dziala frobenius i cartier; usuniete printy
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@ -79,7 +79,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 140,
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"execution_count": 142,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -116,7 +116,6 @@
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"#Any element [f dx, g] is represented as a combination of the basis vectors.\n",
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"\n",
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"def zapis_w_bazie_dr(elt, m, f, j, p):\n",
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" print(elt, 'czy w dr', czy_w_de_rhamie(elt, m, f, j, p))\n",
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" R.<x> = PolynomialRing(GF(p))\n",
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" RR = FractionField(R)\n",
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" f = R(f)\n",
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@ -132,11 +131,9 @@
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" \n",
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" ## zmiana\n",
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" if elt[0]== 0 and elt[1] == 0:\n",
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" print('p1')\n",
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" return zapis\n",
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" \n",
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" if elt[1] == 0:\n",
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" print('p2')\n",
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" elt[0] = R(elt[0])\n",
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" d = elt[0].degree()\n",
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" a = elt[0].coefficients(sparse = false)[d]\n",
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@ -155,11 +152,10 @@
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" Mm = m/delta\n",
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" \n",
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" stopnie2 = stopnie_drugiej_wspolrzednej_bazy_dr(m, f, j, p)\n",
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" inv_stopnie2 = {v: k for k, v in stopnie2.items()} \n",
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" print('d', d, 'a', a, 'dostepne:', stopnie2, 'czy w stopnie 2', d not in stopnie2)\n",
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" inv_stopnie2 = {v: k for k, v in stopnie2.items()}\n",
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" if (d not in stopnie2.values()):\n",
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" print('p3')\n",
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" if d>= 0:\n",
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" if d> 0:\n",
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" print('p3a')\n",
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" j1 = m-j\n",
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" print('?', -j1*Rr+d*Mm)\n",
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@ -523,7 +519,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 141,
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"execution_count": 143,
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"metadata": {},
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"outputs": [
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{
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@ -545,56 +541,90 @@
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"[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",
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"d 0 a 2 dostepne: {0: 1, 1: 2} czy w stopnie 2 False\n",
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"p3\n",
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"p3a\n",
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"? -9\n",
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"[2*x^2 + 2, (3*x^4 + 2*x^3 + 4*x^2 + 3*x + 2)/x^5] czy w dr False\n",
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"p3b\n",
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"[3, (3*x^4 + 2*x^3 + 4*x^2 + 3*x + 2)/x^5] czy w dr True\n",
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"d 1 a 3 dostepne: {0: 1, 1: 2} czy w stopnie 2 False\n",
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"p4\n",
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"k 0 a 3\n",
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"[2*x^2 + 2, (2*x^3 + 4*x^2 + 3*x + 2)/x^5] czy w dr False\n",
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"[3, (2*x^3 + 4*x^2 + 3*x + 2)/x^5] czy w dr True\n",
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"d 2 a 2 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n",
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"p4\n",
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"k 1 a 2\n",
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"[2*x^2 + 4, (4*x^2 + 3*x + 2)/x^5] czy w dr False\n",
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"[0, (4*x^2 + 3*x + 2)/x^5] czy w dr True\n",
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"d 3 a 4 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n",
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"p3\n",
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"p3a\n",
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"? 3\n",
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"[2*x^2 + 4, (3*x + 2)/x^5] czy w dr False\n",
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"[0, (3*x + 2)/x^5] czy w dr True\n",
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"d 4 a 3 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n",
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"p3\n",
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"p3a\n",
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"? 7\n",
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"[2*x^2 + 4, 2/x^5] czy w dr False\n",
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"[0, 2/x^5] czy w dr True\n",
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"d 5 a 2 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n",
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"p3\n",
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"p3a\n",
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"? 11\n",
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"[2*x^2 + 4, 0] czy w dr False\n",
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"p2\n"
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"[0, 0] czy w dr True\n",
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"p1\n",
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"[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",
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"d 1 a 4 dostepne: {0: 1, 1: 2} czy w stopnie 2 False\n",
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"p4\n",
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"k 0 a 4\n",
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"[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",
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"d 3 a 2 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n",
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"p3\n",
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"p3a\n",
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"? 3\n",
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"[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",
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"d 4 a 4 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n",
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"p3\n",
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"p3a\n",
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"? 7\n",
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"[0, (2*x^5 + 3*x^4 + 2*x^3 + 4*x^2 + 3*x + 2)/x^10] czy w dr True\n",
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"d 5 a 2 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n",
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"p3\n",
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"p3a\n",
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"? 11\n",
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"[0, (3*x^4 + 2*x^3 + 4*x^2 + 3*x + 2)/x^10] czy w dr True\n",
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"d 6 a 3 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n",
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"p3\n",
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"p3a\n",
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"? 15\n",
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"[0, (2*x^3 + 4*x^2 + 3*x + 2)/x^10] czy w dr True\n",
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"d 7 a 2 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n",
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"p3\n",
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"p3a\n",
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"? 19\n",
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"[0, (4*x^2 + 3*x + 2)/x^10] czy w dr True\n",
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"d 8 a 4 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n",
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"p3\n",
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"p3a\n",
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"? 23\n",
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"[0, (3*x + 2)/x^10] czy w dr True\n",
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"d 9 a 3 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n",
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"p3\n",
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"p3a\n",
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"? 27\n",
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"[0, 2/x^10] czy w dr True\n",
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"d 10 a 2 dostepne: {0: 1, 1: 2} czy w stopnie 2 True\n",
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"p3\n",
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"p3a\n",
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"? 31\n",
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"[0, 0] czy w dr True\n",
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"p1\n"
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]
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},
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{
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"ename": "KeyError",
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"evalue": "2",
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"output_type": "error",
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"traceback": [
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"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
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"\u001b[0;31mKeyError\u001b[0m Traceback (most recent call last)",
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"\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",
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"\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",
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"\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",
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|
||||
"\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 56\u001b[0m \u001b[0md\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[0mdegree\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 57\u001b[0m \u001b[0ma\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[0mcoefficients\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msparse\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0md\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 58\u001b[0;31m \u001b[0mk\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0minv_stopnie_holo\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0md\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;31m#ktory element bazy jest stopnia d? ten o indeksie k\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 59\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 60\u001b[0m \u001b[0ma1\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[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[0mcoefficients\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msparse\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0md\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||
"\u001b[0;31mKeyError\u001b[0m: 2"
|
||||
]
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"[3 4]\n",
|
||||
"[2 0]"
|
||||
]
|
||||
},
|
||||
"execution_count": 143,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
|
||||
Loading…
Reference in New Issue
Block a user