diff --git a/doc/kryptools.ipynb b/doc/kryptools.ipynb index 8f27eda..fdec51a 100644 --- a/doc/kryptools.ipynb +++ b/doc/kryptools.ipynb @@ -1110,6 +1110,68 @@ "factorint(n, verbose=1)" ] }, + { + "cell_type": "markdown", + "id": "1f6924cd-31e8-4701-bf02-0c8c719e870d", + "metadata": {}, + "source": [ + "There are also tests if a number is a [perfect power](https://en.wikipedia.org/wiki/Perfect_power) (if it is not, `None` will be returned)" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "id": "e8788850-9df6-45d9-9b3f-3ce7b1db13cb", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(10, 2)" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from kryptools import perfect_power\n", + "\n", + "perfect_power(100)" + ] + }, + { + "cell_type": "markdown", + "id": "68b6f3cf-0715-4a02-b5f3-3d5ce47109ff", + "metadata": {}, + "source": [ + "or a prime power (if it is not, `None` will be returned)" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "id": "315a12c6-cd1f-49fa-8599-6cb6a6526d33", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(9973, 100)" + ] + }, + "execution_count": 36, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from kryptools import prime_power\n", + "\n", + "prime_power(9973**100)" + ] + }, { "cell_type": "markdown", "id": "c7e2f616-4da9-458e-897c-701ee5e55cac", @@ -1128,7 +1190,7 @@ }, { "cell_type": "code", - "execution_count": 35, + "execution_count": 37, "id": "9a629204-562c-44eb-a012-7345b97035b5", "metadata": {}, "outputs": [ @@ -1138,7 +1200,7 @@ "[487, 1709]" ] }, - "execution_count": 35, + "execution_count": 37, "metadata": {}, "output_type": "execute_result" } @@ -1159,7 +1221,7 @@ }, { "cell_type": "code", - "execution_count": 36, + "execution_count": 38, "id": "39f76a97-1b88-4b95-aac7-bf403043d7b7", "metadata": {}, "outputs": [ @@ -1169,7 +1231,7 @@ "1709" ] }, - "execution_count": 36, + "execution_count": 38, "metadata": {}, "output_type": "execute_result" } @@ -1190,7 +1252,7 @@ }, { "cell_type": "code", - "execution_count": 37, + "execution_count": 39, "id": "6c0cb7c6-03e5-469f-8420-496813bd26ea", "metadata": {}, "outputs": [ @@ -1200,7 +1262,7 @@ "487" ] }, - "execution_count": 37, + "execution_count": 39, "metadata": {}, "output_type": "execute_result" } @@ -1221,7 +1283,7 @@ }, { "cell_type": "code", - "execution_count": 38, + "execution_count": 40, "id": "e68d0db0-7d1d-4a00-ad6e-10656c829708", "metadata": {}, "outputs": [ @@ -1231,7 +1293,7 @@ "487" ] }, - "execution_count": 38, + "execution_count": 40, "metadata": {}, "output_type": "execute_result" } @@ -1252,7 +1314,7 @@ }, { "cell_type": "code", - "execution_count": 39, + "execution_count": 41, "id": "3b7c0474-835b-4b10-b0d3-a7b8f62eff23", "metadata": {}, "outputs": [ @@ -1262,7 +1324,7 @@ "1709" ] }, - "execution_count": 39, + "execution_count": 41, "metadata": {}, "output_type": "execute_result" } @@ -1283,7 +1345,7 @@ }, { "cell_type": "code", - "execution_count": 40, + "execution_count": 42, "id": "8ee9854b-6ce0-43b6-906d-98f52fb74d8e", "metadata": {}, "outputs": [ @@ -1293,7 +1355,7 @@ "1709" ] }, - "execution_count": 40, + "execution_count": 42, "metadata": {}, "output_type": "execute_result" } @@ -1322,7 +1384,7 @@ }, { "cell_type": "code", - "execution_count": 41, + "execution_count": 43, "id": "46ab20cc-8d39-4d7b-baef-f411cf34deb7", "metadata": {}, "outputs": [], @@ -1355,7 +1417,7 @@ }, { "cell_type": "code", - "execution_count": 42, + "execution_count": 44, "id": "66ae327c-ff14-4bff-b12d-330c1787cd6b", "metadata": {}, "outputs": [], @@ -1378,7 +1440,7 @@ }, { "cell_type": "code", - "execution_count": 43, + "execution_count": 45, "id": "d1ce2beb-4e60-4a56-9943-d47f1945f13a", "metadata": {}, "outputs": [], @@ -1401,7 +1463,7 @@ }, { "cell_type": "code", - "execution_count": 44, + "execution_count": 46, "id": "fb231c7c-293f-4353-8048-1de3d26568e1", "metadata": {}, "outputs": [], @@ -1424,7 +1486,7 @@ }, { "cell_type": "code", - "execution_count": 45, + "execution_count": 47, "id": "ad8d5929-488e-44bc-9263-91044a2886d4", "metadata": {}, "outputs": [ @@ -1456,7 +1518,7 @@ }, { "cell_type": "code", - "execution_count": 46, + "execution_count": 48, "id": "882543ac-a2f7-4448-93bd-d9385d3457f6", "metadata": {}, "outputs": [ @@ -1497,7 +1559,7 @@ }, { "cell_type": "code", - "execution_count": 47, + "execution_count": 49, "id": "4626c758-753b-4d3a-9ed0-99038ca5f280", "metadata": {}, "outputs": [ @@ -1508,7 +1570,7 @@ "[ 35 ]" ] }, - "execution_count": 47, + "execution_count": 49, "metadata": {}, "output_type": "execute_result" } @@ -1531,7 +1593,7 @@ }, { "cell_type": "code", - "execution_count": 48, + "execution_count": 50, "id": "8a2f83a9-7114-43a1-baee-7f6bb6c45f30", "metadata": {}, "outputs": [ @@ -1542,7 +1604,7 @@ "[ 3 ]" ] }, - "execution_count": 48, + "execution_count": 50, "metadata": {}, "output_type": "execute_result" } @@ -1561,7 +1623,7 @@ }, { "cell_type": "code", - "execution_count": 49, + "execution_count": 51, "id": "ef4a7e98-4d55-482b-a264-6aab3283e6ec", "metadata": {}, "outputs": [ @@ -1572,7 +1634,7 @@ "[ 1, 2, 3 ]" ] }, - "execution_count": 49, + "execution_count": 51, "metadata": {}, "output_type": "execute_result" } @@ -1592,7 +1654,7 @@ }, { "cell_type": "code", - "execution_count": 50, + "execution_count": 52, "id": "3bec64e6-937f-4041-a710-cf42c95a8689", "metadata": {}, "outputs": [ @@ -1604,7 +1666,7 @@ "[ 7, 8, 12 ]" ] }, - "execution_count": 50, + "execution_count": 52, "metadata": {}, "output_type": "execute_result" } @@ -1627,7 +1689,7 @@ }, { "cell_type": "code", - "execution_count": 51, + "execution_count": 53, "id": "ab222100-fc64-49b9-b5ef-2d6ae719f15c", "metadata": {}, "outputs": [ @@ -1639,7 +1701,7 @@ "[ 0, 0, 1 ]" ] }, - "execution_count": 51, + "execution_count": 53, "metadata": {}, "output_type": "execute_result" } @@ -1658,7 +1720,7 @@ }, { "cell_type": "code", - "execution_count": 52, + "execution_count": 54, "id": "a99ed976-cbdd-4ce7-8a97-efcee7fd510d", "metadata": {}, "outputs": [ @@ -1668,7 +1730,7 @@ "-9" ] }, - "execution_count": 52, + "execution_count": 54, "metadata": {}, "output_type": "execute_result" } @@ -1687,7 +1749,7 @@ }, { "cell_type": "code", - "execution_count": 53, + "execution_count": 55, "id": "64294f1f-d3ef-41b0-ad59-d68e69c89aba", "metadata": {}, "outputs": [ @@ -1708,7 +1770,7 @@ "[ 0, 