1080 lines
24 KiB
Plaintext
1080 lines
24 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "e8d28f5d-556f-4e0d-9ec8-e039ca35cdf4",
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"metadata": {},
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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": 2,
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"id": "555b4804-430a-43cd-8c2e-1292899c6ea7",
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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) * (t - 1) * (t + 1) * (t^4 - t^3 + t^2 - t + 1) * (t^4 + t^3 + t^2 + t + 1) * (t^6 + t^3 + 1),\n",
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" (-11/90) * (s + 8/9)^-1 * (s + 9/10)^-1 * (s + 1)^-1 * (s^2 - 69/11*s - 72/11),\n",
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" x^5*y^2 + x^2*y^4)"
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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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"load('../Descargas/ZetaFunctionsNewtonND.py')\n",
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"R.<x,y,z> = QQ[]\n",
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"F = z^3+(y^2+x^3)*z+x^2*y^2\n",
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"Z = ZetaFunctions(F)\n",
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"Zmon=Z.monodromy_zeta()\n",
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"Ztop=Z.topological_zeta(local = True)\n",
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"g=(y^2+x^3)*x^2*y^2\n",
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"Zmon, Ztop, g"
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]
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},
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{
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"cell_type": "markdown",
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"id": "b6ea28e6-3ece-4e52-a34a-e00bdf345007",
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"metadata": {},
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"source": [
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"Primera explosión ---> divisor E_1 (6,2)"
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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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"id": "adf9be35-2eda-463f-9581-0f17b879eacb",
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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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"(x^5*y + x^2,\n",
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" x^3*y^3*z + x^2*y^4 + y^2*z + z^3,\n",
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" y^4 + x*y^2,\n",
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" x^4*y^2 + x^2*y^2*z + x^3*z + z^3)"
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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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"g1=g(x=x*y)/y^6\n",
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"F1=F(x=x*y)\n",
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"g1b=g(y=x*y)/x^6\n",
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"F1b=F(y=x*y)\n",
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"g1,F1, g1b, F1b"
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]
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},
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{
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"cell_type": "markdown",
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"id": "1f1c1819-19bc-45c7-8bec-ddd1b9380b55",
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"metadata": {},
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"source": [
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"Aportación de estrato de intersección E_1 (6,2) y g_2=x2"
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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": 26,
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"id": "fa867c2c-1819-4500-bf4b-fd29acfdeb14",
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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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"((-1/2) * (s + 1)^-2 * (s - 1), (-1) * (t - 1)^-1 * (t^2 + t + 1)^-1)"
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]
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},
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"execution_count": 26,
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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(F1)\n",
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"A1=Z1.topological_zeta(local=True, weights=[1,2,1])\n",
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"M1=Z1.monodromy_zeta()\n",
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"A1, M1"
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]
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},
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{
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"cell_type": "markdown",
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"id": "cbef6f22-df04-4d42-ac7f-87917c7d2619",
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"metadata": {},
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"source": [
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"Aportación de estrato abierto de E_1 (6,2)"
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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": 27,
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"id": "239b3798-b6a7-43bb-a94c-d29a366d5617",
