{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "03414fb8-f6f5-4796-a227-6aeed863ab6c", "metadata": {}, "outputs": [], "source": [ "T. = QQ[]\n", "S. = PolynomialRing(QQ, order='neglex')\n", "R. = PolynomialRing(QQ, order='neglex')\n", "f = u^2 * v^2 + u^5 + v^5\n", "g = u^3 * v^3 + u^7 + v^7\n", "F = z^3 - 3 * f(u=x, v=y) * z + 2 * g(u=x, v=y)" ] }, { "cell_type": "code", "execution_count": 2, "id": "c17bb619-1df9-4ea5-bfce-7f77cf56e00d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[Ideal (z, y, x) of Multivariate Polynomial Ring in x, y, z over Rational Field]" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "F.jacobian_ideal().minimal_associated_primes()" ] }, { "cell_type": "code", "execution_count": 3, "id": "f65646af-e328-430f-991d-10a0c2348fee", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h = f^3 - g^2\n", "F.discriminant(z)(x=u, y=v) - 108 * h" ] }, { "cell_type": "code", "execution_count": 4, "id": "00201766-5028-41ba-a13e-4740790a538e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "65" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "F.jacobian_ideal().vector_space_dimension()" ] }, { "cell_type": "code", "execution_count": 5, "id": "d0ebfd8e-9c6f-4dc1-8230-9f3dfcaa2b4d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "148" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h.jacobian_ideal().vector_space_dimension()" ] }, { "cell_type": "code", "execution_count": 6, "id": "73aaa28f-0f0f-4e2e-8c8d-7c8473336e0e", "metadata": {}, "outputs": [], "source": [ "load('/home/artal/Descargas/ZetaFunctionsNewtonND.py')" ] }, { "cell_type": "code", "execution_count": 7, "id": "0e83692e-907b-493a-8911-945c2925e586", "metadata": {}, "outputs": [], "source": [ "Z = ZetaFunctions(h)" ] }, { "cell_type": "code", "execution_count": 8, "id": "75c28fbb-c042-4afc-b79d-e60fbc149628", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[(-1) * v^14,\n", " (-1) * u^14,\n", " (-2) * u^3 * v^10,\n", " (-2) * v^3 * u^10,\n", " (-1) * v^10 * (v^4 + 2*u^3),\n", " (-1) * u^10 * (2*v^3 + u^4),\n", " (-1) * (v + u) * u^3 * v^3 * (2*v^6 - 5*u*v^5 + 5*u^2*v^4 - 5*u^3*v^3 + 5*u^4*v^2 - 5*u^5*v + 2*u^6)]" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "[p.factor() for p in Z.get_polyfaces_dictionary(compact=True)]" ] }, { "cell_type": "code", "execution_count": 9, "id": "9e5736a1-ba87-4f95-8dc0-0ab5b7151bbd", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "False" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Z.is_newton_degenerated(local=True)" ] }, { "cell_type": "code", "execution_count": 10, "id": "35654137-b9d0-46d6-b6e3-5d6261bf8271", "metadata": {}, "outputs": [ { "data": { 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", "text/plain": [ "Graphics object consisting of 20 graphics primitives" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Z.newton_plot()" ] }, { "cell_type": "code", "execution_count": 11, "id": "361b687b-43e1-4db8-be55-2f6a180f10f0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Facet 0: -42 + 4*v + 3*u >= 0\n", " Facet 1: -13 + v + u >= 0\n", " Facet 3: -42 + 3*v + 4*u >= 0\n" ] } ], "source": [ "Z.give_info_facets(compact=True)" ] }, { "cell_type": "code", "execution_count": 12, "id": "3de0f7de-3ed6-4084-b6de-2a0fe4d95579", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-v^14 - 2*u^3*v^10 + 3*u^4*v^9 + 3*u^9*v^4 - 2*u^10*v^3 - u^14" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h1 = sum(h.monomial_coefficient(u^i * v^j) * u^i * v^j for i, j in h.exponents() if (i, j) == (14, 0) or (i, j) == (0, 14) or i + j == 13)\n", "h1" ] }, { "cell_type": "code", "execution_count": 13, "id": "6db00060-6963-4782-a837-db6dc6adadc9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "148" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h1.jacobian_ideal().vector_space_dimension()" ] }, { "cell_type": "code", "execution_count": 14, "id": "70044743-6a40-4234-a9fa-fa9a87064058", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-v^14 + v^15 + 3*u^2*v^12 - 2*u^3*v^10 + 3*u^4*v^9 + 3*u^5*v^10 + 4*u^7*v^7 + 3*u^9*v^4 - 2*u^10*v^3 + 3*u^10*v^5 + 3*u^12*v^2 - u^14 + u^15" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h" ] }, { "cell_type": "code", "execution_count": 15, "id": "2a533b35-964e-4615-ad76-1afd397797b2", "metadata": {}, "outputs": [], "source": [ "def estrato(ff, chi, pesos):\n", " Z1 = ZetaFunctions(ff)\n", " zetamon1 = Z1.monodromy_zeta().value()^chi\n", " zetatop1 = chi * Z1.topological_zeta(local=True, weights=pesos).value()\n", " return zetamon1, zetatop1" ] }, { "cell_type": "code", "execution_count": 16, "id": "effb40ba-8e60-43a1-8d89-ed8cee03ff1d", "metadata": {}, "outputs": [], "source": [ "zetatop=0\n", "zetamon=1" ] }, { "cell_type": "markdown", "id": "df0f6a80-d6c0-4b16-8306-4f5c81545a31", "metadata": {}, "source": [ "$\\check{E}_1$" ] }, { "cell_type": "code", "execution_count": 17, "id": "8b9a319a-2351-425a-8476-c083a125e393", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "((t + 1)^14 * (t^2 - t + 1)^7 * (t^6 - t^5 + t^4 - t^3 + t^2 - t + 1)^7,\n", " (s + 9/14) * (s + 1))" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zetamon1, zetatop1 = estrato(z^3 + x^2 * z^2 + x^7, -7, [2, 1, 1])\n", "zetamon *= zetamon1\n", "zetatop += zetatop1\n", "zetamon1.factor(), zetatop1.denominator().factor()" ] }, { "cell_type": "markdown", "id": "922c65e0-f073-4c4c-a5ba-953a4f997c07", "metadata": {}, "source": [ "${E}_1\\cap E_{4,i}$" ] }, { "cell_type": "code", "execution_count": 18, "id": "a5c32283-70d6-4903-bc3f-e248d46dbb48", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "((t - 1)^2 * (t^2 + t + 1)^2, (s + 9/14) * (s + 2/3) * (s + 1))" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zetamon14, zetatop14 = estrato(z^3 + x^2 * y^7 * z^2 + x^7 * y^21, 2, [2, 7, 1])\n", "zetamon *= zetamon14\n", "zetatop += zetatop14\n", "zetamon14.factor(), zetatop14.denominator().factor()" ] }, { "cell_type": "markdown", "id": "08c192da-a9d5-4bc6-b834-c2ff504d6b5c", "metadata": {}, "source": [ "${E}_1\\cap\\Delta$" ] }, { "cell_type": "code", "execution_count": 19, "id": "20bba556-4db2-4c7a-ac3d-8641ece608d4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "((t + 1)^-7 * (t^2 - t + 1)^-7, (s + 9/14) * (s + 1))" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zetamon1d, zetatop1d = estrato(z^3 + x^2 * z^2 + x^7 * y, 7, [2, 1, 1])\n", "zetamon *= zetamon1d\n", "zetatop += zetatop1d\n", "zetamon1d.factor(), zetatop1d.denominator().factor()" ] }, { "cell_type": "code", "execution_count": 20, "id": "1ec7e8f6-859f-4145-a86f-7a911923a478", "metadata": {}, "outputs": [], "source": [ "zetamone1= zetamon1*zetamon14*zetamon1d\n", "zetatope1= zetatop1 + zetatop14 + zetatop1d" ] }, { "cell_type": "code", "execution_count": 21, "id": "319eeaf1-bc5a-474d-95b3-78de7f894c5c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "((t - 1)^2 * (t + 1)^7 * (t^2 + t + 1)^2 * (t^6 - t^5 + t^4 - t^3 + t^2 - t + 1)^7,\n", " (s + 9/14) * (s + 2/3) * (s + 1))" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zetamone1.factor(), zetatope1.denominator().factor()" ] }, { "cell_type": "markdown", "id": "ae8fc0d1-552a-414a-914a-421964737158", "metadata": {}, "source": [ "$\\check{E}_{2,i}$" ] }, { "cell_type": "code", "execution_count": 22, "id": "34e87485-b397-435a-9d4c-978735f1e394", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "((t - 1)^2 * (t^12 - t^11 + t^9 - t^8 + t^6 - t^4 + t^3 - t + 1)^-2,\n", " (s + 16/21) * (s + 1))" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zetamon2, zetatop2 = estrato(z^3 + x^5 * z + x^7, 2, [3, 1, 1])\n", "zetamon *= zetamon2\n", "zetatop += zetatop2\n", "zetamon2.factor(), zetatop2.denominator().factor()" ] }, { "cell_type": "code", "execution_count": 23, "id": "32307a2d-cb48-4ce4-8130-ddcee91a5b7e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "x^12 - x^11 + x^9 - x^8 + x^6 - x^4 + x^3 - x + 1" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cyclotomic_polynomial(21)" ] }, { "cell_type": "markdown", "id": "50a665ae-6aab-4a09-95a8-820582d36efa", "metadata": {}, "source": [ "${E}_{2,i}\\cap E_{3,i}$" ] }, { "cell_type": "code", "execution_count": 24, "id": "bf417692-9e86-42cb-9bab-7efcea3174cf", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "((t - 1)^2 * (t^2 + t + 1)^2, (s + 29/42) * (s + 16/21) * (s + 1))" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zetamon23, zetatop23= estrato(z^3 + x^5 * y^10 * z + x^7 * y^14, 2, [3, 5, 1])\n", "zetamon *= zetamon23\n", "zetatop += zetatop23\n", "zetamon23.factor(), zetatop23.denominator().factor()" ] }, { "cell_type": "code", "execution_count": 25, "id": "e31a134f-9d4d-4438-abcd-a0ae6881a84f", "metadata": {}, "outputs": [], "source": [ "zetamone2= zetamon2*zetamon23\n", "zetatope2= zetatop2 + zetatop23" ] }, { "cell_type": "code", "execution_count": 26, "id": "22248c64-3b38-4779-abd4-fa532827a1ca", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "((t - 1)^4 * (t^2 + t + 1)^2 * (t^12 - t^11 + t^9 - t^8 + t^6 - t^4 + t^3 - t + 1)^-2,\n", " (s + 29/42) * (s + 1))" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zetamone2.factor(), zetatope2.denominator().factor()" ] }, { "cell_type": "markdown", "id": "bf5405fe-df5b-48c2-973d-cb79fa6e51c8", "metadata": {}, "source": [ "$\\check{E}_{3,i}$" ] }, { "cell_type": "code", "execution_count": 27, "id": "82e29430-e591-41fd-805e-024e718b91a4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "((t - 1)^-2 * (t^2 - t + 1)^2 * (t^12 - t^11 + t^9 - t^8 + t^6 - t^4 + t^3 - t + 1)^2 * (t^12 + t^11 - t^9 - t^8 + t^6 - t^4 - t^3 + t + 1)^2,\n", " (s + 29/42) * (s + 1))" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zetamon3, zetatop3 = estrato(z^3 + x^10 * z + x^14, -2, [5, 1, 1])\n", "zetamon *= zetamon3\n", "zetatop += zetatop3\n", "zetamon3.factor(), zetatop3.denominator().factor()" ] }, { "cell_type": "code", "execution_count": 