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This commit is contained in:
Enrique Artal Bartolo 2024-03-06 08:32:33 +01:00
parent a1de6b17ff
commit f9d401b8c7
2 changed files with 573 additions and 215 deletions
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397
Estratos.ipynb
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@ -2,7 +2,7 @@
"cells": [ "cells": [
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 18, "execution_count": 1,
"id": "03414fb8-f6f5-4796-a227-6aeed863ab6c", "id": "03414fb8-f6f5-4796-a227-6aeed863ab6c",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
@ -17,7 +17,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 19, "execution_count": 2,
"id": "c17bb619-1df9-4ea5-bfce-7f77cf56e00d", "id": "c17bb619-1df9-4ea5-bfce-7f77cf56e00d",
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
@ -27,7 +27,7 @@
"[Ideal (z, y, x) of Multivariate Polynomial Ring in x, y, z over Rational Field]" "[Ideal (z, y, x) of Multivariate Polynomial Ring in x, y, z over Rational Field]"
] ]
}, },
"execution_count": 19, "execution_count": 2,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@ -38,7 +38,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 23, "execution_count": 3,
"id": "f65646af-e328-430f-991d-10a0c2348fee", "id": "f65646af-e328-430f-991d-10a0c2348fee",
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
@ -48,7 +48,7 @@
"0" "0"
] ]
}, },
"execution_count": 23, "execution_count": 3,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@ -60,7 +60,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 22, "execution_count": 4,
"id": "00201766-5028-41ba-a13e-4740790a538e", "id": "00201766-5028-41ba-a13e-4740790a538e",
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
@ -70,7 +70,7 @@
"65" "65"
] ]
}, },
"execution_count": 22, "execution_count": 4,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@ -81,7 +81,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 24, "execution_count": 5,
"id": "d0ebfd8e-9c6f-4dc1-8230-9f3dfcaa2b4d", "id": "d0ebfd8e-9c6f-4dc1-8230-9f3dfcaa2b4d",
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
@ -91,7 +91,7 @@
"148" "148"
] ]
}, },
"execution_count": 24, "execution_count": 5,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@ -102,7 +102,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 27, "execution_count": 6,
"id": "73aaa28f-0f0f-4e2e-8c8d-7c8473336e0e", "id": "73aaa28f-0f0f-4e2e-8c8d-7c8473336e0e",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
@ -112,7 +112,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 28, "execution_count": 7,
"id": "0e83692e-907b-493a-8911-945c2925e586", "id": "0e83692e-907b-493a-8911-945c2925e586",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
@ -122,7 +122,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 47, "execution_count": 8,
"id": "75c28fbb-c042-4afc-b79d-e60fbc149628", "id": "75c28fbb-c042-4afc-b79d-e60fbc149628",
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
@ -138,7 +138,7 @@
" (-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)]" " (-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": 47, "execution_count": 8,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@ -149,7 +149,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 46, "execution_count": 9,
"id": "9e5736a1-ba87-4f95-8dc0-0ab5b7151bbd", "id": "9e5736a1-ba87-4f95-8dc0-0ab5b7151bbd",
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
@ -159,7 +159,7 @@
"False" "False"
] ]
}, },
"execution_count": 46, "execution_count": 9,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@ -170,7 +170,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 38, "execution_count": 10,
"id": "35654137-b9d0-46d6-b6e3-5d6261bf8271", "id": "35654137-b9d0-46d6-b6e3-5d6261bf8271",
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
@ -181,7 +181,7 @@
"Graphics object consisting of 20 graphics primitives" "Graphics object consisting of 20 graphics primitives"
] ]
}, },
