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March 23, 2022 09:01
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Examples_sagemath.ipynb
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{ | |
"cells": [ | |
{ | |
"metadata": {}, | |
"id": "3c0af6ab", | |
"cell_type": "markdown", | |
"source": "# Sagemath\n[https://www.sagemath.org/]\n\nSagemath is a free open-source mathematics software system licensed under the GPL. It builds on top of many existing open-source packages: NumPy, SciPy, matplotlib, Sympy, Maxima, GAP, FLINT, R and many more. \nAccess their combined power through a common, Python-based language or directly via interfaces or wrappers.\n\n\nSagemath is *not* a Python package.\n\nFollow the installation instructions and check the tutorials to get started.\n\n\n## A few useful links\n\n* https://doc.sagemath.org/html/en/installation/index.html — installation instructions (many ways)\n - Sagemath tries to use as many system packages as possible\n - Optional packages can be installed using `sage -i PACKAGE_NAME`. See [https://doc.sagemath.org/html/en/reference/misc/sage/misc/package.html]\n* https://github.com/sagemath/sage/ — sources on GitHub \n* https://doc.sagemath.org/html/en/reference/index.html — reference manual of Sagemath\n* https://doc.sagemath.org/html/en/tutorial/index.html — some tutorials\n* https://www.sagemath.org/sagebook/ — book « Computational Mathematics with Sagemath » \n* https://ask.sagemath.org — get help on coding with Sagemath\n* https://groups.google.com/g/sage-devel — report bugs, get help installing Sagemath, etc.\n* https://cython.org — know more about Cython\n* https://trac.sagemath.org — Sagemath development page (tickets, git, etc.)\n* https://cocalc.com — CoCalc (Collaborative Calculation and Data Science)\n Open free account to use Sagemath online\n\n\n## Examples\nBelow are some (basic) examples of what can be done with sagemath.\n" | |
}, | |
{ | |
"metadata": {}, | |
"id": "00f02239", | |
"cell_type": "markdown", | |
"source": "## Integers, Rationals, etc.\nSeveral rings are defined by default in Sagemath.\nSee e.g., [https://doc.sagemath.org/html/en/reference/rings_standard/index.html]." | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "3ba28607", | |
"cell_type": "code", | |
"source": "a = 1/2\nprint(a)", | |
"execution_count": 1, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": "1/2\n" | |
} | |
] | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "5e1992d5", | |
"cell_type": "code", | |
"source": "type(a)", | |
"execution_count": 2, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": "<class 'sage.rings.rational.Rational'>" | |
}, | |
"execution_count": 2, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
] | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "f2bf5abd", | |
"cell_type": "code", | |
"source": "print(1/2 + 3/4 + 5/6)", | |
"execution_count": 3, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": "25/12\n" | |
} | |
] | |
}, | |
{ | |
"metadata": {}, | |
"id": "35172a0d", | |
"cell_type": "markdown", | |
"source": "You can check in which ring a number belongs" | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "7972cea2", | |
"cell_type": "code", | |
"source": "3/4 in QQ", | |
"execution_count": 4, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": "True" | |
}, | |
"execution_count": 4, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
] | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "71b9b49e", | |
"cell_type": "code", | |
"source": "3/4 in ZZ", | |
"execution_count": 5, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": "False" | |
}, | |
"execution_count": 5, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
] | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "e426c926", | |
"cell_type": "code", | |
"source": "f = 1.2\ntype(f)", | |
"execution_count": 9, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": "<class 'sage.rings.real_mpfr.RealLiteral'>" | |
}, | |
"execution_count": 9, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
] | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "f319cb56", | |
"cell_type": "code", | |
"source": "print(f in RR, f in QQ)", | |
"execution_count": 10, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": "True True\n" | |
} | |
] | |
}, | |
{ | |
"metadata": {}, | |
"id": "d40411b3", | |
"cell_type": "markdown", | |
"source": "and convert a number if it belongs to the ring" | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "a5ddd532", | |
"cell_type": "code", | |
"source": "QQ(f)", | |
"execution_count": 7, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": "6/5" | |
}, | |
"execution_count": 7, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
] | |
}, | |
{ | |
"metadata": {}, | |
"id": "e2be63bf", | |
"cell_type": "markdown", | |
"source": "try f.<TAB> to discover methods associated with numbers in a ring.\n \nYou can also use complex numbers" | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "e10e0d92", | |
"cell_type": "code", | |
"source": "c = 1/2 + 3/4*i\nprint(c)\nprint(type(c))", | |
