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superelliptic_alpha; kxi jako quo

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jgarnek 2022-03-07 12:52:56 +01:00
parent 9794e9e45b
commit 78aa092433
1 changed files with 147 additions and 24 deletions
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171
superelliptic_alpha.ipynb
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@ -2,12 +2,22 @@
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"execution_count": null,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Exiting Sage (CPU time 0m6.48s, Wall time 11m10.64s).\n"
]
}
],
"source": [
"def basis_holomorphic_differentials_degree(f, m, p):\n",
" kxi.<xi> = PolynomialRing(GF(p))\n",
" kxi1.<xi1> = PolynomialRing(GF(p))\n",
" kxi = kxi.quotient(xi1^p)\n",
" xi = kxi(xi1)\n",
" r = f.degree()\n",
" delta = GCD(r, m)\n",
" Rx.<x> = PolynomialRing(kxi)\n",
@ -39,7 +49,9 @@
"def basis_de_rham_degrees(f, m, p):\n",
" r = f.degree()\n",
" delta = GCD(r, m)\n",
" kxi.<xi> = PolynomialRing(GF(p))\n",
" kxi1.<xi1> = PolynomialRing(GF(p))\n",
" kxi = kxi.quotient(xi1^p)\n",
" xi = kxi(xi1)\n",
" Rx.<x> = PolynomialRing(kxi)\n",
" Rxy.<x, y> = PolynomialRing(kxi, 2)\n",
" Fxy = FractionField(Rxy)\n",
@ -79,7 +91,9 @@
"class superelliptic:\n",
" \n",
" def __init__(self, f, m, p):\n",
" kxi.<xi> = PolynomialRing(GF(p))\n",
" kxi1.<xi1> = PolynomialRing(GF(p))\n",
" kxi = kxi.quotient(xi1^p)\n",
" xi = kxi(xi1)\n",
" Rx.<x> = PolynomialRing(kxi)\n",
" Rxy.<x, y> = PolynomialRing(kxi, 2)\n",
" Fxy = FractionField(Rxy)\n",
@ -153,7 +167,9 @@
" basis = self.basis_holomorphic_differentials\n",
" g = self.genus()\n",
" p = self.characteristic\n",
" kxi.<xi> = PolynomialRing(GF(p))\n",
" kxi1.<xi1> = PolynomialRing(GF(p))\n",
" kxi = kxi.quotient(xi1^p)\n",
" xi = kxi(xi1)\n",
" M = matrix(kxi, g, g)\n",
" for i in range(0, len(basis)):\n",
" w = basis[i]\n",
@ -172,7 +188,9 @@
" \n",
"def reduction(C, g):\n",
" p = C.characteristic\n",
" kxi.<xi> = PolynomialRing(GF(p))\n",
" kxi1.<xi1> = PolynomialRing(GF(p))\n",
" kxi = kxi.quotient(xi1^p)\n",
" xi = kxi(xi1)\n",
" Rxy.<x, y> = PolynomialRing(kxi, 2)\n",
" Fxy = FractionField(Rxy)\n",
" f = C.polynomial\n",
@ -198,7 +216,10 @@
"\n",
"def reduction_form(C, g):\n",
" p = C.characteristic\n",
" Rxy.<x, y> = PolynomialRing(GF(p), 2)\n",
" kxi1.<xi1> = PolynomialRing(GF(p))\n",
" kxi = kxi.quotient(xi1^p)\n",
" xi = kxi(xi1)\n",
" Rxy.<x, y> = PolynomialRing(kxi, 2)\n",
" Fxy = FractionField(Rxy)\n",
" f = C.polynomial\n",
" r = f.degree()\n",
@ -206,7 +227,7 @@
" g = reduction(C, g)\n",
"\n",
" g1 = Rxy(0)\n",
" Rx.<x> = PolynomialRing(GF(p))\n",
" Rx.<x> = PolynomialRing(kxi)\n",
" Fx = FractionField(Rx)\n",
" FxRy.<y> = PolynomialRing(Fx)\n",
" \n",
@ -223,7 +244,10 @@
"class superelliptic_function:\n",
" def __init__(self, C, g):\n",
" p = C.characteristic\n",
" Rxy.<x, y> = PolynomialRing(GF(p), 2)\n",
" kxi1.<xi1> = PolynomialRing(GF(p))\n",
" kxi = kxi.quotient(xi1^p)\n",
" xi = kxi(xi1)\n",
" Rxy.<x, y> = PolynomialRing(kxi, 2)\n",
" Fxy = FractionField(Rxy)\n",
" f = C.polynomial\n",
" r = f.degree()\n",
@ -565,7 +589,7 @@
},
{
"cell_type": "code",
"execution_count": 2,
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@ -654,7 +678,7 @@
},
{
"cell_type": "code",
"execution_count": 8,
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
@ -663,19 +687,9 @@
},
{
"cell_type": "code",
"execution_count": 13,
"execution_count": null,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Current Time = 18:11:00\n",
"[1, 2, 3, 4, 5, 6]\n",
"Current Time = 18:11:21\n"
]
}
],
"outputs": [],
"source": [
"now = datetime.now()\n",
"\n",
@ -1923,6 +1937,115 @@
"print(\"Current Time =\", current_time)"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"kxi1.<xi1> = PolynomialRing(GF(p))\n",
"kxi = kxi.quotient(xi1^p)\n",
"xi = kxi(xi1)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Univariate Quotient Polynomial Ring in xibar over Finite Field of size 5 with modulus xi^5"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"kxi2"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"s = kxi2(xi)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"xibar"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"s"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"s^6"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"a = 1+2*s+s^2"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[1, 2, 1, 0, 0]"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"list(a)"
]
},
{
"cell_type": "code",
"execution_count": null,