"execution_count": 38, "execution_count": 10,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@ -192,7 +192,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 49, "execution_count": 11,
"id": "361b687b-43e1-4db8-be55-2f6a180f10f0", "id": "361b687b-43e1-4db8-be55-2f6a180f10f0",
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
@ -212,7 +212,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 43, "execution_count": 12,
"id": "3de0f7de-3ed6-4084-b6de-2a0fe4d95579", "id": "3de0f7de-3ed6-4084-b6de-2a0fe4d95579",
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
@ -222,7 +222,7 @@
"-v^14 - 2*u^3*v^10 + 3*u^4*v^9 + 3*u^9*v^4 - 2*u^10*v^3 - u^14" "-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": 43, "execution_count": 12,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@ -234,7 +234,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 44, "execution_count": 13,
"id": "6db00060-6963-4782-a837-db6dc6adadc9", "id": "6db00060-6963-4782-a837-db6dc6adadc9",
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
@ -244,7 +244,7 @@
"148" "148"
] ]
}, },
"execution_count": 44, "execution_count": 13,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@ -255,7 +255,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 50, "execution_count": 14,
"id": "70044743-6a40-4234-a9fa-fa9a87064058", "id": "70044743-6a40-4234-a9fa-fa9a87064058",
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
@ -265,7 +265,7 @@
"-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" "-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": 50, "execution_count": 14,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@ -276,7 +276,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 68, "execution_count": 15,
"id": "2a533b35-964e-4615-ad76-1afd397797b2", "id": "2a533b35-964e-4615-ad76-1afd397797b2",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
@ -290,7 +290,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 147, "execution_count": 16,
"id": "effb40ba-8e60-43a1-8d89-ed8cee03ff1d", "id": "effb40ba-8e60-43a1-8d89-ed8cee03ff1d",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
@ -309,7 +309,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 148, "execution_count": 17,
"id": "8b9a319a-2351-425a-8476-c083a125e393", "id": "8b9a319a-2351-425a-8476-c083a125e393",
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
@ -320,7 +320,7 @@
" (s + 9/14) * (s + 1))" " (s + 9/14) * (s + 1))"
] ]
}, },
"execution_count": 148, "execution_count": 17,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@ -342,7 +342,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 149, "execution_count": 18,
"id": "a5c32283-70d6-4903-bc3f-e248d46dbb48", "id": "a5c32283-70d6-4903-bc3f-e248d46dbb48",
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
@ -352,7 +352,7 @@
"((t - 1)^2 * (t^2 + t + 1)^2, (s + 9/14) * (s + 2/3) * (s + 1))" "((t - 1)^2 * (t^2 + t + 1)^2, (s + 9/14) * (s + 2/3) * (s + 1))"
] ]
}, },
"execution_count": 149, "execution_count": 18,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@ -374,7 +374,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 150, "execution_count": 19,
"id": "20bba556-4db2-4c7a-ac3d-8641ece608d4", "id": "20bba556-4db2-4c7a-ac3d-8641ece608d4",
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
@ -384,7 +384,7 @@
"((t + 1)^-7 * (t^2 - t + 1)^-7, (s + 9/14) * (s + 1))" "((t + 1)^-7 * (t^2 - t + 1)^-7, (s + 9/14) * (s + 1))"
] ]
}, },
"execution_count": 150, "execution_count": 19,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@ -398,7 +398,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 156, "execution_count": 20,
"id": "1ec7e8f6-859f-4145-a86f-7a911923a478", "id": "1ec7e8f6-859f-4145-a86f-7a911923a478",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
@ -409,7 +409,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 157, "execution_count": 21,
"id": "319eeaf1-bc5a-474d-95b3-78de7f894c5c", "id": "319eeaf1-bc5a-474d-95b3-78de7f894c5c",
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
@ -420,7 +420,7 @@
" (s + 9/14) * (s + 2/3) * (s + 1))" " (s + 9/14) * (s + 2/3) * (s + 1))"
