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dziala frobenius i cartier; usuniete printy

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jgarnek 2021-08-19 13:17:24 +02:00
parent 7951e64332
commit d071f53aae
1 changed files with 67 additions and 37 deletions
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deRhamComputation.ipynb
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@ -79,7 +79,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 140, "execution_count": 142,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
@ -116,7 +116,6 @@
"#Any element [f dx, g] is represented as a combination of the basis vectors.\n", "#Any element [f dx, g] is represented as a combination of the basis vectors.\n",
"\n", "\n",
"def zapis_w_bazie_dr(elt, m, f, j, p):\n", "def zapis_w_bazie_dr(elt, m, f, j, p):\n",
" print(elt, 'czy w dr', czy_w_de_rhamie(elt, m, f, j, p))\n",
" R.<x> = PolynomialRing(GF(p))\n", " R.<x> = PolynomialRing(GF(p))\n",
" RR = FractionField(R)\n", " RR = FractionField(R)\n",
" f = R(f)\n", " f = R(f)\n",
@ -132,11 +131,9 @@
" \n", " \n",
" ## zmiana\n", " ## zmiana\n",
" if elt[0]== 0 and elt[1] == 0:\n", " if elt[0]== 0 and elt[1] == 0:\n",
" print('p1')\n",
" return zapis\n", " return zapis\n",
" \n", " \n",
" if elt[1] == 0:\n", " if elt[1] == 0:\n",
" print('p2')\n",
" elt[0] = R(elt[0])\n", " elt[0] = R(elt[0])\n",
" d = elt[0].degree()\n", " d = elt[0].degree()\n",
" a = elt[0].coefficients(sparse = false)[d]\n", " a = elt[0].coefficients(sparse = false)[d]\n",
@ -155,11 +152,10 @@
" Mm = m/delta\n", " Mm = m/delta\n",
" \n", " \n",
" stopnie2 = stopnie_drugiej_wspolrzednej_bazy_dr(m, f, j, p)\n", " stopnie2 = stopnie_drugiej_wspolrzednej_bazy_dr(m, f, j, p)\n",
" inv_stopnie2 = {v: k for k, v in stopnie2.items()} \n", " inv_stopnie2 = {v: k for k, v in stopnie2.items()}\n",
" print('d', d, 'a', a, 'dostepne:', stopnie2, 'czy w stopnie 2', d not in stopnie2)\n",
" if (d not in stopnie2.values()):\n", " if (d not in stopnie2.values()):\n",
" print('p3')\n", " print('p3')\n",
" if d>= 0:\n", " if d> 0:\n",
" print('p3a')\n", " print('p3a')\n",
" j1 = m-j\n", " j1 = m-j\n",
" print('?', -j1*Rr+d*Mm)\n", " print('?', -j1*Rr+d*Mm)\n",
@ -523,7 +519,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 141, "execution_count": 143,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
@ -545,56 +541,90 @@
"[2*x^2 + 2, (2*x^5 + 3*x^4 + 2*x^3 + 4*x^2 + 3*x + 2)/x^5] czy w dr True\n", "[2*x^2 + 2, (2*x^5 + 3*x^4 + 2*x^3 + 4*x^2 + 3*x + 2)/x^5] czy w dr True\n",
"d 0 a 2 dostepne: {0: 1, 1: 2} czy w stopnie 2 False\n", "d 0 a 2 dostepne: {0: 1, 1: 2} czy w stopnie 2 False\n",
"p3\n", "p3\n",
"p3a\n", "p3b\n",
"? -9\n", "[3, (3*x^4 + 2*x^3 + 4*x^2 + 3*x + 2)/x^5] czy w dr True\n",
"[2*x^2 + 2, (3*x^4 + 2*x^3 + 4*x^2 + 3*x + 2)/x^5] czy w dr False\n",
"d 1 a 3 dostepne: {0: 1, 1: 2} czy w stopnie 2 False\n", "d 1 a 3 dostepne: {0: 1, 1: 2} czy w stopnie 2 False\n",
"p4\n", "p4\n",
"k 0 a 3\n", "k 0 a 3\n",
"[2*x^2 + 2, (2*x^3 + 4*x^2 + 3*x + 2)/x^5] czy w dr False\n", "[3, (2*x^3 + 4*x^2 + 3*x + 2)/x^5] czy w dr True\n",
"d 2 a 2 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n", "d 2 a 2 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n",
"p4\n", "p4\n",
"k 1 a 2\n", "k 1 a 2\n",
"[2*x^2 + 4, (4*x^2 + 3*x + 2)/x^5] czy w dr False\n", "[0, (4*x^2 + 3*x + 2)/x^5] czy w dr True\n",
"d 3 a 4 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n", "d 3 a 4 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n",
"p3\n", "p3\n",
"p3a\n", "p3a\n",
"? 3\n", "? 3\n",
"[2*x^2 + 4, (3*x + 2)/x^5] czy w dr False\n", "[0, (3*x + 2)/x^5] czy w dr True\n",
"d 4 a 3 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n", "d 4 a 3 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n",
"p3\n", "p3\n",
"p3a\n", "p3a\n",
"? 7\n", "? 7\n",
"[2*x^2 + 4, 2/x^5] czy w dr False\n", "[0, 2/x^5] czy w dr True\n",
"d 5 a 2 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n", "d 5 a 2 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n",
"p3\n", "p3\n",
"p3a\n", "p3a\n",
"? 11\n", "? 11\n",
"[2*x^2 + 4, 0] czy w dr False\n", "[0, 0] czy w dr True\n",
"p2\n" "p1\n",
"[0, (4*x^9 + 2*x^7 + 4*x^6 + 2*x^5 + 3*x^4 + 2*x^3 + 4*x^2 + 3*x + 2)/x^10] czy w dr True\n",
"d 1 a 4 dostepne: {0: 1, 1: 2} czy w stopnie 2 False\n",
