487 lines
9.9 KiB
Plaintext
487 lines
9.9 KiB
Plaintext
{
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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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"metadata": {
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"collapsed": false,
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"jupyter": {
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"outputs_hidden": false
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}
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},
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"outputs": [],
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"source": [
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"S.<x, y, z> = PolynomialRing(QQ, order='neglex')\n",
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"f=((y^2+x^3)^2 + x^5*y)*((x^2+y^3)^2 + y^5*x)\n",
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"g=(y^6+x^7)*(x^6+y^7)\n",
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"h = f^3 - g^2\n",
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"F= z^3 - 3 * f * z + 2 * g"
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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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"metadata": {
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"collapsed": false,
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"jupyter": {
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"outputs_hidden": false
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}
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"0"
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]
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},
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"execution_count": 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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"h = f^3 - g^2\n",
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"F.discriminant(z) - 108 * h"
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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": 3,
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"metadata": {
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"collapsed": false,
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"jupyter": {
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"outputs_hidden": false
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}
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"True"
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]
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},
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"execution_count": 3,
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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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"D=F.discriminant(z)\n",
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"# load('ZetaFunctionsNewtonND.py')\n",
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"ZD = ZetaFunctions(D)\n",
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"ZD.is_newton_non_degenerated(local=True)"
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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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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"(-108) * y^26\n",
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"(-216) * x^6 * y^19\n",
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"(-108) * x^26\n",
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"(-216) * y^6 * x^19\n",
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"(-108) * y^19 * (y^7 + 2*x^6)\n",
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"(-216) * (y + x) * x^6 * y^6 * (y^12 - x*y^11 + x^2*y^10 - x^3*y^9 - 2*x^4*y^8 + 2*x^5*y^7 - 2*x^6*y^6 + 2*x^7*y^5 - 2*x^8*y^4 - x^9*y^3 + x^10*y^2 - x^11*y + x^12)\n",
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"(-108) * x^19 * (2*y^6 + x^7)\n"
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]
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}
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],
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"source": [
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"for p in ZD.get_polyfaces_dictionary(compact=True):\n",
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" print(p.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": 5,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"y^13\n",
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"x^6 * y^6\n",
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"x^13\n",
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"y^6 * (y^7 + x^6)\n",
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"x^6 * (y^6 + x^7)\n"
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]
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}
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],
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"source": [
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"for p in ZetaFunctions(g).get_polyfaces_dictionary(compact=True):\n",
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" print(p.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": 6,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"y^10\n",
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"x^10\n",
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"x^4 * y^4\n",
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"y^4 * (y^3 + x^2)^2\n",
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"x^4 * (y^2 + x^3)^2\n"
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]
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}
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],
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"source": [
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"for p in ZetaFunctions(f).get_polyfaces_dictionary(compact=True):\n",
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" print(p.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": 9,
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"metadata": {
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"collapsed": false,
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"jupyter": {
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"outputs_hidden": false
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}
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},
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"outputs": [],
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"source": [
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"def estrato(ff, chi, pesos):\n",
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" Z1 = ZetaFunctions(ff)\n",
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" zetamon1 = Z1.monodromy_zeta().value()^chi\n",
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" zetatop1 = chi * Z1.topological_zeta(local=True, weights=pesos)\n",
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" return zetamon1, zetatop1"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"collapsed": false,
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"jupyter": {
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"outputs_hidden": false
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}
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},
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"source": [
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"Veamos que la resolución larga no aporta\n",
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"\n"
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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": 10,
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"metadata": {},
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"outputs": [],
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"source": [
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"M39, Z39 = estrato(z^3+x^20*y^42*z+x^26*y^52, 1, [5,11,1])\n",
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"M98, Z98 = estrato(z^3+x^42*y^21*z+x^52*y^26, 1, [11,6,1])\n",
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"M38, Z38 = estrato(z^3+x^20*y^21*z+x^26*y^26, 1, [5,6,1])"
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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": 12,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"0"
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]
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},
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"execution_count": 12,
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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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"Z39 + Z98 - Z38"
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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": 13,
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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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"True"
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]
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},
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"execution_count": 13,
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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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"estrato(z^3+x^20*y^42*z+x^26*y^52, 1, [5,11,1]) == estrato(z^3+0*x^20*y^42*z+x^26*y^52, 1, [5,11,1])"
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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": 14,
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"metadata": {
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"collapsed": false,
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"jupyter": {
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"outputs_hidden": false
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}
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},
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"outputs": [],
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"source": [