] ]
}, },
"execution_count": 157, "execution_count": 21,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@ -439,7 +439,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 153, "execution_count": 22,
"id": "34e87485-b397-435a-9d4c-978735f1e394", "id": "34e87485-b397-435a-9d4c-978735f1e394",
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
@ -450,7 +450,7 @@
" (s + 16/21) * (s + 1))" " (s + 16/21) * (s + 1))"
] ]
}, },
"execution_count": 153, "execution_count": 22,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@ -464,7 +464,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 154, "execution_count": 23,
"id": "32307a2d-cb48-4ce4-8130-ddcee91a5b7e", "id": "32307a2d-cb48-4ce4-8130-ddcee91a5b7e",
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
@ -474,7 +474,7 @@
"x^12 - x^11 + x^9 - x^8 + x^6 - x^4 + x^3 - x + 1" "x^12 - x^11 + x^9 - x^8 + x^6 - x^4 + x^3 - x + 1"
] ]
}, },
"execution_count": 154, "execution_count": 23,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@ -493,7 +493,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 155, "execution_count": 24,
"id": "bf417692-9e86-42cb-9bab-7efcea3174cf", "id": "bf417692-9e86-42cb-9bab-7efcea3174cf",
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
@ -503,7 +503,7 @@
"((t - 1)^2 * (t^2 + t + 1)^2, (s + 29/42) * (s + 16/21) * (s + 1))" "((t - 1)^2 * (t^2 + t + 1)^2, (s + 29/42) * (s + 16/21) * (s + 1))"
] ]
}, },
"execution_count": 155, "execution_count": 24,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@ -517,7 +517,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 158, "execution_count": 25,
"id": "e31a134f-9d4d-4438-abcd-a0ae6881a84f", "id": "e31a134f-9d4d-4438-abcd-a0ae6881a84f",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
@ -528,7 +528,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 159, "execution_count": 26,
"id": "22248c64-3b38-4779-abd4-fa532827a1ca", "id": "22248c64-3b38-4779-abd4-fa532827a1ca",
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
@ -539,7 +539,7 @@
" (s + 29/42) * (s + 1))" " (s + 29/42) * (s + 1))"
] ]
}, },
"execution_count": 159, "execution_count": 26,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@ -558,7 +558,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 160, "execution_count": 27,
"id": "82e29430-e591-41fd-805e-024e718b91a4", "id": "82e29430-e591-41fd-805e-024e718b91a4",
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
@ -569,7 +569,7 @@
" (s + 29/42) * (s + 1))" " (s + 29/42) * (s + 1))"
] ]
}, },
"execution_count": 160, "execution_count": 27,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@ -583,7 +583,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 161, "execution_count": 28,
"id": "513c0649-9724-43ed-9f5c-e78cba17b735", "id": "513c0649-9724-43ed-9f5c-e78cba17b735",
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
@ -593,7 +593,7 @@
"x^12 + x^11 - x^9 - x^8 + x^6 - x^4 - x^3 + x + 1" "x^12 + x^11 - x^9 - x^8 + x^6 - x^4 - x^3 + x + 1"
] ]
}, },
"execution_count": 161, "execution_count": 28,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@ -612,7 +612,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 162, "execution_count": 29,
"id": "fa3bd566-3f90-40c8-b3df-fc27e02fc3e0", "id": "fa3bd566-3f90-40c8-b3df-fc27e02fc3e0",
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
@ -622,7 +622,7 @@
"((t - 1)^2 * (t^2 + t + 1)^2, (s + 2/3) * (s + 29/42) * (s + 1))" "((t - 1)^2 * (t^2 + t + 1)^2, (s + 2/3) * (s + 29/42) * (s + 1))"
] ]
}, },
"execution_count": 162, "execution_count": 29,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@ -644,7 +644,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 163, "execution_count": 30,
"id": "16a5e4d8-afb2-43bc-b4bd-ba9d7824e77b", "id": "16a5e4d8-afb2-43bc-b4bd-ba9d7824e77b",
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
@ -655,7 +655,7 @@
" (s + 29/42) * (s + 1))" " (s + 29/42) * (s + 1))"
] ]
}, },