28, "id": "513c0649-9724-43ed-9f5c-e78cba17b735", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "x^12 + x^11 - x^9 - x^8 + x^6 - x^4 - x^3 + x + 1" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cyclotomic_polynomial(42)" ] }, { "cell_type": "markdown", "id": "7f5da880-9e24-45e7-9ab1-b5d8eebaf76c", "metadata": {}, "source": [ "${E}_{3,i}\\cap E_{4,i}$" ] }, { "cell_type": "code", "execution_count": 29, "id": "fa3bd566-3f90-40c8-b3df-fc27e02fc3e0", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "((t - 1)^2 * (t^2 + t + 1)^2, (s + 2/3) * (s + 29/42) * (s + 1))" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zetamon34, zetatop34 = estrato(z^3 + x^14 * y^10 * z + x^21 * y^14, 2, [7, 5, 1])\n", "zetamon *= zetamon34\n", "zetatop += zetatop34\n", "zetamon34.factor(), zetatop34.denominator().factor()" ] }, { "cell_type": "markdown", "id": "4016536c-7dc4-417d-bb0f-496b738517a4", "metadata": {}, "source": [ "${E}_{3,i}\\cap f$" ] }, { "cell_type": "code", "execution_count": 30, "id": "16a5e4d8-afb2-43bc-b4bd-ba9d7824e77b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "((t - 1)^2 * (t^2 - t + 1)^-2 * (t^12 - t^11 + t^9 - t^8 + t^6 - t^4 + t^3 - t + 1)^-2 * (t^12 + t^11 - t^9 - t^8 + t^6 - t^4 - t^3 + t + 1)^-2,\n", " (s + 29/42) * (s + 1))" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zetamon3f, zetatop3f = estrato(z^3 + x * y^10 * z + y^14, 2, [1, 5, 1])\n", "zetamon *= zetamon3f\n", "zetatop += zetatop3f\n", "zetamon3f.factor(), zetatop3f.denominator().factor()" ] }, { "cell_type": "code", "execution_count": 50, "id": "0a03a23a-1e28-4c57-be5c-159500ea7ecc", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1, 0)" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zetamon3 * zetamon3f, zetatop3 + zetatop3f" ] }, { "cell_type": "code", "execution_count": 31, "id": "5468f2df-38ec-4823-9377-31ab2bc6dc11", "metadata": {}, "outputs": [], "source": [ "zetamone23= zetamone2 * zetamon3 * zetamon34 * zetamon3f\n", "zetatope23= zetatope2 + zetatop3 + zetatop34 + zetatop3f" ] }, { "cell_type": "code", "execution_count": 32, "id": "13789e6d-cbba-4fac-93cf-10551da0979a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "((t - 1)^6 * (t^2 + t + 1)^4 * (t^12 - t^11 + t^9 - t^8 + t^6 - t^4 + t^3 - t + 1)^-2,\n", " (s + 2/3) * (s + 1))" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zetamone23.factor(), zetatope23.denominator().factor()" ] }, { "cell_type": "markdown", "id": "ccc32acb-28ef-4628-a51e-3aff997646e9", "metadata": {}, "source": [ "$\\check{E}_{4,i}$" ] }, { "cell_type": "code", "execution_count": 33, "id": "9efeade1-d21c-4ff9-ad19-0b67ddbbab82", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "((t - 1)^4 * (t^2 + t + 1)^4 * (t^6 + t^5 + t^4 + t^3 + t^2 + t + 1)^8 * (t^12 - t^11 + t^9 - t^8 + t^6 - t^4 + t^3 - t + 1)^8,\n", " (s + 2/3) * (s + 1))" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zetamon4, zetatop4 = estrato(z^3 + x^14 * z + x^21, -4, [7, 1, 1])\n", "zetamon *= zetamon4\n", "zetatop += zetatop4\n", "zetamon4.factor(), zetatop4.denominator().factor()" ] }, { "cell_type": "markdown", "id": "a564ec00-2a96-47c8-97ff-5a5f500c626a", "metadata": {}, "source": [ "${E}_{4,i}\\cap g$" ] }, { "cell_type": "code", "execution_count": 34, "id": "9dcde2d8-2a61-48a6-87e8-98ffb547ef16", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "((t - 1)^-2 * (t^2 + t + 1)^-2 * (t^6 + t^5 + t^4 + t^3 + t^2 + t + 1)^-4 * (t^12 - t^11 + t^9 - t^8 + t^6 - t^4 + t^3 - t + 1)^-4,\n", " (s + 2/3) * (s + 1))" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zetamon4g, zetatop4g = estrato(z^3 + x^14 * z + x^21 * y, 2, [7, 1, 1])\n", "zetamon *= zetamon4g\n", "zetatop += zetatop4g\n", "zetamon4g.factor(), zetatop4g.denominator().factor()" ] }, { "cell_type": "code", "execution_count": 52, "id": "87514ec2-df42-4be3-ab90-56cfd3d25e19", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1, 0)" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zetamon4 * zetamon4g^2, zetatop4 + 2 * zetatop4g" ] }, { "cell_type": "markdown", "id": "2981a168-ed29-473e-bc38-4c6864ed7b26", "metadata": {}, "source": [ "${E}_4\\cap\\Delta$" ] }, { "cell_type": "code", "execution_count": 35, "id": "767c1c15-0e88-492f-950a-82a54480a2eb", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "((t^6 + t^5 + t^4 + t^3 + t^2 + t + 1)^-2 * (t^12 - t^11 + t^9 - t^8 + t^6 - t^4 + t^3 - t + 1)^-2,\n", " (s + 2/3) * (s + 1))" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zetamon4d, zetatop4d = estrato(z^3 + x^7 * z^2 + x^21 * y, 2, [7, 1, 1])\n", "zetamon *= zetamon4d\n", "zetatop += zetatop4d\n", "zetamon4d.factor(), zetatop4d.denominator().factor()" ] }, { "cell_type": "code", "execution_count": 36, "id": "5c0f5123-59a7-4660-a298-d0aa238d5694", "metadata": {}, "outputs": [], "source": [ "zetamone4= zetamone23 * zetamon4 * zetamon4g * zetamon4d * zetamon14\n", "zetatope4= zetatope23 + zetatop4 + zetatop4g + zetatop4d + zetatop14" ] }, { "cell_type": "code", "execution_count": 37, "id": "7323db86-9f16-4ded-a39e-e377836e617e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "((t - 1)^10 * (t^2 + t + 1)^8 * (t^6 + t^5 + t^4 + t^3 + t^2 + t + 1)^2,\n", " (s + 9/14) * (s + 2/3) * (s + 1))" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zetamone4.factor(), zetatope4.denominator().factor()" ] }, { "cell_type": "code", "execution_count": 38, "id": "b1d36f9c-e580-410d-a41e-90915236f8d7", "metadata": {}, "outputs": [], "source": [ "zetamon /= (t^3 - 1)^7" ] }, { "cell_type": "code", "execution_count": 39, "id": "3e2c75ac-c59e-48ce-8897-b25dd1283e6a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "t^66 - t^63 + 5*t^59 - 5*t^56 + 8*t^52 - 8*t^49 - 14*t^38 + 14*t^35 - 14*t^31 + 14*t^28 + 8*t^17 - 8*t^14 + 5*t^10 - 5*t^7 + t^3 - 1" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zetamon" ] }, { "cell_type": "code", "execution_count": 40, "id": "2698a314-3799-4832-a9dc-f735c14a1a4a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(s + 9/14) * (s + 2/3) * (s + 1)" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zetatop.denominator().factor()" ] }, { "cell_type": "code", "execution_count": 41, "id": "29a016fb-3316-49b5-9720-843637017b4f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(t - 1)^3 * (t + 1)^7 * (t^2 + t + 1) * (t^6 + t^5 + t^4 + t^3 + t^2 + t + 1)^2 * (t^6 - t^5 + t^4 - t^3 + t^2 - t + 1)^7" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zetamon.factor()" ] }, { "cell_type": "code", "execution_count": 44, "id": "4afe75a2-f9f6-4690-a09b-570ba614d71e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(10/21) * (s + 2/3)^-1 * (s + 1)^-1 * (s + 