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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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"((-1/2) * (s + 1)^-2 * (s - 1), (-1) * (t - 1)^-1 * (t^2 + t + 1)^-1)"
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]
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},
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"execution_count": 27,
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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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"F1t=F1(x=x+2)\n",
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"Z1t = ZetaFunctions(F1t)\n",
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"A1t=Z1t.topological_zeta(local=True, weights=[1,2,1])\n",
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"M1t=Z1t.monodromy_zeta()\n",
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"A1t, M1t"
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]
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},
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{
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"cell_type": "markdown",
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"id": "76776c98-c8d4-499a-a1ee-6aca1d182c21",
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"metadata": {},
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"source": [
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"Segunda explosión E_2 (9,3)"
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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": 28,
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"id": "062e5987-292d-4e31-996a-db366df666b9",
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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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"(x + y,\n",
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" x^4*y^6 + x^3*y^3*z + x^2*y^4*z + z^3,\n",
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" x*y^4 + y^2,\n",
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" x^6*y^2 + x^4*y^2*z + x^3*z + z^3)"
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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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"g2=g1b(x=x*y)/y^3\n",
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"F2=F1b(x=x*y)\n",
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"g2b=g1b(y=x*y)/x^3\n",
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"F2b=F1b(y=x*y)\n",
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"g2, F2, g2b, F2b"
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]
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},
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{
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"cell_type": "markdown",
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"id": "40cd5f3c-2358-466a-9107-27b2dfe415a2",
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"metadata": {},
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"source": [
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"Aportación de estrato de intersección E_2 (9,3) y g_3=y2"
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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": 29,
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"id": "2c6a512e-4d1f-41af-936d-43065a2bef90",
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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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"((1/3) * (s + 1)^-2, (t^6 + t^3 + 1)^-1)"
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]
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},
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"execution_count": 29,
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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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"Z2b = ZetaFunctions(F2b)\n",
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"A2b=Z2b.topological_zeta(local=True, weights=[3,1,1])\n",
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"M2b=Z2b.monodromy_zeta()\n",
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"A2b, M2b"
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]
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},
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{
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"cell_type": "markdown",
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"id": "330f44ff-7833-44c3-a4fa-0e646237ab49",
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"metadata": {},
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"source": [
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"Aportación de estrato abierto de E_1 (6,2)"
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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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"id": "8948fe24-90c2-450c-a6cc-134a2c82d080",
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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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"((1/3) * (s + 1)^-2, (t^6 + t^3 + 1)^-1)"
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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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"F2t=F2(x=x+3)\n",
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"Z2t = ZetaFunctions(F2t)\n",
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"A2t=Z2t.topological_zeta(local=True, weights=[1,3,1])\n",
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"M2t=Z2t.monodromy_zeta()\n",
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"A2t, M2t"
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]