"execution_count": 163, "execution_count": 30,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@ -669,7 +669,28 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 164, "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", "id": "5468f2df-38ec-4823-9377-31ab2bc6dc11",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
@ -680,7 +701,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 165, "execution_count": 32,
"id": "13789e6d-cbba-4fac-93cf-10551da0979a", "id": "13789e6d-cbba-4fac-93cf-10551da0979a",
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
@ -691,7 +712,7 @@
" (s + 2/3) * (s + 1))" " (s + 2/3) * (s + 1))"
] ]
}, },
"execution_count": 165, "execution_count": 32,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@ -710,7 +731,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 166, "execution_count": 33,
"id": "9efeade1-d21c-4ff9-ad19-0b67ddbbab82", "id": "9efeade1-d21c-4ff9-ad19-0b67ddbbab82",
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
@ -721,7 +742,7 @@
" (s + 2/3) * (s + 1))" " (s + 2/3) * (s + 1))"
] ]
}, },
"execution_count": 166, "execution_count": 33,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@ -743,7 +764,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 167, "execution_count": 34,
"id": "9dcde2d8-2a61-48a6-87e8-98ffb547ef16", "id": "9dcde2d8-2a61-48a6-87e8-98ffb547ef16",
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
@ -754,7 +775,7 @@
" (s + 2/3) * (s + 1))" " (s + 2/3) * (s + 1))"
] ]
}, },
"execution_count": 167, "execution_count": 34,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@ -766,6 +787,27 @@
"zetamon4g.factor(), zetatop4g.denominator().factor()" "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", "cell_type": "markdown",
"id": "2981a168-ed29-473e-bc38-4c6864ed7b26", "id": "2981a168-ed29-473e-bc38-4c6864ed7b26",
@ -776,7 +818,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 168, "execution_count": 35,
"id": "767c1c15-0e88-492f-950a-82a54480a2eb", "id": "767c1c15-0e88-492f-950a-82a54480a2eb",
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
@ -787,7 +829,7 @@
" (s + 2/3) * (s + 1))" " (s + 2/3) * (s + 1))"
] ]
}, },
"execution_count": 168, "execution_count": 35,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@ -801,7 +843,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 172, "execution_count": 36,
"id": "5c0f5123-59a7-4660-a298-d0aa238d5694", "id": "5c0f5123-59a7-4660-a298-d0aa238d5694",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
@ -812,7 +854,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 173, "execution_count": 37,
"id": "7323db86-9f16-4ded-a39e-e377836e617e", "id": "7323db86-9f16-4ded-a39e-e377836e617e",
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
@ -823,7 +865,7 @@
" (s + 9/14) * (s + 2/3) * (s + 1))" " (s + 9/14) * (s + 2/3) * (s + 1))"
] ]
}, },
"execution_count": 173, "execution_count": 37,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@ -834,7 +876,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 143, "execution_count": 38,
"id": "b1d36f9c-e580-410d-a41e-90915236f8d7", "id": "b1d36f9c-e580-410d-a41e-90915236f8d7",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
@ -844,7 +886,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 144, "execution_count": 39,
"id": "3e2c75ac-c59e-48ce-8897-b25dd1283e6a", "id": "3e2c75ac-c59e-48ce-8897-b25dd1283e6a",
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
@ -854,7 +896,7 @@
"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" "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": 144, "execution_count": 39,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@ -865,7 +907,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 145, "execution_count": 40,
"id": "2698a314-3799-4832-a9dc-f735c14a1a4a", "id": "2698a314-3799-4832-a9dc-f735c14a1a4a",
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
@ -875,7 +917,7 @@
"(s + 9/14) * (s + 2/3) * (s + 1)" "(s + 9/14) * (s + 2/3) * (s + 1)"
] ]
}, },
"execution_count": 145, "execution_count": 40,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@ -886,7 +928,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 146, "execution_count": 41,