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"M3, Z3 = estrato(z^3+x^20*z+x^26, 1, [5,1,1])\n",
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"M8, Z8 = estrato(z^3+x^21*z+x^26, 1, [6,1,1])"
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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": 15,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"0"
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]
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},
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"execution_count": 15,
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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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"Z38 + Z8 - Z3"
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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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"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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"((t + 1)^-2 * (t^2 - t + 1)^-1 * (t^2 + 1)^-1 * (t^4 - t^2 + 1)^-1 * (t^12 - t^11 + t^10 - t^9 + t^8 - t^7 + t^6 - t^5 + t^4 - t^3 + t^2 - t + 1)^-1,\n",
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" (19/156) * (s + 1/2)^-2 * (s + 1)^-1 * (s^2 + 48/19*s + 39/38))"
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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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"a, b = estrato(z^3+x^4*z^2+x^13, 1, [2,1,1])\n",
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"a.factor(), b.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": 19,
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"metadata": {},
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"outputs": [],
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"source": [
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"T.<s> = QQ[]"
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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": 28,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"0"
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]
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},
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"execution_count": 28,
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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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"A1 = 3 * s / (s + 1) / (78 * s + 39)\n",
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"V1 = 2 / (78 * s + 39)\n",
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"V2 = 1 / (78 * s + 39)\n",
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"M7, Z7 = estrato(z^3 + x^78, 1, [13,1,1])\n",
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"Z7 - (V1 + V2 - A1)"
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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": 30,
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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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"(8/39) * (s + 1/2)^-1 * (s + 1)^-1 * (s + 9/8)"
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]
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},
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"execution_count": 30,
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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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"M7a, Z7a = estrato(z^3 + x^13, 1, [13/6,1,1])\n",
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"Z7a.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": 37,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"0"
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]
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},
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"execution_count": 37,
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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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"(6 * V1 + 6 * V2 - 2 / 3 * A1 - Z7a)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"collapsed": false,
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"jupyter": {
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"outputs_hidden": false
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}
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},
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"source": [
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"Cálculo completo\n",
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"\n"
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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": 9,
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"metadata": {
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"collapsed": false,
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"jupyter": {
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"outputs_hidden": false
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}
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},
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"outputs": [
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{
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"ename": "SyntaxError",
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"evalue": "invalid syntax (3357930205.py, line 3)",
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"output_type": "error",
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"traceback": [
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"\u001b[0;36m Cell \u001b[0;32mIn [9], line 3\u001b[0;36m\u001b[0m\n\u001b[0;31m M17, Z17 = estrato(z**Integer(3)+, Integer(2), [Integer(2),Integer(13),Integer(1)])\u001b[0m\n\u001b[0m ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
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]
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}
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],
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"source": [
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"M1, Zt1 = estrato(z^3+x^4*z^2 + x^13, -13, [2,1,1])\n",
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"M1d, Zt1d = estrato(z^3+x^4*z^2 + x^13*y, 13, [2,1,1])\n",
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"M17, Z17 = estrato(z^3+x^4*y^28*z^2 + x^13*y^78 , 2, [2,13,1])\n",
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"M7, Z7 = estrato(z^3+x^4*z + x^13*y, -4, [13,1,1])\n",
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"M7d, Z7d = estrato(z^3+x^4*z + x^13*y, -4, [13,1,1])\n",
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"M7g, Z7g\n"
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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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"metadata": {
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"collapsed": false,
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"jupyter": {
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"outputs_hidden": false
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}
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Newton's polyhedron of z^3 + x^4*z + x^13:\n",
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" support points = [(0, 0, 3), (4, 0, 1), (13, 0, 0)]\n",
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" vertices = [(0, 0, 3), (4, 0, 1), (13, 0, 0)]\n",
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" number of proper faces = 15\n",
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" Facet 0: z >= 0\n",
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" Facet 1: -13 + 9*z + x >= 0\n",
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" Facet 2: -6 + 2*z + x >= 0\n",
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" Facet 3: x >= 0\n",
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" Facet 4: y >= 0\n"
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]
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},
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{
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"data": {
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"text/plain": [
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"(-1/6) * (s + 2/3)^-1 * (s + 1)^-1 * (s - 2)"
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]
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},
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"execution_count": 55,
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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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"G=z^3+x^4*z + x^13\n",
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"ZG=ZetaFunctions(G)\n",
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"ZG.give_info_newton(faces=False, cones=False, compact = False)\n",
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"ZG.topological_zeta(local= True, weights = [2,1,1])"
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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": null,
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"metadata": {
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"collapsed": false,
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"jupyter": {
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"outputs_hidden": false
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}
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},
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"outputs": [],
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"source": []
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false,
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"jupyter": {
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"outputs_hidden": false
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}
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},
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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 10.3.rc4",
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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": "3.11.1"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 4
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}
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