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},
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{
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"cell_type": "markdown",
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"id": "2efb4eb5-e6bd-43de-8b96-bf3bce3119f6",
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"metadata": {},
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"source": [
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"Tercera explosión E_3 (16,5)"
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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": 31,
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"id": "dd7d3923-e444-4f72-8b3b-cd093db11ed5",
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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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"(x + 1,\n",
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" x^4*y^10 + x^3*y^6*z + x^2*y^6*z + z^3,\n",
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" y + 1,\n",
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" x^10*y^6 + x^6*y^4*z + x^6*y^3*z + z^3)"
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]
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},
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"execution_count": 31,
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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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"g3=g2(x=x*y)/y\n",
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"F3=F2(x=x*y)\n",
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"g3b=g2(y=x*y)/x\n",
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"F3b=F2(y=x*y)\n",
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"g3, F3, g3b, F3b"
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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": 32,
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"id": "61cd0e41-ae53-4dc2-a822-5992ab34d2e2",
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"metadata": {},
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"outputs": [
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{
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"ename": "SyntaxError",
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"evalue": "invalid syntax (1948788351.py, line 1)",
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"output_type": "error",
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"traceback": [
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"\u001b[0;36m Cell \u001b[0;32mIn [32], line 1\u001b[0;36m\u001b[0m\n\u001b[0;31m Aportación de intersección de E_1 (Integer(6),Integer(2)) y E_3 (Integer(16),Integer(5))\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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"Aportación de intersección de E_1 (6,2) y E_3 (16,5)"
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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": 33,
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"id": "e74156ef-b808-4581-9fe5-72cd237c73c3",
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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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"((1/30) * (s + 1)^-2 * (s + 8/9)^-1 * (s^2 + 1/3*s + 8/3),\n",
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" (-1) * (t - 1) * (t^2 + t + 1))"
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]
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},
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"execution_count": 33,
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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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"Z13 = ZetaFunctions(F3)\n",
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"A13=Z13.topological_zeta(local=True, weights=[2,5,1])\n",
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"M13=Z13.monodromy_zeta()\n",
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"A13, M13"
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]
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},
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{
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"cell_type": "markdown",
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"id": "fdc916f8-9529-4a65-b3f5-ca51808d95e3",
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"metadata": {},
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"source": [
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"Aportación de intersección de E_2 (9,3) y E_3 (16,5)"
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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": 34,
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"id": "699c1fd9-b59c-468d-9e17-63e6b189eb64",
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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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"((1/30) * (s + 1)^-2 * (s + 8/9)^-1 * (s^2 + 1/3*s + 8/3),\n",
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" (-1) * (t - 1) * (t^2 + t + 1))"
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]
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},
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"execution_count": 34,
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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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"Z23 = ZetaFunctions(F3b)\n",
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"A23=Z23.topological_zeta(local=True, weights=[5,3,1])\n",
