diff --git a/Suspension10.ipynb b/Suspension10.ipynb new file mode 100644 index 0000000..04e4a6c --- /dev/null +++ b/Suspension10.ipynb @@ -0,0 +1,319 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "60263160-66d3-45f7-a6cd-0042e5c5d37e", + "metadata": {}, + "outputs": [], + "source": [ + "R3. = PolynomialRing(QQ, order='negdeglex')\n", + "R2. = PolynomialRing(QQ, order='negdeglex')\n", + "R1. = QQ[]" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "3e206069-21d2-4ac7-80af-0f997622ce0e", + "metadata": {}, + "outputs": [], + "source": [ + "f = u^5 + v^6\n", + "F = z^10 + f(u=x, v=y)\n", + "Z = ZetaFunctions(F)" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "id": "38a0780c-be08-4a0a-a310-55b279c5528f", + "metadata": {}, + "outputs": [], + "source": [ + "zt = Z.topological_zeta(local=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "e1e6e6cb-1720-4de5-8a9f-751891aa189e", + "metadata": {}, + "outputs": [], + "source": [ + "g0 = v^10 - u^30\n", + "Z0 = ZetaFunctions(g0)\n", + "zt0 = Z0.topological_zeta(local=True, weights=[11, 1])" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "9d2955da-b2cb-4787-b71b-1a435ca6ae5d", + "metadata": {}, + "outputs": [], + "source": [ + "g1 = v^10 - u^6\n", + "Z1 = ZetaFunctions(g1)\n", + "zt1 = Z1.topological_zeta(local=True, weights=[11 / 5, 1])" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "9dce165f-4968-45b0-82bd-9da8322439a9", + "metadata": {}, + "outputs": [], + "source": [ + "g2 = v^10 - u^5\n", + "Z2 = ZetaFunctions(g2)\n", + "zt2 = Z2.topological_zeta(local=True, weights=[11 / 6, 1])" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "69595c54-4c36-47d8-8b69-f3cc40b345b6", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(1/110) * (s + 7/15)^-1 * (s + 1)^-1 * (s + 14/3)" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "g3 = z^10 - x^30 * y\n", + "Z3 = ZetaFunctions(g3)\n", + "zt3 = Z3.topological_zeta(local=True, weights=[11, 1, 1])" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "c7e0fa8e-f750-4945-aa62-6d7a82fed340", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "zt - (-zt0 + zt1 + zt2 + zt3)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "042d2c61-0ddf-4b13-b1ab-ade1de1c430e", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(-1/6) * (s + 7/15)^-1" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "zt10 = Z.topological_zeta(local=True, d=10)\n", + "zt10.factor()" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "1bcb4435-1f60-49a0-b26a-14bd6750bb9b", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1/5/(s + 7/15)" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "zt5 = Z.topological_zeta(local=True, d=5) - zt10\n", + "zt5" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "52bb0b78-f7a7-4717-9c11-25a4cec9de02", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1/6/(s + 7/15)" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "zt2 = Z.topological_zeta(local=True, d=2) - zt10\n", + "zt2" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "e613a530-bfa1-4fa1-9c7c-c52e12ccc1cc", + "metadata": {}, + "outputs": [], + "source": [ + "Zf = ZetaFunctions(f)" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "67800a77-a153-4e9d-9320-75d6db28cbbd", + "metadata": {}, + "outputs": [], + "source": [ + "ztf = Zf.topological_zeta(local=True)\n", + "ztf10 = Zf.topological_zeta(local=True, d=10)\n", + "ztf5 = Zf.topological_zeta(local=True, d=5) - ztf10\n", + "ztf2 = Zf.topological_zeta(local=True, d=2) - ztf10" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "id": "c9ba3ae1-9f6f-440d-961e-a16b3815287e", + "metadata": {}, + "outputs": [], + "source": [ + "p = s + 1 / 10" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "id": "faed1d1e-b23e-4da7-9fed-dd470f6fd1d9", + "metadata": {}, + "outputs": [], + "source": [ + "h = {}\n", + "h[1, 0] = 1 / 10 / p\n", + "h[1, 1] = 9 / 10 * s / (s + 1) * (p + 1) / p\n", + "h[1, 2] = 3 / 10 * s / (s + 1)\n", + "h[1, 5] = 24 / 10 * s / (s + 1)\n", + "h[1, 10] = 99 / 10 * s / (s + 1) \n", + "aux = h[1, 0] + h[1, 1] * ztf(s=p) - h[1, 2] * ztf2(s=p) - h[1, 5] * ztf5(s=p) - h[1, 10] * ztf10(s=p)" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "id": "2c8cd3e8-bc4a-417d-99c6-6903442387ba", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0" + ] + }, + "execution_count": 48, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "aux - zt" + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "id": "39ffdc08-85a3-48db-88f6-edb2b6dcd5c8", + "metadata": {}, + "outputs": [], + "source": [ + "h[2, 0] = 1 / 10 / p\n", + "h[2, 1] = 1 / 10 * (p + 1) / p\n", + "h[2, 2] = 7 / 10\n", + "h[2, 5] = -14 / 10\n", + "h[2, 10] = -89 / 10\n", + "aux = h[2, 0] + h[2, 1] * ztf(s=p) + h[2, 2] * ztf2(s=p) + h[2, 5] * ztf5(s=p) + h[2, 10] * ztf10(s=p)" + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "id": "52a2a318-3955-4fad-b5ea-83244a0282d0", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(1/10) * (s + 1/10)^-1 * (s + 7/15)^-1 * (s + 5/6)" + ] + }, + "execution_count": 64, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(aux - zt2).factor()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3a775a53-ee34-4241-acca-7e768f3cf51d", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "SageMath 10.3.rc3", + "language": "sage", + "name": "sagemath-310" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.1" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}