"id": "29a016fb-3316-49b5-9720-843637017b4f", "id": "29a016fb-3316-49b5-9720-843637017b4f",
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
@ -896,7 +938,7 @@
"(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" "(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": 146, "execution_count": 41,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@ -907,49 +949,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 175, "execution_count": 44,
"id": "274931c8-c536-4f97-9a5d-06a596a92285",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1"
]
},
"execution_count": 175,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"zetamon4 * zetamon4g^2"
]
},
{
"cell_type": "code",
"execution_count": 176,
"id": "dcc73bc3-9e6e-45fe-99ce-6e8b17f6b159",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1"
]
},
"execution_count": 176,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"zetamon3 * zetamon3f"
]
},
{
"cell_type": "code",
"execution_count": 180,
"id": "4afe75a2-f9f6-4690-a09b-570ba614d71e", "id": "4afe75a2-f9f6-4690-a09b-570ba614d71e",
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
@ -959,7 +959,7 @@
"(10/21) * (s + 2/3)^-1 * (s + 1)^-1 * (s + 6/5)" "(10/21) * (s + 2/3)^-1 * (s + 1)^-1 * (s + 6/5)"
] ]
}, },
"execution_count": 180, "execution_count": 44,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
@ -970,29 +970,180 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 181, "execution_count": 53,
"id": "db53f3eb-871a-41d4-bb61-1cda3410c6dd", "id": "f49794ef-91fa-4a5a-b92a-8f2bbcf9cdb6",
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
"data": { "data": {
"text/plain": [ "text/plain": [
"(13/21) * (s + 9/14)^-1 * (s + 2/3)^-1 * (s + 1)^-1 * (s^2 + 43/26*s + 9/13)" "(4/21) * (s + 2/3)^-1 * (s + 1)^-1 * (s - 2)"
] ]
}, },
"execution_count": 181, "execution_count": 53,
"metadata": {}, "metadata": {},
"output_type": "execute_result" "output_type": "execute_result"
} }
], ],
"source": [ "source": [
"zetatope4.factor()" "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", "cell_type": "code",
"execution_count": null, "execution_count": null,
"id": "824c0056-d8c4-40d1-8327-4b2a0498149d", "id": "163eeb8f-efc3-4e60-808e-21d9ce3e535e",
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [] "source": []
@ -1000,7 +1151,7 @@
], ],
"metadata": { "metadata": {
"kernelspec": { "kernelspec": {
"display_name": "SageMath 10.3.beta8", "display_name": "SageMath 10.3.rc1",
"language": "sage", "language": "sage",
"name": "sagemath-devel" "name": "sagemath-devel"
}, },
@ -1014,7 +1165,7 @@
"name": "python", "name": "python",
"nbconvert_exporter": "python", "nbconvert_exporter": "python",
"pygments_lexer": "ipython3", "pygments_lexer": "ipython3",
"version": "3.12.1" "version": "3.12.2"
} }
}, },
"nbformat": 4, "nbformat": 4,

391
resolucionlarga.ipynb
View File

@ -2,12 +2,14 @@
"cells": [ "cells": [
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 3, "execution_count": 1,
"metadata": { "metadata": {
"collapsed": false "collapsed": false,
"jupyter": {
"outputs_hidden": false
}
}, },
"outputs": [ "outputs": [],
],
"source": [ "source": [
"S.<x, y, z> = PolynomialRing(QQ, order='neglex')\n", "S.<x, y, z> = PolynomialRing(QQ, order='neglex')\n",
"f=((y^2+x^3)^2 + x^5*y)*((x^2+y^3)^2 + y^5*x)\n", "f=((y^2+x^3)^2 + x^5*y)*((x^2+y^3)^2 + y^5*x)\n",
@ -18,9 +20,12 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 4, "execution_count": 2,
"metadata": { "metadata": {
"collapsed": false "collapsed": false,
"jupyter": {
"outputs_hidden": false
}
}, },
"outputs": [ "outputs": [
{ {
@ -29,9 +34,8 @@
"0" "0"
] ]
}, },
"execution_count": 4, "execution_count": 2,
"metadata": { "metadata": {},
},
"output_type": "execute_result" "output_type": "execute_result"
} }
], ],
@ -42,78 +46,125 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 5, "execution_count": 3,
"metadata": { "metadata": {
"collapsed": false "collapsed": false,
"jupyter": {
"outputs_hidden": false
}
}, },
"outputs": [ "outputs": [