6/5)" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zetatope23.factor()" ] }, { "cell_type": "code", "execution_count": 53, "id": "f49794ef-91fa-4a5a-b92a-8f2bbcf9cdb6", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(4/21) * (s + 2/3)^-1 * (s + 1)^-1 * (s - 2)" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zetatop4.factor()" ] }, { "cell_type": "code", "execution_count": 64, "id": "824c0056-d8c4-40d1-8327-4b2a0498149d", "metadata": {}, "outputs": [], "source": [ "zetamonsing1, zetatopsing1 = estrato(z^3 + x^7, 2, [3, 1, 1])\n", "zetamonsing2, zetatopsing2 = estrato(z^3 + x^14 * y^7, 2, [5, 3, 1])\n", "zetamonsing3, zetatopsing3 = estrato(z^3 + x^14 * y^21, 2, [5, 7, 1])" ] }, { "cell_type": "code", "execution_count": 65, "id": "7ba883c3-3446-463c-88b6-db5bdf7355ad", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(10/21) * (s + 2/3)^-1 * (s + 1)^-1 * (s + 6/5)" ] }, "execution_count": 65, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zetatopsing = zetatopsing1 + zetatopsing2 + zetatopsing3\n", "zetatopsing.factor()" ] }, { "cell_type": "code", "execution_count": 66, "id": "74569c3a-4cae-4e4d-8bb0-2c3ccac5fcce", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(10/21) * (s + 2/3)^-1 * (s + 1)^-1 * (s + 6/5)" ] }, "execution_count": 66, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zetatope23.factor()" ] }, { "cell_type": "code", "execution_count": 67, "id": "c11914fb-cd4f-4825-9c3f-e5c35338d71b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(t - 1)^6 * (t^2 + t + 1)^4 * (t^12 - t^11 + t^9 - t^8 + t^6 - t^4 + t^3 - t + 1)^-2" ] }, "execution_count": 67, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zetamonsing = zetamonsing1 * zetamonsing2 * zetamonsing3\n", "zetamonsing.factor()" ] }, { "cell_type": "code", "execution_count": 68, "id": "8e3794f3-e198-48ea-8939-b816e5960d88", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(t - 1)^6 * (t^2 + t + 1)^4 * (t^12 - t^11 + t^9 - t^8 + t^6 - t^4 + t^3 - t + 1)^-2" ] }, "execution_count": 68, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zetamone23.factor()" ] }, { "cell_type": "code", "execution_count": 69, "id": "d8661277-212c-4841-8112-66f2460c261b", "metadata": {}, "outputs": [], "source": [ "prueba = ZetaFunctions(v^3 - u^7)" ] }, { "cell_type": "code", "execution_count": 83, "id": "8e8e601e-8ffb-4cdc-ab5a-60ae4f7ee2ef", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(5/21) * (s + 2/3)^-1 * (s + 1)^-1 * (s + 6/5)" ] }, "execution_count": 83, "metadata": {}, "output_type": "execute_result" } ], "source": [ "prueba.topological_zeta(local=True, weights=[7 / 3, 1])" ] }, { "cell_type": "code", "execution_count": 84, "id": "a2f47e18-d020-48db-a469-85768410c661", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(5/84) * (s + 2/3)^-1 * (s + 1)^-1 * (s + 6/5)" ] }, "execution_count": 84, "metadata": {}, "output_type": "execute_result" } ], "source": [ "prueba1 = ZetaFunctions(v^3 - u^28)\n", "prueba1.topological_zeta(local=True, weights=[28 / 3, 1])" ] }, { "cell_type": "code", "execution_count": null, "id": "163eeb8f-efc3-4e60-808e-21d9ce3e535e", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath 10.3.rc4", "language": "sage", "name": "sagemath-devel" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.1" } }, "nbformat": 4, "nbformat_minor": 5 }