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"M23=Z23.monodromy_zeta()\n",
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"A13, M23"
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]
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},
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{
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"cell_type": "markdown",
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"id": "f8c4cef1-0d85-4dd1-9c84-1feeeebd81c7",
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"metadata": {},
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"source": [
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"Aportación de estrato abierto de E_3 (16,5)"
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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": 35,
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"id": "253d9222-7bfb-463a-bca6-6aa883f9eda9",
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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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"((-7/45) * (s + 8/9)^-1 * (s + 1)^-1 * (s - 8/7),\n",
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" (-1) * (t - 1)^-1 * (t^2 + t + 1)^-1 * (t^6 + t^3 + 1)^-2)"
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]
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},
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"execution_count": 35,
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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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"F3t=F3(x=x+3)\n",
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"Z3t = ZetaFunctions(F3t)\n",
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"A3t=Z3t.topological_zeta(local=True, weights=[1,5,1])\n",
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"M3t=Z3t.monodromy_zeta()\n",
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"A3t, M3t"
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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": 36,
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"id": "52ccfc68-0bb7-47ee-b70c-e9e2982bc645",
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"metadata": {},
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"outputs": [
|
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{
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"data": {
|
|
"text/plain": [
|
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"((-7/45) * (s + 8/9)^-1 * (s + 1)^-1 * (s - 8/7),\n",
|
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" (-1) * (t - 1)^-1 * (t^2 + t + 1)^-1 * (t^6 + t^3 + 1)^-2)"
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]
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},
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"execution_count": 36,
|
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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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"F3bt=F3b(y=y+3)\n",
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"Z3bt = ZetaFunctions(F3bt)\n",
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"A3bt=Z3bt.topological_zeta(local=True, weights=[5,1,1])\n",
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"M3bt=Z3bt.monodromy_zeta()\n",
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"A3bt, M3bt"
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]
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},
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{
|
|
"cell_type": "markdown",
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|
"id": "1fd26ac5-19fd-4dad-9015-87354ac4074a",
|
|
"metadata": {},
|
|
"source": [
|
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"Aportación de intersección de E_3 (16,5) y g_1"
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|
]
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|
},
|
|
{
|
|
"cell_type": "code",
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|
"execution_count": 37,
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|
"id": "ed999fd8-d5fc-4f59-a1b1-a5162637d51b",
|
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"metadata": {},
|
|
"outputs": [
|
|
{
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"data": {
|
|
"text/plain": [
|
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"((1/6) * (s + 8/9)^-1 * (s + 9/10)^-1 * (s + 1)^-1 * (s^2 + 142/75*s + 24/25),\n",
|
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" (t + 1) * (t - 1)^2 * (t^2 + t + 1) * (t^4 - t^3 + t^2 - t + 1) * (t^4 + t^3 + t^2 + t + 1))"
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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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"F30=F3(x=x-1)\n",
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"Z30 = ZetaFunctions(F30)\n",
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"A30=Z30.topological_zeta(local=True, weights=[1,5,1])\n",
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"M30=Z30.monodromy_zeta()\n",
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"A30, M30"
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]
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},
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|
{
|
|
"cell_type": "code",
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|
"execution_count": 38,
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|
"id": "7856f357-7f92-49c5-a87c-0684a24f93fd",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
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"data": {
|
|
"text/plain": [
|
|
"((1/6) * (s + 8/9)^-1 * (s + 9/10)^-1 * (s + 1)^-1 * (s^2 + 142/75*s + 24/25),\n",
|