{ {
"data": { "data": {
"text/plain": [ "text/plain": [
"False" "True"
] ]
}, },
"execution_count": 5, "execution_count": 3,
"metadata": { "metadata": {},
},
"output_type": "execute_result" "output_type": "execute_result"
} }
], ],
"source": [ "source": [
"D=F.discriminant(z)\n", "D=F.discriminant(z)\n",
"load('ZetaFunctionsNewtonND.py')\n", "# load('ZetaFunctionsNewtonND.py')\n",
"ZD = ZetaFunctions(D)\n", "ZD = ZetaFunctions(D)\n",
"ZD.is_newton_degenerated(local=True)" "ZD.is_newton_non_degenerated(local=True)"
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 6, "execution_count": 4,
"metadata": { "metadata": {},
"collapsed": false
},
"outputs": [ "outputs": [
{ {
"name": "stdout", "name": "stdout",
"output_type": "stream", "output_type": "stream",
"text": [ "text": [
"Newton's polyhedron of -108*y^26 + 108*y^30 + 324*x*y^29 + 648*x^2*y^27 + 324*x^2*y^28 + 1296*x^3*y^26 + 108*x^3*y^27 + 648*x^3*y^28 + 1620*x^4*y^24 + 648*x^4*y^25 + 1944*x^4*y^27 + 1944*x^5*y^23 + 3888*x^5*y^25 + 1944*x^5*y^26 + 324*x^5*y^27 - 216*x^6*y^19 + 2160*x^6*y^21 + 324*x^6*y^22 + 7776*x^6*y^24 + 648*x^6*y^25 + 2592*x^6*y^26 + 1080*x^7*y^20 + 9720*x^7*y^22 + 3888*x^7*y^23 + 1944*x^7*y^24 + 5832*x^7*y^25 + 1620*x^8*y^18 + 11664*x^8*y^21 + 13608*x^8*y^23 + 5184*x^8*y^24 + 1296*x^8*y^25 + 324*x^9*y^17 + 12960*x^9*y^19 + 1944*x^9*y^20 + 4860*x^9*y^21 + 21384*x^9*y^22 + 1620*x^9*y^23 + 6048*x^9*y^24 + 648*x^10*y^15 + 7776*x^10*y^18 + 30132*x^10*y^20 + 9720*x^10*y^21 + 7776*x^10*y^22 + 10368*x^10*y^23 + 324*x^10*y^24 + 9720*x^11*y^16 + 6480*x^11*y^18 + 30132*x^11*y^19 + 28512*x^11*y^21 + 7776*x^11*y^22 + 2916*x^11*y^23 + 1944*x^12*y^15 + 36288*x^12*y^17 + 4860*x^12*y^18 + 19440*x^12*y^19 + 33696*x^12*y^20 + 4104*x^12*y^21 + 8424*x^12*y^22 + 3456*x^13*y^13 + 4860*x^13*y^15 + 19440*x^13*y^16 + 55728*x^13*y^18 + 12960*x^13*y^19 + 15552*x^13*y^20 + 11016*x^13*y^21 + 648*x^13*y^22 + 25164*x^14*y^14 + 25920*x^14*y^16 + 42768*x^14*y^17 + 4860*x^14*y^18 + 34992*x^14*y^19 + 6804*x^14*y^20 + 3240*x^14*y^21 + 648*x^15*y^10 + 1944*x^15*y^12 + 4860*x^15*y^13 + 58752*x^15*y^15 + 6480*x^15*y^16 + 34992*x^15*y^17 + 31104*x^15*y^18 + 5508*x^15*y^19 + 6480*x^15*y^20 + 108*x^15*y^21 + 9720*x^16*y^11 + 19440*x^16*y^13 + 25920*x^16*y^14 + 6480*x^16*y^15 + 60264*x^16*y^16 + 9720*x^16*y^17 + 15552*x^16*y^18 + 6480*x^16*y^19 + 648*x^16*y^20 + 324*x^17*y^9 + 36288*x^17*y^12 + 42768*x^17*y^14 + 34992*x^17*y^15 + 9720*x^17*y^16 + 23328*x^17*y^17 + 3888*x^17*y^18 + 1620*x^17*y^19 + 1620*x^18*y^8 + 7776*x^18*y^10 + 6480*x^18*y^11 + 4860*x^18*y^12 + 55728*x^18*y^13 + 4860*x^18*y^14 + 31104*x^18*y^15 + 15552*x^18*y^16 + 3888*x^18*y^17 + 2160*x^18*y^18 - 216*x^19*y^6 + 12960*x^19*y^9 + 30132*x^19*y^11 + 19440*x^19*y^12 + 12960*x^19*y^13 + 34992*x^19*y^14 + 5508*x^19*y^15 + 6480*x^19*y^16 + 1620*x^19*y^17 + 1080*x^20*y^7 + 1944*x^20*y^9 + 30132*x^20*y^10 + 33696*x^20*y^12 + 15552*x^20*y^13 + 6804*x^20*y^14 + 6480*x^20*y^15 + 648*x^20*y^16 + 2160*x^21*y^6 + 11664*x^21*y^8 + 4860*x^21*y^9 + 9720*x^21*y^10 + 28512*x^21*y^11 + 4104*x^21*y^12 + 11016*x^21*y^13 + 3240*x^21*y^14 + 108*x^21*y^15 + 324*x^22*y^6 + 9720*x^22*y^7 + 21384*x^22*y^9 + 7776*x^22*y^10 + 7776*x^22*y^11 + 8424*x^22*y^12 + 648*x^22*y^13 + 1944*x^23*y^5 + 3888*x^23*y^7 + 13608*x^23*y^8 + 1620*x^23*y^9 + 10368*x^23*y^10 + 2916*x^23*y^11 + 1620*x^24*y^4 + 7776*x^24*y^6 + 1944*x^24*y^7 + 5184*x^24*y^8 + 6048*x^24*y^9 + 324*x^24*y^10 + 648*x^25*y^4 + 3888*x^25*y^5 + 648*x^25*y^6 + 5832*x^25*y^7 + 1296*x^25*y^8 - 108*x^26 + 1296*x^26*y^3 + 1944*x^26*y^5 + 2592*x^26*y^6 + 648*x^27*y^2 + 108*x^27*y^3 + 1944*x^27*y^4 + 324*x^27*y^5 + 324*x^28*y^2 + 648*x^28*y^3 + 324*x^29*y + 108*x^30:\n", "(-108) * y^26\n",