"execution_count": 11, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": "3/4*I + 1/2\n<class 'sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_gaussian'>\n" | |
} | |
] | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "7c992e7f", | |
"cell_type": "code", | |
"source": "c + 1.5", | |
"execution_count": 14, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": "2.00000000000000 + 0.750000000000000*I" | |
}, | |
"execution_count": 14, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
] | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "dce99620", | |
"cell_type": "code", | |
"source": "c^2", | |
"execution_count": 15, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": "3/4*I - 5/16" | |
}, | |
"execution_count": 15, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
] | |
}, | |
{ | |
"metadata": {}, | |
"id": "72080dea", | |
"cell_type": "markdown", | |
"source": "By default, symbol `i` is used for complex numbers. If you have already used it elsewhere, you can restore its default value using `reset(i)`." | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "8bb61134", | |
"cell_type": "code", | |
"source": "i = 4\nprint(i)\nreset('i')\nprint(i)", | |
"execution_count": 16, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": "4\nI\n" | |
} | |
] | |
}, | |
{ | |
"metadata": {}, | |
"id": "1186f62d", | |
"cell_type": "markdown", | |
"source": "Sagemath can manipulate very large numbers." | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "772b4c4e", | |
"cell_type": "code", | |
"source": "a = 100\nprint(a)\nprint(factor(a))\nprint(factorial(100))\nprint(factor(factorial(100)))", | |
"execution_count": 17, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": "100\n2^2 * 5^2\n93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000\n2^97 * 3^48 * 5^24 * 7^16 * 11^9 * 13^7 * 17^5 * 19^5 * 23^4 * 29^3 * 31^3 * 37^2 * 41^2 * 43^2 * 47^2 * 53 * 59 * 61 * 67 * 71 * 73 * 79 * 83 * 89 * 97\n" | |
} | |
] | |
}, | |
{ | |
"metadata": {}, | |
"id": "c8d3d39a", | |
"cell_type": "markdown", | |
"source": "## Symbolic math" | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "7646d9bc", | |
"cell_type": "code", | |
"source": "x = var('x')\nf(x) = 1 - sin(x)^2\nprint(f)\nshow(f)\nprint(latex(f))\nplot(f)", | |
"execution_count": 25, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": "x |--> -sin(x)^2 + 1\n" | |
}, | |
{ | |
"data": { | |
"text/html": "<html>\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}x \\ {\\mapsto}\\ -\\sin\\left(x\\right)^{2} + 1\\]</html>", | |
"text/latex": "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}x \\ {\\mapsto}\\ -\\sin\\left(x\\right)^{2} + 1$$", | |
"text/plain": "x |--> -sin(x)^2 + 1" | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
}, | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": "x \\ {\\mapsto}\\ -\\sin\\left(x\\right)^{2} + 1\n" | |
}, | |
{ | |
"data": { | |
"image/png": 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+fdC3L1SsCP37Ox2RSGBRHyURD0ybZn7r7t8fkpJCq+N2oFIfJf8aNAhefNG0uujWzeloRPzCo1dyjSiJnMXcuWZ10KOPKkmS0DVkCOzdazp5x8SY1XEiokRJ5IwWLTIrhO67z7QBUJIkocqy4LXXTLL04IMmWbrlFqejEnGelp+IFGLdOmjXDq67ziyl1pYP/uFyuahXrx7x8fFOhxJ2SpQw08xt2sBdd4GHu82IhDTVKIkUYNs2aNkSqlWDr76CcuWcjij8qEbJOYcPm2QpPR2WLIGGDZ2OSMQntNebSFH89hvcfDOcdx4sWKAkScJPdDTMnw9/+5tJmP77X6cjEnGOEiWRkxw8CLfdBvv3w2efQeXKTkck4oxy5eCTT6B0aVOr9PvvTkck4gwlSiLHHTlidljfsgU+/RQuvdTpiEScFRsLCxdCdjbcfjv8+afTEYn4nxIlEcz2DV27mlVuH3wAV1/tdEQigeHyy83IUno6/POf4HY7HZGIfylREsH0kJkxwzxuuMHpaEQCS9Om8O67pm6pb1+noxHxLyVKEvZmzTL7t730EnTo4HQ0IoHptttg3DgYM8b0FBMJF2o4KWEtNdXsddW5c/jt3yZyrrp3h4wM6NULatWCW291OiIR31MfJQlb338PLVpAgwamYDUy0umIBEzDSZfLhdvtJiMjQ32UAozbbZpRLloEy5ebnx+RIOVRHyUlShKW9uwxSVKJErBihdk1XQKLGk4GroMH4ZprzGq41auhShWnIxIpEjWcFClITo75jfh//zOreZQkiZyb886Djz4yo0u33w6HDjkdkYjvKFGSsGLb8MgjsGoVfPghXHaZ0xGJBKdq1eDjj2HjRujYEY4dczoiEd9QoiRh5aWXYOZMmD7d7OUmIkV39dXw9tswbx4MGOB0NCK+oURJwsYHH8CgQaZnktoAiHjH7bfDyJHwyiswbZrT0Yh4n4q5JSxs2GCKt9u0gdmzwfKohE+cpGLu4GHbpnXA9OmweLH5WRMJAlr1JgJmhVvTpqYANS0NypZ1OiLxhBKl4JKbCzfeCD/8AGvWmBomkQCnVW8iR49C+/awb58p3laSJOIbkZHw3ntQsqRZVXr4sNMRiXiHEiUJaU89ZaYC3nsPLrnE6WhEQltsrKkF/PZbMxVX/AkLEecpUZKQNX06jB4Nr70G113ncDDiMZfLRb169YiPj3c6FCmCuDiYMgXeeMP87IkEO9UoSUhatcp0Du7UCSZNUvF2MFKNUnB76ikYNcpsD3TTTU5HI1IgFXNLeNq5E5o0MZt2LloEUVFORyRFoUQpuLndZtPcNWvg66/h0kudjkjkNCrmlvBz+LApJC1RAubOVZIk4pSICHjnHTj/fLjjDrM/nEgwUqIkIaVXL1i3znQK1kadIs6qWNGsNv35Z+jSRcXdEpyUKEnImD4dJk8GlwtUBywSGOrVg9dfh3ffNYsrRIKNEiUJCevXQ48e8PDD5jdXEQkc99wD/fqZAu/UVKejETk3KuaWoLd3ryneLlfOdN4uXdrpiMQbVMwdWo4eNavftm6Fb76BqlWdjkhExdwSBmwbOneG7GxTvK0kSSQwlSxp9lksUQLuuw+OHHE6IhHPKFGSoDZsmCkWnTFDy49DhRpOhq7YWJgzB1auhKefdjoaEc9o6k2C1uLFZhPO/v1h6FCnoxFv09Rb6Bo71qxQfecdsxejiEPUcFJC186d0LixWVHz+edmWF9CixKl0GXb8MAD8PHHpl7p8sudjkjClBIlCU1HjsANN8BPP5kX2dhYpyMSX1CiFNoOHDD7wpUpY6bioqOdjkjCkIq5JTQlJpoX1nffVZLkT+PHj6dWrVpER0cTFxdH6lnWec+aNYuGDRtSpkwZqlatyr/+9S/27Nnjp2gl0JUrZ+qVtmyBJ55wOhqRwilRkqDy/vswYoQp4m7Vyulowsfs2bPp06cPAwcOJD09ndatW9OmTRsyMzMLPH/ZsmV06tSJLl26sHHjRubMmcPXX39N165d/Ry5BLKGDWHMGJgwwdQriQQiTb1J0Pj5Z2jUyPRimTMHLI8GTcUbmjVrRuPGjUlOTs47VrduXdq1a0dSUtJp5w8fPpzk5GR+/PHHvGNjx47l1VdfZfv27R5dU1Nv4cG24Z//hI8+Ur2S+J2m3iR0HDkCHTqYvaOmTFGS5E+5ubmsXbuWhISEfMcTEhJIS0sr8DktW7bkl19+YcGCBdi2za+//sp7773Hbbfd5o+QJYhYFkycaBpQ3nuv2dhaJJAoUZKgMHAgrF1rGtZVqOB0NOElOzsbt9tN7CkFYbGxsezatavA57Rs2ZJZs2bRvn17IiMjqVKlChUqVGDs2LGFXicnJ4f9+/fne0h4UL2SBDIlShLwPv3U1CQlJUHTpk5HE76sU4bxbNs+7dgJmzZtolevXjz77LOsXbuWhQsXsm3bNrp3717o509KSiImJibvUb16da/GL4FN9UoSqFSjJAFt507zAhofb3qulFBq73e5ubmUKVOGOXPmcOedd+Yd7927N+vWrWPJkiWnPadjx44cPnyYOXPm5B1btmwZrVu3ZufOnVQtYKOvnJwccnJy8v6+f/9+qlevrhqlMGLb8OCDMH++6pXEL1SjJMHN7TZFnpGR8MYbSpKcEhkZSVxcHCkpKfmOp6Sk0LJlywKfc+jQIUqc8g2LiIgAzEhUQaKioihfvny+h4QXyzIjShddpHolCRx665GA9eKLsHQpvPUWXHih09GEt759+zJlyhSmTZvG5s2beeKJJ8jMzMybSktMTKRTp05557dt25b333+f5ORkfvrpJ5YvX06vXr1o2rQpF110kVNfhgSBcuVMj7QtW8z2RCJO08YPEpCWLIEhQ+DZZ+Haa52ORtq3b8+ePXsYMmQIWVlZ1K9fnwULFlCzZk0AsrKy8vVU6ty5MwcOHGDcuHE8+eSTVKhQgRtuuIFXXnnFqS9BgkjDhqYusVcvSEgALZYUJ6lGSQJOdrZ5obziCvjiCzg+YyNhRn2Uwpttw//9H3z9NXz7LVSp4nREEoJUoyTBx7ahSxfIyYFZs5QkiYQry4LXXze1iQ89BMeOOR2RhCslShJQJk0yK16mTjUFnSISvipXhhkz4PPPYfRop6ORcKVESQLGiWZzjz4Kd9zhdDQiEggSEuDJJ+GZZyA93eloJBypRkkCQk4OtGgBhw6ZDtxlyzodkTjF5XLhcrlwu91kZGSoRkn0+iC+4lGNkhIlCQhPP22G1leuhMaNnY5GAoGKueVkW7ea14YHHoDJk52ORkKEirklOHz5pVkK/NJLSpJEpGC1a8Nrr5lNsd97z+loJJxoREkctWePaQVQuzakpKj7tvxFI0pyKtuG++4zbUO+/Ra0HaAUk0aUJLDZtincPnRIW5SIyNlZllkZW66c2RPO7XY6IgkHemsSx7z+Osyda+oNLr7Y6WhEJBhUrAhvvgmpqTB8uNPRSDhQoiSO+P57sz3Bww/D3Xc7HY2IBJNrroGnnoJBg2DdOqejkVCnGiXxuyNHoGVL2LvX9EU57zynI5JApBolOZOcHGja1HTs/vpriI52OiIJQqpRksA0ZIj5LfCtt5QkiUjRREXBzJmQkWFGlkR8RYmS+NXKlTB0KDz7LMTHOx2NBCKXy0W9evWI1w0iZ9GgAbzwAowYAUuWOB2NhCpNvYnfHDoEV18NFSrA8uVQsqTTEUkg09SbeMLthuuvh8xM0zJAt4qcA029SWB55hnzYvbGG0qSRMQ7IiLMa8qePdCnj9PRSChSoiR+8eWXMHYsvPIK1KnjdDQiEkpq1TJdu19/HT780OloJNRo6k18bu9euOoquOIKdd8Wz2nqTc6FbUO7drBiBWzYAJUrOx2RBAFNvUlg6N0b9u83v+0pSRIRX7CsvzbLfeQRkziJeIPetsSn5s2DGTNgzBioUcPpaEQklFWubJKl+fNh2jSno5FQoak38Zndu6F+fdNcct488xufiKc09SZF9fDDMGcOrF8Pl17qdDQSwDT1Js6xbejWzfx50iQlSSLiP6NHQ6VK8NBD2jhXik+JkvjEjBlm9cnEiSqqlHOjhpNSXOXLm5YBy5aZ1bYixaGpN/G6zEyzyq1dO/NiJVIUmnqT4urd29QsrVtnVt2KnMKjuQ4lSuJVtg033wybN8N335ku3CJFoURJiuuPP6BhQ4iNhaVLTXNKkZOoRkn8b+pU0ytp8mQlSSLirLJlTVuSFStMQ0qRolCiJF6zfTs8+aRZcXLLLU5HIyICrVubKbiBA2HrVqejkWCkqTfxCtuGW281020bNmg0SYpPU2/iLYcOQaNGZiVcaqqm4CSPpt7Ef6ZPh4ULTSsAJUkiEkjKlDFTcCtXwqhRTkcjwUaJkhTbjh3wxBOmZ8mttzodjYjI6Vq1Mq9T//kPbNnidDQSTDT1JsVi29C2LXzzDWzcCBUrOh2RhApNvYm3/fmnmYI7/3zTY0lTcGFPU2/iezNnwiefmMaSSpLEG9RwUnyldGkzBbdqFYwc6XQ0Eiw0oiRFtnMnXHmlGVGaMcPpaCTUaERJfOWpp0zH7vR0qFvX6WjEQWo4Kb5j23DHHfD112bK7fzznY5IQo0SJfGVP/+Eq682o+CaggtrmnoT33nrLfjoI5gwQUmSiASX0qVNc9xVq2DcOKejkUCnREnO2a5d8Pjj8MADZlRJwsP48eOpVasW0dHRxMXFkZqaWui5nTt3xrKs0x5XXnmlHyMWKVyrVtCzJwwYANu2OR2NBDIlSnJObBt69IBSpWDMGKejEX+ZPXs2ffr0YeDAgaSnp9O6dWvatGlDZmZmgee/9tprZGVl5T22b9/O+eefz7333uvnyEUKl5RkmlB262Ze20QKoholOSfvvAP33w9z58JddzkdjfhLs2bNaNy4McnJyXnH6tatS7t27UhKSjrr8z/44APuuusutm3bRs2aNT26pmqUxB8+/9xs5D11qtl+ScKKapTEu377DR57DO67T0lSOMnNzWXt2rUkJCTkO56QkEBaWppHn2Pq1KncdNNNHidJIv6SkACdO0PfvmYlr8iplCiJx/r0MR9V/BhesrOzcbvdxMbG5jseGxvLrl27zvr8rKwsPv30U7p27XrG83Jycti/f3++h4g/jBgB0dHw739rCk5Op0RJPPLJJ2al26hRcOGFTkcjTrCs/KPUtm2fdqwg06dPp0KFCrRr1+6M5yUlJRETE5P3qF69enHCFfHY+eeDywUffghz5jgdjQQaJUpyVgcOmALum2+GBx90Ohrxt0qVKhEREXHa6NHu3btPG2U6lW3bTJs2jY4dOxIZGXnGcxMTE9m3b1/eY/v27cWOXcRTd99tHo89Bnv2OB2NBBIlSnJWAwbA77+bbUo8GECQEBMZGUlcXBwpKSn5jqekpNCyZcszPnfJkiX88MMPdOnS5azXiYqKonz58vkeIv40bhwcOfJXmYEIKFGSs0hLM0PSL70EqsMNX3379mXKlClMmzaNzZs388QTT5CZmUn37t0BMxrUqVOn0543depUmjVrRv369f0dssg5q1LFlBe8+SYsWOB0NBIoSjodgASunBzo2hWaNjXD0RK+2rdvz549exgyZAhZWVnUr1+fBQsW5K1iy8rKOq2n0r59+5g7dy6vvfaaEyGLFMlDD8Hbb8Ojj5rtmTSwKeqjJIV67jnTkO2bb0ADAuJv6qMkTvn5Z/Oa16kTjB/vdDTiQ+qjJEW3YYNJkhITlSSJSHi55BJ4+WVIToalS52ORpymESU5jdtt9kHavx/S0yEqyumIJBxpREmcdOwY/P3vZiHL+vV6HQxRGlGSohk3DlavhilT9OIgIuGpRAmYNAl+/NGMrkv4UqIk+fz8s2kH0LMnnGXlt4hPuFwu6tWrR3x8vNOhSJirXx/694ehQ2HzZqejEado6k3y2Da0aQObNpnVHuXKOR2RhDNNvUkgOHwYGjQwrQMWLzYjTRIyNPUm5+bNN+Gzz0wBo5IkERGzB9zEiZCaClOnOh2NOEEjSgJAdjbUqWN20n7rLaejEdGIkgSWf/0L5s2DLVvM6JKEBI0oief69TOrPEaPdjoSEZHAM3w4lCql7U3CkRIlYdEieOMNGDYMKld2OhoRkcBzwQXmF8nZs+GTT5yORvxJU29hToWKEqg09SaBxrbhllvM9NvGjXDeeU5HJMWkqTc5u6FDTUuAiROVJImInIllmcUuv/0Gzz7rdDTiL3prDGObN5s2/c88A3XrOh2NiEjgu/RSGDwYXnsN1q51OhrxB029haljx+C66yArC777ziyBFQkELpcLl8uF2+0mIyNDU28ScI4cgfh4Mwq/ejWULOl0RFJEHk29KVEKU1OnQteu8MUXcOONTkcjcjrVKEkgW70amjc3i2CefNLpaKSIlChJwXbvNj2T2rY1q91EApESJQl0vXubPTE3boRLLnE6GikCFXNLwfr2NUPGw4c7HYmISPB68UU4/3zo0cOsiJPQpEQpzKSkwKxZJkm68EKnoxERCV7lysH48bBwoemvJKFJU29h5M8/4aqr4OKL4auvzFJXkUClqTcJFvfcY/aC27zZjDBJ0NDUm+T34ouwfbvpmaQkSUTEO8aMMc17ExOdjkR8QYlSmNi4EV59FQYMgNq1nY5GRCR0XHSRad47aRKkpTkdjXibpt7CwLFj0Lo1ZGfDt99CVJTTEYmcnabeJJi43aZdQG6uaUSp3kpBQVNvYkyZYn7LmThRSZIEPpfLRb169YiPj3c6FBGPRUTAhAmwYYOZipPQoRGlELdrl9me5M47Ydo0p6MR8ZxGlCQY9eplXms3b4bq1Z2ORs5CI0oC/fqZ33SGDXM6EhGR0PfCC1C+vGlGKaFBiVIIW7TI9EwaNgwuuMDpaEREQl9MDIweDfPmwccfOx2NeIOm3kJUbi40aGCaSi5ZYjpxiwQTTb1JsLJtuOUW2LoVNm2CMmWcjkgKoam3cDZ8OPzwg+kaqyRJRMR/LAtcLlMj+sILTkcjxaW30BC0bZv54XziCdOJW0RE/Otvf4OBA80vrRs3Oh2NFIem3kKMbUPbtrB+vVl1cd55TkckUjSaepNgl5NjSiAqV1YJRIDS1Fs4+vBD+OQTeO01JUkiIk6KioLkZFi2DN54w+lopKg0ohRC/vjD9Ey66iqz2kL7uUkwcrlcuFwu3G43GRkZGlGSoPfgg7BwoSnu1grkgOLRu6QSpRDSv7/pCLtxI1x6qdPRiBSPpt4kVPz6q9lj8557zE4JEjA09RZONm6EkSNN8aCSJBGRwBEbCy+/DFOnmmk4CS4aUQoBtg3XXWeWomrTWwkVGlGSUHLsGLRsaUokvvkGSpVyOiJBI0rhY8YMWLrU9ExSkiQiEnhKlDCb5m7aZDp3S/BQohTkfv8dnnoK7r8fbrzR6WgklI0fP55atWoRHR1NXFwcqampZzw/JyeHgQMHUrNmTaKiorjsssuYpp2ZJYw1amQ2zR08GDIznY5GPKVEKcgNGGB6dYwY4XQkEspmz55Nnz59GDhwIOnp6bRu3Zo2bdqQeYZX+/vuu48vv/ySqVOnsnXrVt5++23q1Knjx6hFAs+QIVChAvTp43Qk4inVKAWxVaugRQvTM+nxx52ORkJZs2bNaNy4McnJyXnH6tatS7t27UhKSjrt/IULF9KhQwd++uknzj///CJdUzVKEqreecfMAixYAG3aOB1NWFONUig7ehR69DBDuT16OB2NhLLc3FzWrl1LQkJCvuMJCQmkpaUV+Jz58+fTpEkTXn31VapVq8YVV1xBv379+PPPPwu9Tk5ODvv378/3EAlF7dvDDTeYX3APH3Y6GjkbJUpBKjkZ1q0zxYElSzodjYSy7Oxs3G43sbGx+Y7Hxsaya9euAp/z008/sWzZMjZs2MC8efMYPXo07733Hj179iz0OklJScTExOQ9qlev7tWvQyRQWBaMG2fqlIYNczoaORslSkEoKwv+8x949FFo2tTpaCRcWKe0erdt+7RjJxw7dgzLspg1axZNmzbl1ltvZeTIkUyfPr3QUaXExET27duX99i+fbvXvwaRQFG3LvTtC0OHmo3MJXApUQpCTz5p2gAMHep0JBIOKlWqRERExGmjR7t37z5tlOmEqlWrUq1aNWJiYvKO1a1bF9u2+eWXXwp8TlRUFOXLl8/3EAllgwbBhRealXASuJQoBZkvvoC334bhw6FiRaejkXAQGRlJXFwcKSkp+Y6npKTQsmXLAp/TqlUrdu7cycGDB/OOZWRkUKJECS6++GKfxisSLMqWhVGjzN6cH33kdDRSGK16CyI5OdCgAVSpAosXa9Nb8Z/Zs2fTsWNHJkyYQIsWLZg0aRKTJ09m48aN1KxZk8TERHbs2MGMGTMAOHjwIHXr1qV58+Y8//zzZGdn07VrV6699lomT57s0TW16k3CgW2blW9bt5qtqMqUcTqisOLRu6jKgIPIsGHw00/w/vtKksS/2rdvz549exgyZAhZWVnUr1+fBQsWULNmTQCysrLy9VQ677zzSElJ4fHHH6dJkyZccMEF3Hfffbz44otOfQkiAcmyYOxYqF/f7Ac3ZIjTEcmpNKIUJP77X1P899hj8OqrTkcj4nsaUZJwMmiQeW3fsAEuv9zpaMKGR0MOSpSCxF13mQaTW7ZAuXJORyPie0qUJJwcOgRXXgm1a8Onn2rWwE/UcDJULFwI8+bByJFKkkREQlGZMmaXhc8+M6/3Ejg0ohTgcnLM3HWNGmbFm37LkFDncrlwuVy43W4yMjI0oiRhpW1bWL8eNm82q+LEpzT1FgqGDoXnnjM/OPXqOR2NiP9o6k3C0bZt5rW+Tx8oYBtF8S5NvQW7zEx48UXo3VtJkohIOKhVCxITYcQIU5MqztOIUgC75x5ISzP9NVSbJOFGI0oSrg4fNiUXNWuq5MLHNKIUzD7/HObONb9VKEkSEQkf0dGmt9KiRfDuu05HIxpRCkAnOnBXrQpffaXfJiQ8aURJwp3awvicRpSC1ahR8OOPMG6ckiQRkXA1ejT873/w/PNORxLelCgFmO3b4YUXzG7S9es7HY2IiDilRg3TsXv0aNOxW5yhqbcAc999kJpqCrg12yDhTFNvIpCba0oxYmO1GboPaOot2HzxBcyZA8OHK0mS8OVyuahXrx7x8fFOhyLiuMhIU4axdCnMmuV0NOFJI0oBQr81iOSnESWRv7RvD0uWmMLuChWcjiZkaEQpmIweDT/8oAJuERE53ciRcPCg2alB/EuJUgD45RcYMgQeewyuusrpaEREJNBUqwaDB5tfptetczqa8KKptwDQoYOZbtu6FWJinI5GJDBo6k0kvyNH4OqrTQ3rsmVQQkMdxaWpt2CwaBHMng3DhilJEhGRwpUqZUaUVqyAGTOcjiZ8aETJQbm50KgRXHCBWdGg2iSRv2hESaRg//wnpKRARoYKu4tJI0qBbswYM92mAm4REfHUsGHw55+mGaX4nhIlh+zcadrS9+wJDRs6HY2IiASLiy4y7x/jx6uw2x809eaQBx6AL780I0oaOhX5i8vlwuVy4Xa7ycjI0NSbSAFOFHbHxJjdHFTYXSQezeUoUXLA4sVw/fUwfTo89JDT0YgEJtUoiZyZ3kuKTYlSIDpyxBRwV6ig3wJEzkSJksjZPfCA2f5Khd1FomLuQDR2rGlB73IpSRIRkeIZPtwUdj/7rNORhC69VftRVpbprNqjhxlVEhERKY6LLjLvKy6XCrt9RVNvfvTgg/D556aAu2JFp6MRCWyaehPxjEo6ikxTb4Fk6VKYNQteeUVJkoiIeE+pUmZEKS0NZs50OprQoxElPzhyBBo3hvPOg+XLle2LeEIjSiLnRoXd50wjSoHC5YKNG1XALSIivqPCbt/Q27aP7doFzz0H3bubUSUROTOXy0W9evWIj493OhSRoKLCbt/Q1JuPdeoECxaYodDzz3c6GpHgoak3kXN3orC7YkVTG6tZjDPS1JvTUlNNYd0rryhJEhER3ytVymy0vny5Cru9RSNKPnL0qJlqK1PGrERQVi9ybjSiJFJ0998PixZpP9Gz0IiSk8aPhw0bTGavJElERPxp+HA4dEiF3d6gt3Af+PVXGDQIunWDJk2cjkbEO8aPH0+tWrWIjo4mLi6O1NTUQs9dvHgxlmWd9tiyZYsfIxYJX9WqmYVELhesX+90NMFNiZIP9O8PJUvCSy85HYmId8yePZs+ffowcOBA0tPTad26NW3atCEzM/OMz9u6dStZWVl5j8svv9xPEYtI795Qpw707AnFr7IJX0qUvGz5cnjjDXj5ZbjgAqejEfGOkSNH0qVLF7p27UrdunUZPXo01atXJzk5+YzPq1y5MlWqVMl7RERE+CliEVFht3coUfKio0dN5h4fD126OB2NiHfk5uaydu1aEhIS8h1PSEggLS3tjM+9+uqrqVq1KjfeeCNfffXVGc/Nyclh//79+R4iUjzXXw8dOsBTT8HevU5HE5yUKHnRhAnw7bfqwC2hJTs7G7fbTWxsbL7jsbGx7Nq1q8DnVK1alUmTJjF37lzef/99ateuzY033sjSpUsLvU5SUhIxMTF5j+rVq3v16xAJVycKu597zulIgpPaA3jJ7t1wxRVw330waZLT0Yh4z86dO6lWrRppaWm0aNEi7/hLL73EzJkzPS7Qbtu2LZZlMX/+/AL/PScnh5ycnLy/79+/n+rVq6s9gIgXDB9u6me/+QYaNnQ6moCh9gD+9MwzEBEBQ4c6HYmId1WqVImIiIjTRo9279592ijTmTRv3pzvv/++0H+PioqifPny+R4i4h0q7C46JUpesGIFvP66SZIqVXI6GhHvioyMJC4ujpSUlHzHU1JSaNmypcefJz09napVq3o7PBHxgAq7i66k0wEEO7fbZOhxcdC1q9PRiPhG37596dixI02aNKFFixZMmjSJzMxMunfvDkBiYiI7duxgxowZAIwePZpLLrmEK6+8ktzcXN58803mzp3L3LlznfwyRMLayYXdt9+ujt2eUqJUTBMnQno6rFxppt5EQlH79u3Zs2cPQ4YMISsri/r167NgwQJq1qwJQFZWVr6eSrm5ufTr148dO3ZQunRprrzySj755BNuvfVWp74EEcHUKtWpYwq7X3vN6WiCg4q5i+G330wB9913w5QpTkcjElq015uIb6iwO49HxdxKlIqha1eYOxcyMuDCC52ORiS0KFES8Y0jR0yCdMEFsHQpWB6lCyFJq958aeVKmDrVFHArSRIRkWBxorB72TJ4802nowl8GlEqArcbmjY1f169WrVJIt7kcrlwuVy43W4yMjI0oiTiIx06wOLFsHUrxMQ4HY0jNPXmKxMmQI8ekJYGJ/XfExEv0tSbiG/t2AG1a5syktGjnY7GEZp684XsbBgwAP71LyVJIiISvKpVM6vfxo41229JwTSidI66dYM5c8xQZeXKTkcjEro0oiTie7m50KhR2BZ2a0TJ21avNm0AXnhBSZKIiAS/yEgVdp+NRpQ85HZD8+bm49dfq4BbxNc0oiTiP2Fa2K0RJW+aMgXWrAGXS0mSiIiEluHD4eBBU7Mk+SlR8kB2NiQmqoBbRERC08UXq7C7MJp684AKuEX8T1NvIv6Vm2s6dleqFDaF3Zp684ZVq8y024svKkkS8QeXy0W9evWIj493OhSRsKLC7oJpROkM3G5o1gyOHVMBt4i/aURJxBlhVNitEaXimjIF1q5VAbeIiIQPFXbnp0SpECrgFhGRcHSisHvcOBV2g6beCvXII/DeeyrgFnGKpt5EnBMmhd2aeiuqVatg6lQVcIuISHg6ubB71iyno3GWRpROoQJukcCgESUR57VvD0uWhGxht0aUimLyZBVwi4iIAIwYYQq7Bw92OhLnKFE6SXY2DBigAm4REREwhd3PPms6dn/3ndPROEOJ0kkSE8G24eWXnY5EJHyp4aRIYOnTBy6/HHr2NO+R4UY1SsetXGlGkVwu+Pe/nY5GRFSjJBI4vvwSbroJZs6EBx90Ohqv8ahGSYkSpoC7aVOTKauAWyQwKFESCSzt25tWAVu2hExht4q5PTV5MnzzjQq4RURECjNiBBw4EH6F3WGfKP32mwq4RUREziZcC7vDfuqta1eYO1cduEUCjabeRALPiY7dF15o+isFecduTb2dzcqVpgP3Sy8pSRIRETmbyEgzopSaCm+95XQ0/hG2I0oq4BYJbBpREglc991nkqWtWyGIfzw1onQmkyapgFtERKQoRo4Mn8LusEyUfvsNBg6Ehx9WAbdIoFHDSZHAd/HFMGgQjBkT+oXdYTn11qULvP8+ZGSYgjQRCTyaehMJbLm50KABxMbC4sVBWditqbeCLF8O06bB0KFKkkRERIoqMhLGjTNNKEO5sDusRpSOHoXGjSE6GlasUG2SSCDTiJJIcAjiwm6NKJ1qzBjYsAGSk5UkiYiIeEOoF3aHTaL0yy/w3HNmw9u4OKejEQk+48ePp1atWkRHRxMXF0dqaqpHz1u+fDklS5akUaNGvg1QRBwR6oXdYZMo9e0LZcvCiy86HYlI8Jk9ezZ9+vRh4MCBpKen07p1a9q0aUNmZuYZn7dv3z46derEjTfe6KdIRcQJTzwBf/sbPPaY6U8YSsKiRumzz+CWW+DNN+Gf/3Q6GpHg06xZMxo3bkxycnLesbp169KuXTuSkpIKfV6HDh24/PLLiYiI4IMPPmDdunUeX1M1SiLB5Ysv4B//CKr3WtUoARw+DD17wvXXwwMPOB2NSPDJzc1l7dq1JCQk5DuekJBAWlpaoc97/fXX+fHHH3nuuec8uk5OTg779+/P9xCR4HHTTXDvvdCvH4TSj2/IJ0qvvAKZmaYDdxD2eBBxXHZ2Nm63m9jY2HzHY2Nj2bVrV4HP+f7773nmmWeYNWsWJUuW9Og6SUlJxMTE5D2qV69e7NhFxL9GjDBJUigVdod0ovTDD5CUZLLbunWdjkYkuFmn/KZh2/ZpxwDcbjcPPPAAzz//PFdccYXHnz8xMZF9+/blPbZv317smEXEv6pXh2ef/WuVeSgI2Rol24Y2bWDLFti0CcqUcToikeCUm5tLmTJlmDNnDnfeeWfe8d69e7Nu3TqWLFmS7/y9e/dSsWJFIk7qwXHs2DFs2yYiIoLPP/+cG2644azXVY2SSHAKoo7d4V2jNHeuKeIeO1ZJkkhxREZGEhcXR0pKSr7jKSkptGzZ8rTzy5cvz3fffce6devyHt27d6d27dqsW7eOZs2a+St0EXFAZKR57w2Vjt2eFQ8EmQMHoE8fuP12aNvW6WhEgl/fvn3p2LEjTZo0oUWLFkyaNInMzEy6d+8OmGmzHTt2MGPGDEqUKEH9+vXzPb9y5cpER0efdlxEQtM//mEKu598Em67DSpUcDqiogvJRGnwYPj9dzNHKiLF1759e/bs2cOQIUPIysqifv36LFiwgJo1awKQlZV11p5KIhJeRo0y9cEDBsD48U5HU3QhV6P07bdmP7cXX4RnnnE6GhEpKtUoiQS/MWPMDM+KFRCAs+4e1SiFVKJ07Bi0bg3/+x+sW2fmSUUkOClREgl+bjc0bWren7/+GjzsFuIv4VfMPX06pKWZIT4lSSIiIs6KiICJE2H9ehg3zuloiiZkEqU9e+Dpp+HBB+G665yORkSKyuVyUa9ePeLj450ORUS8oEkTs0PGoEFmg/pgEzJTb926wbvvwtatpneDiAQ3Tb2JhI59+6BOHWjZ0rTvCRDhM/W2YgVMngxDhypJEhERCTQxMTB6NLz/Pnz8sdPRnJugH1E6etQM65UqBStXmvlQEQl+GlESCS0BuGNGeIwouVymJUByspIkERGRQGVZ5j171y4YMsTpaDwX1InSzp2mOKxHDzOqJCIiIoHrssvgP/+BESOCZ9PcoJ56u/deSE01w3jB3B5dRE6nqTeR0JSTAw0bwoUXwpIlUMK5IZvQnnr7+GN47z1THKYkSUREJDhERcGECbBsGbz+utPRnF1QjigdPAhXXgn16sGCBWbeU0RCi0aURELbQw+ZQY8tW8zokgNCd0Rp8GD47TfTgVtJkkhoUcNJkfAwbJhZCff0005HcmZBN6KUng7x8fDSS9C/vz+vLCL+pBElkdA3ebJpGL14MVx7rd8vH3qb4rrd0Ly5KQRbu9b0ThKR0KRESST0ObyZfehNvblcJkGaOFFJkoiISLArUcIUdmdkwPDhTkdTsKBJlH75BQYOhO7doUULp6MRERERb7jqKujbF154AX76yeloThc0U2933WX2dNuyxewZIyKhTVNvIuHjjz/MSnY/r2YPnam3Dz+EefNgzBglSSIiIqGmbFkYNw4WLjQ9EgNJwI8oHThgMsyGDeGjj9QOQCRcaERJJPycmD3atAkqVvT55UJjROnZZ+H3302mqSRJREQkdI0da6bhnnnG6Uj+EtCJ0tq1Zrrt+efhkkucjkZE/EENJ0XCV7Vq8PLLMGkSLF3qdDRGwE69HT0KzZqZ3klr1kDJkr64iogEKk29iYSnE72V9uyB9evN3nA+EtxTb2PHmi7ckyYpSRIREQkXJUqY9/6ffoKhQ52OJkATpcxMGDQIHnsMmjZ1OhoRERHxpyuvNHVKSUmmsNtJATf1Zttwxx2mPmnzZtCIu0h40tSbSHg7fBgaNYILLoDUVDPS5GXBOfU2b55pAzB2rJIkERGRcBUdbbYsS0szU3FOCagRpb17Tc+k+Hj44AO1AxAJZxpREhGARx6Bd981U3DVqnn1UwffiNJTT8HBg2bzWyVJIiIi8uqrULo09OrlzPUDJlH66iuYMgWGDYOLL3Y6GhEREQkEFSuanorvv29mm/wtIKbeDh2CBg3MkNpXX/mkYEtEgoTL5cLlcuF2u8nIyNDUm4hg23D77fDNN15d6OXR3FVAJEpPP22yxW+/hSuuKO5nE5FQoBolETlZZqZpG9CpkynR8YLgqFFaswZGjIDBg5UkiYiISMFq1ICXXoLkZLMSzl8cHVE6cgSaNDFTbatXQ6lSxQ1FREKFRpRE5FRuN7RsaRZ+ffNNsbc3CfwRpWHDYONGmDpVSZKIiIicWUQETJ4MGRmma7c/OJYobd0KQ4bAk09C48ZORSEinho/fjy1atUiOjqauLg4UlNTCz132bJltGrVigsuuIDSpUtTp04dRo0a5cdoRSRUNWgAiYlmH7jvvvP99RyZejt2DK69FnbtMgXcpUsXNwQR8aXZs2fTsWNHxo8fT6tWrZg4cSJTpkxh06ZN1KhR47Tz09PT2bJlCw0aNKBs2bIsW7aMRx99lFGjRtGtWzePrqmpNxEpTE6OGWQpWxZWrDAjTUUQuKvekpPh3/82rQCuu664lxcRX2vWrBmNGzcmOTk571jdunVp164dSR6Of991112ULVuWmTNnenS+EiUROZOVK0290vDh0LdvkT5FYNYo/fIL9O8P3bopSRIJBrm5uaxdu5aEhIR8xxMSEkjzcOlJeno6aWlpXHvttYWek5OTw/79+/M9REQK07w59O4N//kP/PCD767j10TJtqF7dyhXzrQkF5HAl52djdvtJjY2Nt/x2NhYdu3adcbnXnzxxURFRdGkSRN69uxJ165dCz03KSmJmJiYvEf16tW9Er+IhK4XX4TYWLMfXPEnyArm10TpnXfgk09g/HiIifHnlUWkuKxTNmC0bfu0Y6dKTU1lzZo1TJgwgdGjR/P2228Xem5iYiL79u3Le2zfvt0rcYtI6Cpb1qyCW7zYbIPmCyV982lPl51tNrS791644w5/XVVEiqtSpUpEREScNnq0e/fu00aZTlWrVi0ArrrqKn799VcGDx7M/fffX+C5UVFRRBWzKYqIhJ+bboKHH4Z+/eDWW812aN7ktxGlJ54wjaLGjvXXFUXEGyIjI4mLiyMlJSXf8ZSUFFq2bOnx57Ftm5ycHG+HJyLC8OFQpgz06OH9KTi/jCi53WaqbdQoM5coIsGlb9++dOzYkSZNmtCiRQsmTZpEZmYm3bt3B8y02Y4dO5gxYwZgNratUaMGderUAUxfpeHDh/P444879jWISOiqWNGU9cyfb3b9iIz03uf2S6IUEQHjxvnjSiLiC+3bt2fPnj0MGTKErKws6tevz4IFC6hZsyYAWVlZZGZm5p1/7NgxEhMT2bZtGyVLluSyyy7j5Zdf5tFHH3XqSxCREHfnnebhbY7u9SYiUhj1URIRHwvMPkoiIiIiwUKJkoiIiEghlCiJSEBxuVzUq1eP+Ph4p0MREfFKjZKIiNdZllUe2AfE2Lat/UxExBFKlEQkIFmm7Xc54ICtFyoRcYgSJREREZFCqEZJREREpBBKlEREREQKoURJREREpBBKlEREREQKoURJREREpBBKlEREREQKoURJREREpBBKlEREREQKoURJREREpBBKlEREREQKUbI4Tz5pLyYRERGRYHPWvSSLlShhkqR9xfwcIiIiIk6IAfaf6YRibYp7jiNK5YBfgIuBA0W+qOdWA039cB1dq3h0X+hahdG9oWsVJlTvjVD8XvnzWkW5L3w7onT8k58xEzvB5FR5QXn0nOKwLOuYP66jaxX7Gif+qPtC1zr1Oif+qHtD1zr1Oif+GFL3Rih+r/x5LV/dF6FczO3StYLqWv4Sqv9/oXotfwrV/8NQvZY/+evrCtXvVVDfF8WaejunC1lWeUw9U4y/slgJfLovpDC6N6QwujekIL66L/w5opQDPH/8o8gJui+kMLo3pDC6N6QgPrkv/DaiJCIiIhJsQrlGSURERKRYlCiJiIiIFEKJkoiIiEghlCiJiIiIFMKniZJlWQMty0qzLOuQZVl7PXyOZVnWYMuydlqW9adlWYsty7rSl3GKf1mWVdGyrJmWZe07/phpWVaFszxnumVZ9imPlX4KWXzEsqx/W5a1zbKsw5ZlrbUsq/VZzr/2+HmHLcv6ybKs7v6KVfznXO4Ly7KuK+C1wbYsq44/YxbfsyzrGsuyPjqeH9iWZbXz4DnFfs3w9YhSJDAHSD6H5zwN9AUeA+KBXUCKZVnafDd0vAU0Am45/mgEzPTgeQuBqic9bvVNeOIPlmW1B0YDLwFXA6nAp5Zl1Sjk/FrAguPnXQ0MBcZYlnW3XwIWvzjX++Iktcn/+vC9D8MUZ5QF1mPyg7Py1muGX9oDWJbVGRht23aFs5xnATuPn/vK8WNRwK9Af9u2J/o4VPExy7LqApuA5rZtrzp+rDmwAqhj2/bWQp43Hahg23Y7P4UqPmZZ1irgG9u2e5x0bDPwgW3biQWc/wpwu23bdU86NgFoaNt2C3/ELL5XhPviOuAroKJt23v9FKY4zLIsG7jTtu0PznCOV14zAq1GqRZQBfj8xAHbtnOAJUBLp4ISr2oB7DuRJAHYtr0S0031bN/j6yzL2m1ZVoZlWZMty6rsy0DFdyzLigTiOOln/bjPKfw+aFHA+Z8BTSzLKuXdCMUJRbwvTki3LCvLsqwvLcu63icBSrDxymtGoCVKVY5//PWU47+e9G8S3KoAuws4vpszf48/Bf4J3AA8iZmWXXR8xFGCTyUggnP7Wa9SyPklj38+CX5FuS+ygG7A3cBdwFbgS8uyrvFVkBI0vPKaUfJcr2pZ1mDgubOcFm/b9ppz/dwnOXU+0CrgmAQQT++L4x8L+l6e8Xts2/bsk/66wbKsNcB/gduA9z2PVALMuf6sF3R+QccluHl8Xxyfrj95yn6FZVnVgX7AUt+EJ0Gk2K8Z55woAeOAd85yzs9F+LxgCrfBZIFZJx2vzOlZoQQWT++LBkBsAf92IefwPbZtO8uyrP8Cl3v6HAko2YCb00cJzvSzvquQ848Ce7wanTilKPdFQVYCD3orKAlaXnnNOOdEybbtbMzN7AvbMF/YP4B0yJuzvhbo76Nrihd4el9YlrUCiLEsq6lt26uPH2sGxABpnl7PsqwLgOrkT6glSNi2nWtZ1lrMz/q8k/7pH8CHhTxtBdD2lGMJwBrbto94P0rxtyLeFwW5Gr02iJdeM3zdR6mGZVmNgBpAhGVZjY4/zjvpnC2WZd0JYJsleKOBAZZl3WlZVn1gOnAIs6Rcgpxt25sxy/wnW5bV/PiKt8nAxyeveDv5vrAs6zzLsoZbltXCsqxLjq9y+QiTmM077SISLEYCXS3LetiyrLqWZY3CvFZMALAsK8myrBknnT8BqGlZ1sjj5z8MdAGG+z1y8aVzui8sy+pjWVY7y7IutyzrSsuykjD1SuMciV585vh7QaPjeQVAreN/r3H8333ymlGUqbdzMQR46KS/px//eD2w+Pifa2NGE054FSgNjAcqAquABNu2D/g0UvGnfwJj+Gs1wnxO74tx8n3hBq4COgEVML8pfgW0130RvGzbnn18ZPBZTN+bDcCttm3/9/gpVTFvkCfO32ZZ1q3AKKAnppVIL9u25/o3cvGlc70vMP36hgPVgD+BjcBttm0v8F/U4idNMK/9J4w8/vENoDM+es3wSx8lERERkWAUaO0BRERERAKGEiURERGRQihREhERESmEEiURERGRQihREhERESmEEiURERGRQihREhERESmEEiURERGRQihREhERESmEEiURERGRQihREhERESmEEiURERGRQvw/cnLDj7nAFwEAAAAASUVORK5CYII=\n", | |
"text/plain": "Graphics object consisting of 1 graphics primitive" | |
}, | |
"execution_count": 25, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
] | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "7cc9dd64", | |
"cell_type": "code", | |
"source": "print(f(pi/2))\nprint(f(pi/4))", | |
"execution_count": 19, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": "0\n1/2\n" | |
} | |
] | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "75478e53", | |
"cell_type": "code", | |
"source": "show(f.differentiate())\nshow(f.differentiate(2))\nshow(f.simplify_trig())", | |
"execution_count": 24, | |
"outputs": [ | |
{ | |
"data": { | |
"text/html": "<html>\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}x \\ {\\mapsto}\\ -2 \\, \\cos\\left(x\\right) \\sin\\left(x\\right)\\]</html>", | |
"text/latex": "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}x \\ {\\mapsto}\\ -2 \\, \\cos\\left(x\\right) \\sin\\left(x\\right)$$", | |
"text/plain": "x |--> -2*cos(x)*sin(x)" | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
}, | |
{ | |
"data": { | |
"text/html": "<html>\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}x \\ {\\mapsto}\\ -2 \\, \\cos\\left(x\\right)^{2} + 2 \\, \\sin\\left(x\\right)^{2}\\]</html>", | |
"text/latex": "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}x \\ {\\mapsto}\\ -2 \\, \\cos\\left(x\\right)^{2} + 2 \\, \\sin\\left(x\\right)^{2}$$", | |
"text/plain": "x |--> -2*cos(x)^2 + 2*sin(x)^2" | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
}, | |
{ | |
"data": { | |
"text/html": "<html>\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}x \\ {\\mapsto}\\ \\cos\\left(x\\right)^{2}\\]</html>", | |
"text/latex": "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}x \\ {\\mapsto}\\ \\cos\\left(x\\right)^{2}$$", | |
"text/plain": "x |--> cos(x)^2" | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
] | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "32b457fb", | |
"cell_type": "code", | |
"source": "g = (f^2).integrate(x)\nshow(g)\nplot(g)", | |
"execution_count": 29, | |
"outputs": [ | |
{ | |
"data": { | |
"text/html": "<html>\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}x \\ {\\mapsto}\\ \\frac{3}{8} \\, x + \\frac{1}{32} \\, \\sin\\left(4 \\, x\\right) + \\frac{1}{4} \\, \\sin\\left(2 \\, x\\right)\\]</html>", | |
"text/latex": "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}x \\ {\\mapsto}\\ \\frac{3}{8} \\, x + \\frac{1}{32} \\, \\sin\\left(4 \\, x\\right) + \\frac{1}{4} \\, \\sin\\left(2 \\, x\\right)$$", | |
"text/plain": "x |--> 3/8*x + 1/32*sin(4*x) + 1/4*sin(2*x)" | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": "Graphics object consisting of 1 graphics primitive" | |
}, | |
"execution_count": 29, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
] | |
}, | |
{ | |
"metadata": {}, | |
"id": "c0543c54", | |
"cell_type": "markdown", | |
"source": "Symbolic functions on multiple variables." | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "190ddf08", | |
"cell_type": "code", | |
"source": "x, y, z = var('x y z')\nf(x, y, z) = x + 2*y + 3*z^2\nshow(f)", | |
"execution_count": 31, | |
"outputs": [ | |
{ | |
"data": { | |
"text/html": "<html>\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( x, y, z \\right) \\ {\\mapsto} \\ 3 \\, z^{2} + x + 2 \\, y\\]</html>", | |
"text/latex": "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( x, y, z \\right) \\ {\\mapsto} \\ 3 \\, z^{2} + x + 2 \\, y$$", | |
"text/plain": "(x, y, z) |--> 3*z^2 + x + 2*y" | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
] | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "4ed79a53", | |
"cell_type": "code", | |
"source": "show(f(1))\nshow(f(1, 2))\nshow(f(1, 2, 3))", | |