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" (t + 1) * (t - 1)^2 * (t^2 + t + 1) * (t^4 - t^3 + t^2 - t + 1) * (t^4 + t^3 + t^2 + t + 1))"
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]
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},
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"execution_count": 38,
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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": [
|
|
"F3b0=F3b(y=y-1)\n",
|
|
"Z3b0 = ZetaFunctions(F3b0)\n",
|
|
"A3b0=Z3b0.topological_zeta(local=True, weights=[5,1,1])\n",
|
|
"M3b0=Z3b0.monodromy_zeta()\n",
|
|
"A3b0, M3b0"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "dc98fc4f-cb55-4c1b-ab70-74da3356a3d5",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "2214bc22-c6f8-4cf1-b7b3-7ef60d1bf5e5",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 49,
|
|
"id": "9328b08b-cc6a-42fa-818f-c9c6b237f40b",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"0"
|
|
]
|
|
},
|
|
"execution_count": 49,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"T.<s> = QQ[]\n",
|
|
"A=A1+A2b+A13+A23-A3t+A30\n",
|
|
"B=(-11/90) * (s + 8/9)^-1 * (s + 9/10)^-1 * (s + 1)^-1 * (s^2 - 69/11*s - 72/11)\n",
|
|
"A-B"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "95641a8c-4454-45fa-8353-9278d5937ee3",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "7eea46a4-1439-40de-a16c-be14ce2de2fa",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "2bb58afd",
|
|
"metadata": {},
|
|
"source": []
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 24,
|
|
"id": "823aaa80",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"((-1) * (t - 1) * (t + 1) * (t^4 - t^3 + t^2 - t + 1) * (t^4 + t^3 + t^2 + t + 1) * (t^6 + t^3 + 1),\n",
|
|
" (-11/90) * (s + 8/9)^-1 * (s + 9/10)^-1 * (s + 1)^-1 * (s^2 - 69/11*s - 72/11),\n",
|
|
" x^5*y^2 + x^2*y^4)"
|
|
]
|
|
},
|
|
"execution_count": 24,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"load('ZetaFunctionsNewtonND.py')\n",
|
|
"R.<x,y,z> = QQ[]\n",
|
|
"F = z^3+(y^2+x^3)*z+x^2*y^2\n",
|
|
"Z = ZetaFunctions(F)\n",
|
|
"Zmon=Z.monodromy_zeta()\n",
|
|
"Ztop=Z.topological_zeta(local = True)\n",
|
|
"g=(y^2+x^3)*x^2*y^2\n",
|
|
"Zmon, Ztop, g"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "70c3cf27",
|
|
"metadata": {},
|
|
"source": [
|
|
"Primera explosión ---> divisor E_1 (6,2)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 25,
|
|
"id": "b68f383a",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"(x^5*y + x^2,\n",
|
|
" x^3*y^3*z + x^2*y^4 + y^2*z + z^3,\n",
|
|
" y^4 + x*y^2,\n",
|
|
" x^4*y^2 + x^2*y^2*z + x^3*z + z^3)"
|
|
]
|
|
},
|
|
"execution_count": 25,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"g1=g(x=x*y)/y^6\n",
|
|
"F1=F(x=x*y)\n",
|
|
"g1b=g(y=x*y)/x^6\n",
|
|
"F1b=F(y=x*y)\n",
|
|
"g1,F1, g1b, F1b"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "aacd2b71",
|
|
"metadata": {},
|
|
"source": [
|
|
"Aportación de estrato de intersección E_1 (6,2) y g_2=x2"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 26,
|
|
"id": "80675fc5",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"((-1/2) * (s + 1)^-2 * (s - 1), (-1) * (t - 1)^-1 * (t^2 + t + 1)^-1)"
|
|
]
|
|
},
|
|
"execution_count": 26,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"Z1 = ZetaFunctions(F1)\n",
|
|
"A1=Z1.topological_zeta(local=True, weights=[1,2,1])\n",
|
|
"M1=Z1.monodromy_zeta()\n",
|
|
"A1, M1"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "724f3e35",
|
|
"metadata": {},
|
|
"source": [
|
|
"Aportación de estrato abierto de E_1 (6,2)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 27,
|
|
"id": "c78f4bf8",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"((-1/2) * (s + 1)^-2 * (s - 1), (-1) * (t - 1)^-1 * (t^2 + t + 1)^-1)"
|
|
]
|
|
},
|
|
"execution_count": 27,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"F1t=F1(x=x+2)\n",
|
|
"Z1t = ZetaFunctions(F1t)\n",
|
|
"A1t=Z1t.topological_zeta(local=True, weights=[1,2,1])\n",
|
|
"M1t=Z1t.monodromy_zeta()\n",
|
|
"A1t, M1t"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "d5b62001",
|
|
"metadata": {},
|
|
"source": [
|
|
"Segunda explosión E_2 (9,3)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 28,
|
|
"id": "5918cb49",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"(x + y,\n",
|
|
" x^4*y^6 + x^3*y^3*z + x^2*y^4*z + z^3,\n",
|
|
" x*y^4 + y^2,\n",
|
|
" x^6*y^2 + x^4*y^2*z + x^3*z + z^3)"
|
|
]
|
|
},
|
|
"execution_count": 28,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"g2=g1b(x=x*y)/y^3\n",
|
|
"F2=F1b(x=x*y)\n",
|
|
"g2b=g1b(y=x*y)/x^3\n",
|
|
"F2b=F1b(y=x*y)\n",
|
|
"g2, F2, g2b, F2b"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "d60dcc57",
|
|
"metadata": {},
|
|
"source": [
|
|
"Aportación de estrato de intersección E_2 (9,3) y g_3=y2"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 29,
|
|
"id": "7c5fb9eb",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"((1/3) * (s + 1)^-2, (t^6 + t^3 + 1)^-1)"
|
|
]
|
|
},
|
|
"execution_count": 29,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"Z2b = ZetaFunctions(F2b)\n",
|
|
"A2b=Z2b.topological_zeta(local=True, weights=[3,1,1])\n",
|
|
"M2b=Z2b.monodromy_zeta()\n",
|
|
"A2b, M2b"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "4a56a110",
|
|
"metadata": {},
|
|
"source": [
|
|
"Aportación de estrato abierto de E_1 (6,2)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 30,
|
|
"id": "4079d302",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"((1/3) * (s + 1)^-2, (t^6 + t^3 + 1)^-1)"
|
|
]
|
|
},
|
|
"execution_count": 30,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"F2t=F2(x=x+3)\n",
|
|
"Z2t = ZetaFunctions(F2t)\n",
|
|
"A2t=Z2t.topological_zeta(local=True, weights=[1,3,1])\n",
|
|
