mon Sep 17 00:00:00 2001 From: Enrique Artal Date: Fri, 28 Jun 2024 10:47:04 +0200 Subject: [PATCH] deformacion generica 1 --- DeformacionGenerica.ipynb | 376 ++++++++++++++++++++++++++++++++++++++ 1 file changed, 376 insertions(+) create mode 100644 DeformacionGenerica.ipynb diff --git a/DeformacionGenerica.ipynb b/DeformacionGenerica.ipynb new file mode 100644 index 0000000..9213037 --- /dev/null +++ b/DeformacionGenerica.ipynb @@ -0,0 +1,376 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "72d5a30c-1a59-4a55-9680-fdfa7979625b", + "metadata": {}, + "outputs": [], + "source": [ + "# load('zetas_triples_general.py')\n", + "R. = PolynomialRing(QQ, order='neglex')\n", + "S. = PolynomialRing(QQ, order='neglex')\n", + "f = (v - u^2)^2 + u * v^3\n", + "g = f^2 + v^6\n", + "p = v - u^2\n", + "F = z^3 - 3 * f(u=x, v=y) * z + 2 * g(u=x, v=y)\n", + "h = F.discriminant(z)(x=u, y=v)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "57f4e587-fd6a-4aa2-8423-78e8b5f0d2dd", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "41" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "F.jacobian_ideal().vector_space_dimension()" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "93b0a2d7-b561-4251-a991-34e8c69fbf89", + "metadata": {}, + "outputs": [], + "source": [ + "# (F + 1 * p(u=x, v=y) * z^2).jacobian_ideal().vector_space_dimension()" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "id": "a932f83b-81ad-47d2-8c2e-b944239fc364", + "metadata": {}, + "outputs": [], + "source": [ + "# load('zetas_triples_general.py')\n", + "R. = PolynomialRing(QQ, order='neglex')\n", + "S. = PolynomialRing(QQ, order='neglex')\n", + "f = v^2 - u^7 + u^5 * v\n", + "f2 = v^2\n", + "g = f^2 + (v + u^2)^6\n", + "g1 = 3 / 2 * v * f\n", + "g3 = v^3\n", + "F = z^3 - 3 * f(u=x, v=y) * z + 2 * g(u=x, v=y)\n", + "h = F.discriminant(z)(x=u, y=v)" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "id": "65fb99b3-89fb-4fb7-a0d4-667050dd5cab", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "41" + ] + }, + "execution_count": 44, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "F.jacobian_ideal().vector_space_dimension()" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "id": "8cc358aa-03d1-4b9c-b4ff-87b0324bd55b", + "metadata": {}, + "outputs": [], + "source": [ + "t = -3\n", + "F1 = F - 3 * f2(u=x, v=y) * t^2 * z + 2 * g1(u=x, v=y) * t + 2 * g3(u=x, v=y) * t^3" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "id": "d21a93b0-b0c4-4cd2-b648-f4bca8f78376", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "41" + ] + }, + "execution_count": 54, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "F1.jacobian_ideal().vector_space_dimension()" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "id": "9974eefe-db38-4da1-b438-eb56f6effbe4", + "metadata": {}, + "outputs": [], + "source": [ + "def nwt(p):\n", + " return p(u=u^2, v=u^7 * (v + 1))" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "id": "05705617-d0f6-464a-a9a0-4cefb5bce4d1", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "u^14 * (2*v + v^2 + u^3 + u^3*v)" + ] + }, + "execution_count": 48, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "nwt(f).factor()" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "id": "4eb24e43-3a10-4db9-8502-8c62289a3fe7", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "u^24 * (1 + 6*u^3 + 6*u^3*v + 4*u^4*v^2 + 4*u^4*v^3 + u^4*v^4 + 15*u^6 + 30*u^6*v + 15*u^6*v^2 + 4*u^7*v + 6*u^7*v^2 + 2*u^7*v^3 + 20*u^9 + 60*u^9*v + 60*u^9*v^2 + 20*u^9*v^3 + u^10 + 2*u^10*v + u^10*v^2 + 15*u^12 + 60*u^12*v + 90*u^12*v^2 + 60*u^12*v^3 + 15*u^12*v^4 + 6*u^15 + 30*u^15*v + 60*u^15*v^2 + 60*u^15*v^3 + 30*u^15*v^4 + 6*u^15*v^5 + u^18 + 6*u^18*v + 15*u^18*v^2 + 20*u^18*v^3 + 15*u^18*v^4 + 6*u^18*v^5 + u^18*v^6)" + ] + }, + "execution_count": 49, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "nwt(g).factor()" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "id": "28776340-947d-4ed6-a492-79f9341b9f18", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(1 + v)^2 * u^14" + ] + }, + "execution_count": 50, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "nwt(f2).factor()" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "id": "358b6044-7de1-4bfe-9e4f-283adfc93aca", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(3/2) * (1 + v) * u^21 * (2*v + v^2 + u^3 + u^3*v)" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "nwt(g1).factor()" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "id": "cda085bf-987d-44c2-8dbd-ae21afaa3251", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(1 + v)^3 * u^21" + ] + }, + "execution_count": 40, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "nwt(g3).factor()" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "id": "9684ce50-7ff0-4b4c-9580-497c3e3b3964", + "metadata": {}, + "outputs": [], + "source": [ + "h1 = F1.discriminant(z)(x=u, y=v)" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "id": "220532f1-226a-4898-9ff8-5f0344a7de16", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[(-27) * (v^2 - u^7) * (3965*v^4 + 2735*u^7*v^2 + 2048*u^14)]" + ] + }, + "execution_count": 42, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Z1 = ZetaFunctions(h1)\n", + "[q.factor() for q in Z1.get_polyfaces_dictionary(compact=True) if q.number_of_terms() > 1]" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "17c661cd-7293-41a1-b9ec-2e71269ae582", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[(108) * u^21 * (3*v^2 - 2*u^3)]" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "h1a = S(h1(u=u^2, v=u^7 * (1 + v)) / u^21)\n", + "Z1a = ZetaFunctions(h1a)\n", + "[q.factor() for q in Z1a.get_polyfaces_dictionary(compact=True) if q.number_of_terms() > 1]" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "id": "aa670fe5-7aa2-4b88-9e85-4351e528b2a1", + "metadata": {}, + "outputs": [], + "source": [ + "Rt. = QQ[]\n", + "Ft = Rt(F - 3 * f2(u=x, v=y) * t^2 * z + 2 * g1(u=x, v=y) * t + 2 * g3(u=x, v=y) * t^3)" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "id": "198a37ca-5a9d-4fe4-8949-e9ca06d48119", + "metadata": {}, + "outputs": [], + "source": [ + "J = Rt.ideal([Ft.derivative(a) for a in Rt.gens()[:-1]] + [Ft])" + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "id": "77792a73-db8e-43a5-93b7-dacb75f92c4f", + "metadata": {}, + "outputs": [], + "source": [ + "Gt = Ft(z=z + y * t)" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "id": "18ec2301-7665-436a-9a9c-e1070d99dfd1", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3*y*z^2" + ] + }, + "execution_count": 67, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Gt.derivative(t)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0fa40cb1-67c3-40c4-bf4b-60dd202979d2", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "SageMath 10.4.rc0", + "language": "sage", + "name": "sagemath-devel" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.3" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}