"execution_count": 33, | |
"outputs": [ | |
{ | |
"data": { | |
"text/html": "<html>\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}3 \\, z^{2} + 2 \\, y + 1\\]</html>", | |
"text/latex": "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}3 \\, z^{2} + 2 \\, y + 1$$", | |
"text/plain": "3*z^2 + 2*y + 1" | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
}, | |
{ | |
"data": { | |
"text/html": "<html>\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}3 \\, z^{2} + 5\\]</html>", | |
"text/latex": "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}3 \\, z^{2} + 5$$", | |
"text/plain": "3*z^2 + 5" | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
}, | |
{ | |
"data": { | |
"text/html": "<html>\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}32\\]</html>", | |
"text/latex": "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}32$$", | |
"text/plain": "32" | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
] | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "7dc9de04", | |
"cell_type": "code", | |
"source": "g = f + 2*x^3\nshow(g)", | |
"execution_count": 34, | |
"outputs": [ | |
{ | |
"data": { | |
"text/html": "<html>\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( x, y, z \\right) \\ {\\mapsto} \\ 2 \\, x^{3} + 3 \\, z^{2} + x + 2 \\, y\\]</html>", | |
"text/latex": "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left( x, y, z \\right) \\ {\\mapsto} \\ 2 \\, x^{3} + 3 \\, z^{2} + x + 2 \\, y$$", | |
"text/plain": "(x, y, z) |--> 2*x^3 + 3*z^2 + x + 2*y" | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
] | |
}, | |
{ | |
"metadata": {}, | |
"id": "b021f2bc", | |
"cell_type": "markdown", | |
"source": "Solve an equation." | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "ca01ff3e", | |
"cell_type": "code", | |
"source": "x = var('x')\nf(x) = x^2 + 3*x + 2\nsolve(f, x)", | |
"execution_count": 35, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": "[x == -2, x == -1]" | |
}, | |
"execution_count": 35, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
] | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "c36bde5f", | |
"cell_type": "code", | |
"source": "solve([f(x) == 1], x)", | |
"execution_count": 36, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": "[x == -1/2*sqrt(5) - 3/2, x == 1/2*sqrt(5) - 3/2]" | |
}, | |
"execution_count": 36, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
] | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "84dbd1b8", | |
"cell_type": "code", | |
"source": "x, y = var('x y')\nsolve([2*x^2 + 3*y == 1], x)", | |
"execution_count": 37, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": "[x == -sqrt(-3/2*y + 1/2), x == sqrt(-3/2*y + 1/2)]" | |
}, | |
"execution_count": 37, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
] | |
}, | |
{ | |
"metadata": {}, | |
"id": "72b6332d", | |
"cell_type": "markdown", | |
"source": "## Linear algebra\n[https://doc.sagemath.org/html/en/reference/matrices/index.html]\n" | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "501ea4dd", | |
"cell_type": "code", | |
"source": "A = Matrix([[1,2,3],[3,2,1],[1,1,1]])\nprint(A)\nprint(latex(A))\nshow(A)", | |
"execution_count": 39, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": "[1 2 3]\n[3 2 1]\n[1 1 1]\n\\left(\\begin{array}{rrr}\n1 & 2 & 3 \\\\\n3 & 2 & 1 \\\\\n1 & 1 & 1\n\\end{array}\\right)\n" | |
}, | |
{ | |
"data": { | |
"text/html": "<html>\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrr}\n1 & 2 & 3 \\\\\n3 & 2 & 1 \\\\\n1 & 1 & 1\n\\end{array}\\right)\\]</html>", | |
"text/latex": "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrr}\n1 & 2 & 3 \\\\\n3 & 2 & 1 \\\\\n1 & 1 & 1\n\\end{array}\\right)$$", | |
"text/plain": "[1 2 3]\n[3 2 1]\n[1 1 1]" | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
] | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "58eba78a", | |
"cell_type": "code", | |
"source": "show(A.kernel())", | |
"execution_count": 40, | |
"outputs": [ | |
{ | |
"data": { | |
"text/html": "<html>\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{RowSpan}_{\\Bold{Z}}\\left(\\begin{array}{rrr}\n1 & 1 & -4\n\\end{array}\\right)\\]</html>", | |
"text/latex": "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{RowSpan}_{\\Bold{Z}}\\left(\\begin{array}{rrr}\n1 & 1 & -4\n\\end{array}\\right)$$", | |
"text/plain": "Free module of degree 3 and rank 1 over Integer Ring\nEchelon basis matrix:\n[ 1 1 -4]" | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
] | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "a6312eb9", | |
"cell_type": "code", | |
"source": "A.eigenvalues()", | |
"execution_count": 41, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": "[5, 0, -1]" | |
}, | |
"execution_count": 41, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
] | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "095d1bd8", | |
"cell_type": "code", | |
"source": "show(A^2 + A.transpose())", | |
"execution_count": 42, | |
"outputs": [ | |
{ | |
"data": { | |
"text/html": "<html>\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrr}\n11 & 12 & 9 \\\\\n12 & 13 & 13 \\\\\n8 & 6 & 6\n\\end{array}\\right)\\]</html>", | |