"p4\n",
"k 0 a 4\n",
"[0, (2*x^7 + 4*x^6 + 2*x^5 + 3*x^4 + 2*x^3 + 4*x^2 + 3*x + 2)/x^10] czy w dr True\n",
"d 3 a 2 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n",
"p3\n",
"p3a\n",
"? 3\n",
"[0, (4*x^6 + 2*x^5 + 3*x^4 + 2*x^3 + 4*x^2 + 3*x + 2)/x^10] czy w dr True\n",
"d 4 a 4 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n",
"p3\n",
"p3a\n",
"? 7\n",
"[0, (2*x^5 + 3*x^4 + 2*x^3 + 4*x^2 + 3*x + 2)/x^10] czy w dr True\n",
"d 5 a 2 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n",
"p3\n",
"p3a\n",
"? 11\n",
"[0, (3*x^4 + 2*x^3 + 4*x^2 + 3*x + 2)/x^10] czy w dr True\n",
"d 6 a 3 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n",
"p3\n",
"p3a\n",
"? 15\n",
"[0, (2*x^3 + 4*x^2 + 3*x + 2)/x^10] czy w dr True\n",
"d 7 a 2 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n",
"p3\n",
"p3a\n",
"? 19\n",
"[0, (4*x^2 + 3*x + 2)/x^10] czy w dr True\n",
"d 8 a 4 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n",
"p3\n",
"p3a\n",
"? 23\n",
"[0, (3*x + 2)/x^10] czy w dr True\n",
"d 9 a 3 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n",
"p3\n",
"p3a\n",
"? 27\n",
"[0, 2/x^10] czy w dr True\n",
"d 10 a 2 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n",
"p3\n",
"p3a\n",
"? 31\n",
"[0, 0] czy w dr True\n",
"p1\n"
] ]
}, },
{ {
"ename": "KeyError", "data": {
"evalue": "2", "text/plain": [
"output_type": "error", "[3 4]\n",
"traceback": [ "[2 0]"
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", ]
"\u001b[0;31mKeyError\u001b[0m Traceback (most recent call last)", },
"\u001b[0;32m<ipython-input-141-86a3d5ca17ee>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mmacierz_frob_dr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "execution_count": 143,
"\u001b[0;32m<ipython-input-132-3ef6f7d47fcd>\u001b[0m in \u001b[0;36mmacierz_frob_dr\u001b[0;34m(p, m, f, j)\u001b[0m\n\u001b[1;32m 12\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mk\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbaza\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 13\u001b[0m \u001b[0mfrob\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfrobenius_dr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbaza\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mj\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 14\u001b[0;31m \u001b[0mv\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mzapis_w_bazie_dr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfrob\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 15\u001b[0m \u001b[0mA\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmatrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mv\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 16\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mA\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtranspose\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "metadata": {},
"\u001b[0;32m<ipython-input-140-9ce96c4e8631>\u001b[0m in \u001b[0;36mzapis_w_bazie_dr\u001b[0;34m(elt, m, f, j, p)\u001b[0m\n\u001b[1;32m 85\u001b[0m \u001b[0mj1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 86\u001b[0m \u001b[0melt1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0melt\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mj1\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md1\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mderivative\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mm\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0md1\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md1\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mRR\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0melt\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mR\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 87\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mzapis_w_bazie_dr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0melt1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 88\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 89\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'p4'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "output_type": "execute_result"
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"\u001b[0;31mKeyError\u001b[0m: 2"
]
} }
], ],
"source": [ "source": [