"M2t=Z2t.monodromy_zeta()\n",
|
|
"A2t, M2t"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "95e60d58",
|
|
"metadata": {},
|
|
"source": [
|
|
"Tercera explosión E_3 (16,5)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 31,
|
|
"id": "69cffddc",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"(x + 1,\n",
|
|
" x^4*y^10 + x^3*y^6*z + x^2*y^6*z + z^3,\n",
|
|
" y + 1,\n",
|
|
" x^10*y^6 + x^6*y^4*z + x^6*y^3*z + z^3)"
|
|
]
|
|
},
|
|
"execution_count": 31,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"g3=g2(x=x*y)/y\n",
|
|
"F3=F2(x=x*y)\n",
|
|
"g3b=g2(y=x*y)/x\n",
|
|
"F3b=F2(y=x*y)\n",
|
|
"g3, F3, g3b, F3b"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 32,
|
|
"id": "15da5854",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"ename": "SyntaxError",
|
|
"evalue": "invalid syntax (1948788351.py, line 1)",
|
|
"output_type": "error",
|
|
"traceback": [
|
|
"\u001b[0;36m Cell \u001b[0;32mIn [32], line 1\u001b[0;36m\u001b[0m\n\u001b[0;31m Aportación de intersección de E_1 (Integer(6),Integer(2)) y E_3 (Integer(16),Integer(5))\u001b[0m\n\u001b[0m ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"Aportación de intersección de E_1 (6,2) y E_3 (16,5)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 33,
|
|
"id": "c2f28966",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"((1/30) * (s + 1)^-2 * (s + 8/9)^-1 * (s^2 + 1/3*s + 8/3),\n",
|
|
" (-1) * (t - 1) * (t^2 + t + 1))"
|
|
]
|
|
},
|
|
"execution_count": 33,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"Z13 = ZetaFunctions(F3)\n",
|
|
"A13=Z13.topological_zeta(local=True, weights=[2,5,1])\n",
|
|
"M13=Z13.monodromy_zeta()\n",
|
|
"A13, M13"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "d5937892",
|
|
"metadata": {},
|
|
"source": [
|
|
"Aportación de intersección de E_2 (9,3) y E_3 (16,5)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 34,
|
|
"id": "3b735845",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"((1/30) * (s + 1)^-2 * (s + 8/9)^-1 * (s^2 + 1/3*s + 8/3),\n",
|
|
" (-1) * (t - 1) * (t^2 + t + 1))"
|
|
]
|
|
},
|
|
"execution_count": 34,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"Z23 = ZetaFunctions(F3b)\n",
|
|
"A23=Z23.topological_zeta(local=True, weights=[5,3,1])\n",
|
|
"M23=Z23.monodromy_zeta()\n",
|
|
"A13, M23"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "11af23cc",
|
|
"metadata": {},
|
|
"source": [
|
|
"Aportación de estrato abierto de E_3 (16,5)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 35,
|
|
"id": "ac2bc045",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"((-7/45) * (s + 8/9)^-1 * (s + 1)^-1 * (s - 8/7),\n",
|
|
" (-1) * (t - 1)^-1 * (t^2 + t + 1)^-1 * (t^6 + t^3 + 1)^-2)"
|
|
]
|
|
},
|
|
"execution_count": 35,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"F3t=F3(x=x+3)\n",
|
|
"Z3t = ZetaFunctions(F3t)\n",
|
|
"A3t=Z3t.topological_zeta(local=True, weights=[1,5,1])\n",
|
|
"M3t=Z3t.monodromy_zeta()\n",
|
|
"A3t, M3t"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 36,
|
|
"id": "634cf890",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"((-7/45) * (s + 8/9)^-1 * (s + 1)^-1 * (s - 8/7),\n",
|
|
" (-1) * (t - 1)^-1 * (t^2 + t + 1)^-1 * (t^6 + t^3 + 1)^-2)"
|
|
]
|
|
},
|
|
"execution_count": 36,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"F3bt=F3b(y=y+3)\n",
|
|
"Z3bt = ZetaFunctions(F3bt)\n",
|
|
"A3bt=Z3bt.topological_zeta(local=True, weights=[5,1,1])\n",
|
|
"M3bt=Z3bt.monodromy_zeta()\n",
|
|
"A3bt, M3bt"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "692b49ed",
|
|
"metadata": {},
|
|
"source": [
|
|
"Aportación de intersección de E_3 (16,5) y g_1"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 37,
|
|
"id": "bb1fe1fb",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"((1/6) * (s + 8/9)^-1 * (s + 9/10)^-1 * (s + 1)^-1 * (s^2 + 142/75*s + 24/25),\n",
|
|
" (t + 1) * (t - 1)^2 * (t^2 + t + 1) * (t^4 - t^3 + t^2 - t + 1) * (t^4 + t^3 + t^2 + t + 1))"
|
|
]
|
|
},
|
|
"execution_count": 37,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"F30=F3(x=x-1)\n",
|
|
"Z30 = ZetaFunctions(F30)\n",
|
|
"A30=Z30.topological_zeta(local=True, weights=[1,5,1])\n",
|
|
"M30=Z30.monodromy_zeta()\n",
|
|
"A30, M30"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 38,
|
|
"id": "449e86f1",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"((1/6) * (s + 8/9)^-1 * (s + 9/10)^-1 * (s + 1)^-1 * (s^2 + 142/75*s + 24/25),\n",
|
|
" (t + 1) * (t - 1)^2 * (t^2 + t + 1) * (t^4 - t^3 + t^2 - t + 1) * (t^4 + t^3 + t^2 + t + 1))"
|
|
]
|
|
},
|
|
"execution_count": 38,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"F3b0=F3b(y=y-1)\n",
|
|
"Z3b0 = ZetaFunctions(F3b0)\n",
|
|
"A3b0=Z3b0.topological_zeta(local=True, weights=[5,1,1])\n",
|
|
"M3b0=Z3b0.monodromy_zeta()\n",
|
|
"A3b0, M3b0"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "66af979c",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "961e7c1f",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 49,
|
|
"id": "a269acd5",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"0"
|
|
]
|
|
},
|
|
"execution_count": 49,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"T.<s> = QQ[]\n",
|
|
"A=A1+A2b+A13+A23-A3t+A30\n",
|
|
"B=(-11/90) * (s + 8/9)^-1 * (s + 9/10)^-1 * (s + 1)^-1 * (s^2 - 69/11*s - 72/11)\n",
|
|
"A-B"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "7d561179",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "5894ac92",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "SageMath 10.3",
|
|
"language": "sage",
|
|
"name": "sagemath"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 3
|
|
},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython3",
|
|
"version": "3.12.2"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|