0, 1 ]" ] }, - "execution_count": 53, + "execution_count": 55, "metadata": {}, "output_type": "execute_result" } @@ -1729,7 +1791,7 @@ }, { "cell_type": "code", - "execution_count": 54, + "execution_count": 56, "id": "47961b0f-e632-4d1c-9445-de3c217bce10", "metadata": {}, "outputs": [ @@ -1739,7 +1801,7 @@ "2" ] }, - "execution_count": 54, + "execution_count": 56, "metadata": {}, "output_type": "execute_result" } @@ -1753,7 +1815,7 @@ }, { "cell_type": "code", - "execution_count": 55, + "execution_count": 57, "id": "d9cfb165-6e94-413b-9a91-5c5aa3870aa3", "metadata": {}, "outputs": [ @@ -1774,7 +1836,7 @@ "[ 0, 0, 1 ]" ] }, - "execution_count": 55, + "execution_count": 57, "metadata": {}, "output_type": "execute_result" } @@ -1803,7 +1865,7 @@ }, { "cell_type": "code", - "execution_count": 56, + "execution_count": 58, "id": "0f5a048b-767e-4848-bb23-c898365ee9dc", "metadata": {}, "outputs": [ @@ -1815,7 +1877,7 @@ "[ 0, 0, 1 ]" ] }, - "execution_count": 56, + "execution_count": 58, "metadata": {}, "output_type": "execute_result" } @@ -1837,7 +1899,7 @@ }, { "cell_type": "code", - "execution_count": 57, + "execution_count": 59, "id": "61bad2d5-2fad-4f5a-b4cf-206fca8e09fd", "metadata": {}, "outputs": [ @@ -1848,7 +1910,7 @@ "[ 0, 1 ]" ] }, - "execution_count": 57, + "execution_count": 59, "metadata": {}, "output_type": "execute_result" } @@ -1872,7 +1934,7 @@ }, { "cell_type": "code", - "execution_count": 58, + "execution_count": 60, "id": "5712d013-c037-4b03-9f62-13fdaaae855b", "metadata": {}, "outputs": [ @@ -1882,7 +1944,7 @@ "5.0" ] }, - "execution_count": 58, + "execution_count": 60, "metadata": {}, "output_type": "execute_result" } @@ -1903,7 +1965,7 @@ }, { "cell_type": "code", - "execution_count": 59, + "execution_count": 61, "id": "0c56dbdc-caa4-4783-8c2f-8f586a8dc4a1", "metadata": {}, "outputs": [ @@ -1913,7 +1975,7 @@ "0.3521856535823236" ] }, - "execution_count": 59, + "execution_count": 61, "metadata": {}, "output_type": "execute_result" } @@ -1934,7 +1996,7 @@ }, { "cell_type": "code", - "execution_count": 60, + "execution_count": 62, "id": "c3f8c523-114c-46b9-968d-4eb31615de4b", "metadata": {}, "outputs": [ @@ -1952,7 +2014,7 @@ "[ 0 ]" ] }, - "execution_count": 60, + "execution_count": 62, "metadata": {}, "output_type": "execute_result" } @@ -1978,7 +2040,7 @@ }, { "cell_type": "code", - "execution_count": 61, + "execution_count": 63, "id": "b8ba76ae-092c-4f12-9a05-0b33fd54ebb2", "metadata": {}, "outputs": [ @@ -1996,7 +2058,7 @@ "[ 0 ]" ] }, - "execution_count": 61, + "execution_count": 63, "metadata": {}, "output_type": "execute_result" } @@ -2020,7 +2082,7 @@ }, { "cell_type": "code", - "execution_count": 62, + "execution_count": 64, "id": "bd6ea8c7-85ba-4b8d-97d6-f3176e9a22d4", "metadata": {}, "outputs": [ @@ -2038,7 +2100,7 @@ "[ 0 ]" ] }, - "execution_count": 62, + "execution_count": 64, "metadata": {}, "output_type": "execute_result" } @@ -2063,7 +2125,7 @@ }, { "cell_type": "code", - "execution_count": 63, + "execution_count": 65, "id": "ee41707c-8d92-468d-9a94-18b6bd44053c", "metadata": {}, "outputs": [ @@ -2075,7 +2137,7 @@ "[ 1, -1, 1 ]" ] }, - "execution_count": 