" support points = [(0, 26, 0), (0, 30, 0), (1, 29, 0), (2, 27, 0), (2, 28, 0), (3, 26, 0), (3, 27, 0), (3, 28, 0), (4, 24, 0), (4, 25, 0), (4, 27, 0), (5, 23, 0), (5, 25, 0), (5, 26, 0), (5, 27, 0), (6, 19, 0), (6, 21, 0), (6, 22, 0), (6, 24, 0), (6, 25, 0), (6, 26, 0), (7, 20, 0), (7, 22, 0), (7, 23, 0), (7, 24, 0), (7, 25, 0), (8, 18, 0), (8, 21, 0), (8, 23, 0), (8, 24, 0), (8, 25, 0), (9, 17, 0), (9, 19, 0), (9, 20, 0), (9, 21, 0), (9, 22, 0), (9, 23, 0), (9, 24, 0), (10, 15, 0), (10, 18, 0), (10, 20, 0), (10, 21, 0), (10, 22, 0), (10, 23, 0), (10, 24, 0), (11, 16, 0), (11, 18, 0), (11, 19, 0), (11, 21, 0), (11, 22, 0), (11, 23, 0), (12, 15, 0), (12, 17, 0), (12, 18, 0), (12, 19, 0), (12, 20, 0), (12, 21, 0), (12, 22, 0), (13, 13, 0), (13, 15, 0), (13, 16, 0), (13, 18, 0), (13, 19, 0), (13, 20, 0), (13, 21, 0), (13, 22, 0), (14, 14, 0), (14, 16, 0), (14, 17, 0), (14, 18, 0), (14, 19, 0), (14, 20, 0), (14, 21, 0), (15, 10, 0), (15, 12, 0), (15, 13, 0), (15, 15, 0), (15, 16, 0), (15, 17, 0), (15, 18, 0), (15, 19, 0), (15, 20, 0), (15, 21, 0), (16, 11, 0), (16, 13, 0), (16, 14, 0), (16, 15, 0), (16, 16, 0), (16, 17, 0), (16, 18, 0), (16, 19, 0), (16, 20, 0), (17, 9, 0), (17, 12, 0), (17, 14, 0), (17, 15, 0), (17, 16, 0), (17, 17, 0), (17, 18, 0), (17, 19, 0), (18, 8, 0), (18, 10, 0), (18, 11, 0), (18, 12, 0), (18, 13, 0), (18, 14, 0), (18, 15, 0), (18, 16, 0), (18, 17, 0), (18, 18, 0), (19, 6, 0), (19, 9, 0), (19, 11, 0), (19, 12, 0), (19, 13, 0), (19, 14, 0), (19, 15, 0), (19, 16, 0), (19, 17, 0), (20, 7, 0), (20, 9, 0), (20, 10, 0), (20, 12, 0), (20, 13, 0), (20, 14, 0), (20, 15, 0), (20, 16, 0), (21, 6, 0), (21, 8, 0), (21, 9, 0), (21, 10, 0), (21, 11, 0), (21, 12, 0), (21, 13, 0), (21, 14, 0), (21, 15, 0), (22, 6, 0), (22, 7, 0), (22, 9, 0), (22, 10, 0), (22, 11, 0), (22, 12, 0), (22, 13, 0), (23, 5, 0), (23, 7, 0), (23, 8, 0), (23, 9, 0), (23, 10, 0), (23, 11, 0), (24, 4, 0), (24, 6, 0), (24, 7, 0), (24, 8, 0), (24, 9, 0), (24, 10, 0), (25, 4, 0), (25, 5, 0), (25, 6, 0), (25, 7, 0), (25, 8, 0), (26, 0, 0), (26, 3, 0), (26, 5, 0), (26, 6, 0), (27, 2, 0), (27, 3, 0), (27, 4, 0), (27, 5, 0), (28, 2, 0), (28, 3, 0), (29, 1, 0), (30, 0, 0)]\n", "(-216) * x^6 * y^19\n",
" vertices = [(0, 26, 0), (26, 0, 0), (19, 6, 0), (6, 19, 0)]\n", "(-108) * x^26\n",
" number of proper faces = 19\n", "(-216) * y^6 * x^19\n",
" Facet 0: -156 + 7*y + 6*x >= 0\n", "(-108) * y^19 * (y^7 + 2*x^6)\n",
" Facet 1: -25 + y + x >= 0\n", "(-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",
" Facet 2: -156 + 6*y + 7*x >= 0\n", "(-108) * x^19 * (2*y^6 + x^7)\n"
" Facet 3: x >= 0\n",
" Facet 4: y >= 0\n",
" Facet 5: z >= 0\n"
] ]
} }
], ],
"source": [ "source": [
"ZD.give_info_newton(faces=False, cones=False, compact = False)" "for p in ZD.get_polyfaces_dictionary(compact=True):\n",
" print(p.factor())"
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 7, "execution_count": 5,
"metadata": { "metadata": {},
"collapsed": false
},
"outputs": [ "outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"y^13\n",
"x^6 * y^6\n",
"x^13\n",
"y^6 * (y^7 + x^6)\n",
"x^6 * (y^6 + x^7)\n"
]
}
], ],
"source": [
"for p in ZetaFunctions(g).get_polyfaces_dictionary(compact=True):\n",
" print(p.factor())"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"y^10\n",
"x^10\n",
"x^4 * y^4\n",
"y^4 * (y^3 + x^2)^2\n",
"x^4 * (y^2 + x^3)^2\n"
]
}
],
"source": [
"for p in ZetaFunctions(f).get_polyfaces_dictionary(compact=True):\n",
" print(p.factor())"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [ "source": [
"def estrato(ff, chi, pesos):\n", "def estrato(ff, chi, pesos):\n",
" Z1 = ZetaFunctions(ff)\n", " Z1 = ZetaFunctions(ff)\n",
" zetamon1 = Z1.monodromy_zeta().value()^chi\n", " zetamon1 = Z1.monodromy_zeta().value()^chi\n",
" zetatop1 = chi * Z1.topological_zeta(local=True, weights=pesos).value()\n", " zetatop1 = chi * Z1.topological_zeta(local=True, weights=pesos)\n",
" return zetamon1, zetatop1" " return zetamon1, zetatop1"
] ]
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"metadata": { "metadata": {
"collapsed": false "collapsed": false,
"jupyter": {
"outputs_hidden": false
}
}, },
"source": [ "source": [
"Veamos que la resolución larga no aporta\n", "Veamos que la resolución larga no aporta\n",
@ -122,37 +173,193 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 8, "execution_count": 10,
