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