63, + "execution_count": 65, "metadata": {}, "output_type": "execute_result" } @@ -2098,7 +2160,7 @@ }, { "cell_type": "code", - "execution_count": 64, + "execution_count": 66, "id": "694c25e5-d01f-4acf-ab57-69bffb0fb9a8", "metadata": {}, "outputs": [ @@ -2110,7 +2172,7 @@ "[ 4, 2, 9 ]" ] }, - "execution_count": 64, + "execution_count": 66, "metadata": {}, "output_type": "execute_result" } @@ -2139,7 +2201,7 @@ }, { "cell_type": "code", - "execution_count": 65, + "execution_count": 67, "id": "df0886b4-54d8-4fe7-a665-e9b908c41060", "metadata": {}, "outputs": [ @@ -2152,7 +2214,7 @@ "[ 49, -45, 29, 735 ]" ] }, - "execution_count": 65, + "execution_count": 67, "metadata": {}, "output_type": "execute_result" } @@ -2180,7 +2242,7 @@ }, { "cell_type": "code", - "execution_count": 66, + "execution_count": 68, "id": "6ff2fa77-eebd-4f1c-a894-f3a9c294bfc7", "metadata": {}, "outputs": [ @@ -2190,7 +2252,7 @@ "0.9962449639096419" ] }, - "execution_count": 66, + "execution_count": 68, "metadata": {}, "output_type": "execute_result" } @@ -2209,7 +2271,7 @@ }, { "cell_type": "code", - "execution_count": 67, + "execution_count": 69, "id": "e9009a78-4e62-40a8-b231-987bd4e42a86", "metadata": {}, "outputs": [ @@ -2219,7 +2281,7 @@ "367.329164515002" ] }, - "execution_count": 67, + "execution_count": 69, "metadata": {}, "output_type": "execute_result" } @@ -2242,7 +2304,7 @@ }, { "cell_type": "code", - "execution_count": 68, + "execution_count": 70, "id": "5a07021d-93e6-41fe-8a66-523c0faad0f9", "metadata": {}, "outputs": [ @@ -2255,7 +2317,7 @@ "[ 823300, -1867613, 1986482, -1699706 ]" ] }, - "execution_count": 68, + "execution_count": 70, "metadata": {}, "output_type": "execute_result" } @@ -2275,7 +2337,7 @@ }, { "cell_type": "code", - "execution_count": 69, + "execution_count": 71, "id": "7ef33518-5192-4603-8df3-21f4524aaf76", "metadata": {}, "outputs": [ @@ -2285,7 +2347,7 @@ "0.0002031966189726793" ] }, - "execution_count": 69, + "execution_count": 71, "metadata": {}, "output_type": "execute_result" } @@ -2304,7 +2366,7 @@ }, { "cell_type": "code", - "execution_count": 70, + "execution_count": 72, "id": "fbef8bf6-10be-4aea-b672-ddadfa0b705f", "metadata": {}, "outputs": [ @@ -2314,7 +2376,7 @@ "0.015520618275460585" ] }, - "execution_count": 70, + "execution_count": 72, "metadata": {}, "output_type": "execute_result" } @@ -2333,7 +2395,7 @@ }, { "cell_type": "code", - "execution_count": 71, + "execution_count": 73, "id": "7a652c7d-9726-47cc-b2a6-ad22c4dec5f4", "metadata": {}, "outputs": [ @@ -2346,7 +2408,7 @@ "[ 15226425 ]" ] }, - "execution_count": 71, + "execution_count": 73, "metadata": {}, "output_type": "execute_result" } @@ -2374,7 +2436,7 @@ }, { "cell_type": "code", - "execution_count": 72, + "execution_count": 74, "id": "4e9e3dfb-564c-4a59-9d71-9e4be59b4cac", "metadata": {}, "outputs": [ @@ -2384,7 +2446,7 @@ "True" ] }, - "execution_count": 72, + "execution_count": 74, "metadata": {}, "output_type": "execute_result" } @@ -2404,7 +2466,7 @@ }, { "cell_type": "code", - "execution_count": 73, + "execution_count": 75, "id": "b81fe34e-3337-484c-900d-21fa9d7a2945", "metadata": {}, "outputs": [ @@ -2414,7 +2476,7 @@ "False" ] }, - "execution_count": 73, + "execution_count": 75, "metadata": {}, "output_type": "execute_result" } @@ -2434,7 +2496,7 @@ }, { "cell_type": "code", - "execution_count": 74, + "execution_count": 76, "id": "a871a91f-fff2-4645-b868-c31972228de2", "metadata": {}, "outputs": [ @@ -2444,7 +2506,7 @@ "True" ] }, - "execution_count": 74, + "execution_count": 76, "metadata": {}, "output_type": "execute_result" } @@ -2472,7 +2534,7 @@ }, { "cell_type": "code", - "execution_count": 75, + "execution_count": 77, "id": "d3c69787-da17-4cd3-b282-a68ee4d177e6", "metadata": {}, "outputs": [ @@ -2482,7 +2544,7 @@ "(2 x^2 + 2, 4 x^3 + 3 x^2 + 2 x + 1)" ] }, - "execution_count": 75, + "execution_count": 77, "metadata": {}, "output_type": "execute_result" } @@ -2506,7 +2568,7 @@ }, { "cell_type": "code", - "execution_count": 76, + "execution_count": 78, "id": "93326765-bb08-4c15-9d1a-97b1440ba986", "metadata": {}, "outputs": [ @@ -2516,7 +2578,7 @@ "8 x^5 + 6 x^4 + 12 x^3 + 8 x^2 + 4 x + 2" ] }, - "execution_count": 76, + "execution_count": 78, "metadata": {}, "output_type": "execute_result" } @@ -2535,7 +2597,7 @@ }, { "cell_type": "code", - "execution_count": 77, + "execution_count": 79, "id": "81d433fc-6dcd-42a7-97ef-362913bf99c0", "metadata": {}, "outputs": [ @@ -2545,7 +2607,7 @@ "(2.0 x + 1.5, -2.0 x - 2.0)" ] }, - "execution_count": 77, + "execution_count": 79, "metadata": {}, "output_type": "execute_result" } @@ -2567,7 +2629,7 @@ }, { "cell_type": "code", - "execution_count": 78, + "execution_count": 80, "id": "f1e28f9a-0366-44a7-9649-d4d2b74a9280", "metadata": {}, "outputs": [ @@ -2577,7 +2639,7 @@ "(2.0 x + 1.5, -2.0 x - 2.0)" ] }, - "execution_count": 78, + "execution_count": 80, "metadata": {}, "output_type": "execute_result" } @@ -2596,7 +2658,7 @@ }, { "cell_type": "code", - "execution_count": 79, + "execution_count": 81, "id": "1377b01d-eded-4d0b-892c-75740cb3e8a8", "metadata": {}, "outputs": [ @@ -2606,7 +2668,7 @@ "2 + 2 x^2" ] }, - "execution_count": 79, + "execution_count": 81, "metadata": {}, "output_type": "execute_result" } @@ -2620,7 +2682,7 @@ }, { "cell_type": "code", - "execution_count": 80, + "execution_count": 82, "id": "424c40e8-564e-4c64-b0f1-5122f6c7a41e", "metadata": {}, "outputs": [], @@ -2638,7 +2700,7 @@ }, { "cell_type": "code", - "execution_count": 81, + "execution_count": 83, "id": "f8094d46-9ca8-46dc-9be3-96eb363b3ade", "metadata": {}, "outputs": [ @@ -2648,7 +2710,7 @@ "(2 x + 3/2, -2 x - 2)" ] }, - "execution_count": 81, + "execution_count": 83, "metadata": {}, "output_type": "execute_result" } @@ -2670,7 +2732,7 @@ }, { "cell_type": "code", - "execution_count": 82, + "execution_count": 84, "id": "c121753b-dc2c-4000-9f14-b71b78f65d60", "metadata": {}, "outputs": [ @@ -2680,7 +2742,7 @@ "-2 x - 2" ] }, - "execution_count": 82, + "execution_count": 84, "metadata": {}, "output_type": "execute_result" } @@ -2700,7 +2762,7 @@ }, { "cell_type": "code", - "execution_count": 83, + "execution_count": 85, "id": "f26253d7-43fd-4242-96ca-5032a309e48e", "metadata": {}, "outputs": [ @@ -2710,7 +2772,7 @@ "2" ] }, - "execution_count": 