"metadata": { "metadata": {},
"collapsed": false "outputs": [],
}, "source": [
"M39, Z39 = estrato(z^3+x^20*y^42*z+x^26*y^52, 1, [5,11,1])\n",
"M98, Z98 = estrato(z^3+x^42*y^21*z+x^52*y^26, 1, [11,6,1])\n",
"M38, Z38 = estrato(z^3+x^20*y^21*z+x^26*y^26, 1, [5,6,1])"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [ "outputs": [
{ {
"data": { "data": {
"text/plain": [ "text/plain": [
"(0, 0)" "0"
] ]
}, },
"execution_count": 8, "execution_count": 12,
"metadata": { "metadata": {},
},
"output_type": "execute_result" "output_type": "execute_result"
} }
], ],
"source": [ "source": [
"M3, Z3 = estrato(z^3+x^26,-1, [5,1,1])\n", "Z39 + Z98 - Z38"
"M9, Z9 = estrato(z^3+x^52,-1, [11,1,1])\n", ]
"M8, Z8 = estrato(z^3+x^26,1, [6,1,1])\n", },
"M39, Z39 = estrato(z^3+x^26*y^52,1, [5,11,1])\n", {
"M98, Z98 = estrato(z^3+x^52*y^26, 1, [11,6,1])\n", "cell_type": "code",
"M9f, Z9f = estrato(z^3+x^50*y*z + x^52, 1, [11,1,1])\n", "execution_count": 13,
"Z3 + Z39 + Z98 + Z8, Z9 + Z9f\n" "metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"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])"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"M3, Z3 = estrato(z^3+x^20*z+x^26, 1, [5,1,1])\n",
"M8, Z8 = estrato(z^3+x^21*z+x^26, 1, [6,1,1])"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Z38 + Z8 - Z3"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"((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",
" (19/156) * (s + 1/2)^-2 * (s + 1)^-1 * (s^2 + 48/19*s + 39/38))"
]
},
"execution_count": 39,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a, b = estrato(z^3+x^4*z^2+x^13, 1, [2,1,1])\n",
"a.factor(), b.factor()"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [],
"source": [
"T.<s> = QQ[]"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0"
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"A1 = 3 * s / (s + 1) / (78 * s + 39)\n",
"V1 = 2 / (78 * s + 39)\n",
"V2 = 1 / (78 * s + 39)\n",
"M7, Z7 = estrato(z^3 + x^78, 1, [13,1,1])\n",
"Z7 - (V1 + V2 - A1)"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(8/39) * (s + 1/2)^-1 * (s + 1)^-1 * (s + 9/8)"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"M7a, Z7a = estrato(z^3 + x^13, 1, [13/6,1,1])\n",
"Z7a.factor()"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0"
]
},
"execution_count": 37,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(6 * V1 + 6 * V2 - 2 / 3 * A1 - Z7a)"
] ]
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"metadata": { "metadata": {
"collapsed": false "collapsed": false,
"jupyter": {
"outputs_hidden": false
}
}, },
"source": [ "source": [
"Cálculo completo\n", "Cálculo completo\n",
@ -163,7 +370,10 @@
"cell_type": "code", "cell_type": "code",
"execution_count": 9, "execution_count": 9,
"metadata": { "metadata": {
"collapsed": false "collapsed": false,
"jupyter": {
"outputs_hidden": false
}
}, },
"outputs": [ "outputs": [
{ {
@ -188,7 +398,10 @@
"cell_type": "code", "cell_type": "code",
"execution_count": 55, "execution_count": 55,
"metadata": { "metadata": {
"collapsed": false "collapsed": false,
"jupyter": {
"outputs_hidden": false
}
}, },
"outputs": [ "outputs": [
{ {
@ -213,8 +426,7 @@
] ]
}, },
"execution_count": 55, "execution_count": 55,
"metadata": { "metadata": {},
},
"output_type": "execute_result" "output_type": "execute_result"
} }
], ],
@ -227,53 +439,48 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 0, "execution_count": null,
"metadata": { "metadata": {
"collapsed": false "collapsed": false,
"jupyter": {
"outputs_hidden": false
}
}, },
"outputs": [ "outputs": [],
], "source": []
"source": [
]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 0, "execution_count": null,
"metadata": { "metadata": {
"collapsed": false "collapsed": false,
"jupyter": {
"outputs_hidden": false
}
}, },
"outputs": [ "outputs": [],
], "source": []
"source": [
]
} }
], ],
"metadata": { "metadata": {
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"--matplotlib=inline", "codemirror_mode": {
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