83, + "execution_count": 85, "metadata": {}, "output_type": "execute_result" } @@ -2729,7 +2791,7 @@ }, { "cell_type": "code", - "execution_count": 84, + "execution_count": 86, "id": "1b33195a-0c3c-46c4-94b9-94c9ca0dee0e", "metadata": {}, "outputs": [ @@ -2739,7 +2801,7 @@ "4" ] }, - "execution_count": 84, + "execution_count": 86, "metadata": {}, "output_type": "execute_result" } @@ -2766,7 +2828,7 @@ }, { "cell_type": "code", - "execution_count": 85, + "execution_count": 87, "id": "cf284301-bb0d-44dc-b3cf-51ef187b01ad", "metadata": {}, "outputs": [ @@ -2776,7 +2838,7 @@ "x^4 + x^2 + x + 1" ] }, - "execution_count": 85, + "execution_count": 87, "metadata": {}, "output_type": "execute_result" } @@ -2808,7 +2870,7 @@ }, { "cell_type": "code", - "execution_count": 86, + "execution_count": 88, "id": "85ce3cb2-faf5-4a75-b624-dfff2b2ce255", "metadata": {}, "outputs": [ @@ -2818,7 +2880,7 @@ "141" ] }, - "execution_count": 86, + "execution_count": 88, "metadata": {}, "output_type": "execute_result" } @@ -2850,7 +2912,7 @@ }, { "cell_type": "code", - "execution_count": 87, + "execution_count": 89, "id": "6abad578-adfe-4389-b4dc-865494102c6a", "metadata": {}, "outputs": [ @@ -2875,7 +2937,7 @@ "[ 0x8c, 0xa1, 0x89, 0xd, 0xbf, 0xe6, 0x42, 0x68, 0x41, 0x99, 0x2d, 0xf, 0xb0, 0x54, 0xbb, 0x16 ]" ] }, - "execution_count": 87, + "execution_count": 89, "metadata": {}, "output_type": "execute_result" } @@ -2925,7 +2987,7 @@ }, { "cell_type": "code", - "execution_count": 88, + "execution_count": 90, "id": "763cab51-af5d-423d-b8cf-f6436db1280a", "metadata": {}, "outputs": [ @@ -2935,7 +2997,7 @@ "- x + 1" ] }, - "execution_count": 88, + "execution_count": 90, "metadata": {}, "output_type": "execute_result" } @@ -2965,7 +3027,7 @@ }, { "cell_type": "code", - "execution_count": 89, + "execution_count": 91, "id": "3e8b7f54-ea20-44ce-a0d3-e9cb6d7ef54b", "metadata": {}, "outputs": [ @@ -2982,7 +3044,7 @@ "False" ] }, - "execution_count": 89, + "execution_count": 91, "metadata": {}, "output_type": "execute_result" } @@ -3016,7 +3078,7 @@ }, { "cell_type": "code", - "execution_count": 90, + "execution_count": 92, "id": "728c317c-4f71-4a23-bdad-2a0f8f43c60d", "metadata": {}, "outputs": [ @@ -3026,7 +3088,7 @@ "True" ] }, - "execution_count": 90, + "execution_count": 92, "metadata": {}, "output_type": "execute_result" } @@ -3048,7 +3110,7 @@ }, { "cell_type": "code", - "execution_count": 91, + "execution_count": 93, "id": "99fed470-0bbb-4975-a391-c6d755a9a635", "metadata": {}, "outputs": [ @@ -3058,7 +3120,7 @@ "30" ] }, - "execution_count": 91, + "execution_count": 93, "metadata": {}, "output_type": "execute_result" } @@ -3085,7 +3147,7 @@ }, { "cell_type": "code", - "execution_count": 92, + "execution_count": 94, "id": "284175c0-2153-4d71-9488-c6a902abfde4", "metadata": {}, "outputs": [ @@ -3154,7 +3216,7 @@ }, { "cell_type": "code", - "execution_count": 93, + "execution_count": 95, "id": "e6829610-8540-4ff3-9011-fe29a5397ca8", "metadata": {}, "outputs": [ @@ -3245,7 +3307,7 @@ }, { "cell_type": "code", - "execution_count": 94, + "execution_count": 96, "id": "8d4c4b43-e593-407a-92f8-86b653a09c8a", "metadata": {}, "outputs": [ @@ -3320,7 +3382,7 @@ }, { "cell_type": "code", - "execution_count": 95, + "execution_count": 97, "id": "143fbfa9-37f0-46a5-88e8-77881d3d9092", "metadata": {}, "outputs": [ @@ -3330,7 +3392,7 @@ "x^256 + 1" ] }, - "execution_count": 95, + "execution_count": 97, "metadata": {}, "output_type": "execute_result" } @@ -3356,7 +3418,7 @@ }, { "cell_type": "code", - "execution_count": 96, + "execution_count": 98, "id": "703e1f66-401d-40be-a0f9-d3f08ced2b14", "metadata": {}, "outputs": [ @@ -3366,7 +3428,7 @@ "-1" ] }, - "execution_count": 96, + "execution_count": 98, "metadata": {}, "output_type": "execute_result" } @@ -3387,7 +3449,7 @@ }, { "cell_type": "code", - "execution_count": 97, + "execution_count": 99, "id": "84d4ef9e-1484-48c8-b5a8-75a00f178c72", "metadata": {}, "outputs": [ @@ -3397,7 +3459,7 @@ "6 x^5 + 5 x^4 + 4 x^3 + 3 x^2 + 2 x + 1" ] }, - "execution_count": 97, + "execution_count": 99, "metadata": {}, "output_type": "execute_result" } @@ -3439,7 +3501,7 @@ }, { "cell_type": "code", - "execution_count": 98, + "execution_count": 100, "id": "9b566550-f23c-4fbc-8b7c-63bbee8e0c72", "metadata": {}, "outputs": [ @@ -3478,7 +3540,7 @@ }, { "cell_type": "code", - "execution_count": 99, + "execution_count": 101, "id": "55c29e0c-e0c2-409a-af23-6590fd9cc545", "metadata": {}, "outputs": [ @@ -3488,7 +3550,7 @@ "(113, 91)" ] }, - "execution_count": 99, + "execution_count": 101, "metadata": {}, "output_type": "execute_result" } @@ -3510,7 +3572,7 @@ }, { "cell_type": "code", - "execution_count": 100, + "execution_count": 102, "id": "f980a2d0-4413-4812-a73d-1bab72a744f3", "metadata": {}, "outputs": [ @@ -3520,7 +3582,7 @@ "True" ] }, - "execution_count": 100, + "execution_count": 102, "metadata": {}, "output_type": "execute_result" } @@ -3539,7 +3601,7 @@ }, { "cell_type": "code", - "execution_count": 101, + "execution_count": 103, "id": "2a3d8e7d-71b3-4a93-b6cc-803f00432c56", "metadata": {}, "outputs": [ @@ -3549,7 +3611,7 @@ "129" ] }, - "execution_count": 101, + "execution_count": 103, "metadata": {}, "output_type": "execute_result" } @@ -3569,7 +3631,7 @@ }, { "cell_type": "code", - "execution_count": 102, + "execution_count": 104, "id": "76d3b602-4903-4218-b34c-a39fbe392ad1", "metadata": {}, "outputs": [ @@ -3579,7 +3641,7 @@ "0" ] }, - "execution_count": 102, + "execution_count": 104, "metadata": {}, "output_type": "execute_result" } @@ -3598,7 +3660,7 @@ }, { "cell_type": "code", - "execution_count": 103, + "execution_count": 105, "id": "bb93b5fc-99c9-4977-8299-9342b84e143d", "metadata": {}, "outputs": [], @@ -3618,7 +3680,7 @@ }, { "cell_type": "code", - "execution_count": 104, + "execution_count": 106, "id": "41e18357-da42-4cd7-bd4e-1c3355f1c69d", "metadata": {}, "outputs": [], @@ -3643,7 +3705,7 @@ }, { "cell_type": "code", - "execution_count": 105, + "execution_count": 107, "id": "af81d5f2-a524-4555-8e74-06a0c9a7ea08", "metadata": {}, "outputs": [ @@ -3654,7 +3716,7 @@ " 0x03449ef2ed30a8deb96e584a08c329adbf1be87ce40f1a0e7b4e86178682c41a9c)" ] }, - "execution_count": 105, + "execution_count": 107, "metadata": {}, "output_type": "execute_result" }