"text/latex": "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrr}\n11 & 12 & 9 \\\\\n12 & 13 & 13 \\\\\n8 & 6 & 6\n\\end{array}\\right)$$", | |
"text/plain": "[11 12 9]\n[12 13 13]\n[ 8 6 6]" | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
] | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "942fb5df", | |
"cell_type": "code", | |
"source": "A = Matrix([[1,2,3],[3,2,1],[1,1,1/2]])\nshow(A)", | |
"execution_count": 43, | |
"outputs": [ | |
{ | |
"data": { | |
"text/html": "<html>\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrr}\n1 & 2 & 3 \\\\\n3 & 2 & 1 \\\\\n1 & 1 & \\frac{1}{2}\n\\end{array}\\right)\\]</html>", | |
"text/latex": "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrr}\n1 & 2 & 3 \\\\\n3 & 2 & 1 \\\\\n1 & 1 & \\frac{1}{2}\n\\end{array}\\right)$$", | |
"text/plain": "[ 1 2 3]\n[ 3 2 1]\n[ 1 1 1/2]" | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
] | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "ddde333d", | |
"cell_type": "code", | |
"source": "show(A^2)", | |
"execution_count": 44, | |
"outputs": [ | |
{ | |
"data": { | |
"text/html": "<html>\\[\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrr}\n10 & 9 & \\frac{13}{2} \\\\\n10 & 11 & \\frac{23}{2} \\\\\n\\frac{9}{2} & \\frac{9}{2} & \\frac{17}{4}\n\\end{array}\\right)\\]</html>", | |
"text/latex": "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrr}\n10 & 9 & \\frac{13}{2} \\\\\n10 & 11 & \\frac{23}{2} \\\\\n\\frac{9}{2} & \\frac{9}{2} & \\frac{17}{4}\n\\end{array}\\right)$$", | |
"text/plain": "[ 10 9 13/2]\n[ 10 11 23/2]\n[ 9/2 9/2 17/4]" | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
] | |
}, | |
{ | |
"metadata": {}, | |
"id": "212d2227", | |
"cell_type": "markdown", | |
"source": "## Combinatorics\n[https://doc.sagemath.org/html/en/reference/combinat/index.html]" | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "82e1c30e", | |
"cell_type": "code", | |
"source": "P5 = Partitions(5)\nP5", | |
"execution_count": 45, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": "Partitions of the integer 5" | |
}, | |
"execution_count": 45, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
] | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "6a0d2d0c", | |
"cell_type": "code", | |
"source": "list(P5)", | |
"execution_count": 46, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": "[[5], [4, 1], [3, 2], [3, 1, 1], [2, 2, 1], [2, 1, 1, 1], [1, 1, 1, 1, 1]]" | |
}, | |
"execution_count": 46, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
] | |
}, | |
{ | |
"metadata": {}, | |
"id": "0b37f939", | |
"cell_type": "markdown", | |
"source": "## Graph Theory\n[https://doc.sagemath.org/html/en/reference/graphs/index.html]" | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "6a45352e", | |
"cell_type": "code", | |
"source": "G = graphs.PetersenGraph()\nprint(\"diameter =\", G.diameter())\nprint(\"treewidth =\", G.treewidth())\nshow(G)", | |
"execution_count": 47, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": "diameter = 2\ntreewidth = 4\n" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": "Graphics object consisting of 26 graphics primitives" | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
] | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "e9e21b2e", | |
"cell_type": "code", | |
"source": "C = G.coloring()\nprint(C)\nG.plot(partition=C)", | |
"execution_count": 48, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": "[[0, 2, 6], [1, 3, 5, 9], [4, 7, 8]]\n" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": "Graphics object consisting of 26 graphics primitives" | |
}, | |
"execution_count": 48, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
] | |
}, | |
{ | |
"metadata": {}, | |
"id": "6e3eddb3", | |
"cell_type": "markdown", | |
"source": "You can list the induced connected subgraphs on 4 vertices" | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "265e733b", | |
"cell_type": "code", | |
"source": "len(list(G.connected_subgraph_iterator(4)))", | |
"execution_count": 50, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": "125" | |
}, | |
"execution_count": 50, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
] | |
}, | |
{ | |
"metadata": {}, | |
"id": "f687d166", | |
"cell_type": "markdown", | |
"source": "List the simple paths from 0 to 3" | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "5032b076", | |
"cell_type": "code", | |
"source": "for P in G.shortest_simple_paths(0, 3):\n print(P)", | |
"execution_count": 53, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": "[0, 4, 3]\n[0, 1, 2, 3]\n[0, 5, 8, 3]\n[0, 5, 7, 2, 3]\n[0, 1, 6, 8, 3]\n[0, 1, 6, 9, 4, 3]\n[0, 5, 7, 9, 4, 3]\n[0, 4, 9, 7, 2, 3]\n[0, 4, 9, 6, 8, 3]\n[0, 4, 9, 6, 1, 2, 3]\n[0, 4, 9, 7, 5, 8, 3]\n[0, 5, 7, 9, 6, 8, 3]\n[0, 1, 6, 9, 7, 2, 3]\n[0, 5, 8, 6, 1, 2, 3]\n[0, 5, 8, 6, 9, 4, 3]\n[0, 1, 2, 7, 9, 4, 3]\n[0, 1, 2, 7, 5, 8, 3]\n[0, 1, 2, 7, 9, 6, 8, 3]\n[0, 5, 8, 6, 9, 7, 2, 3]\n[0, 1, 6, 9, 7, 5, 8, 3]\n[0, 5, 7, 9, 6, 1, 2, 3]\n[0, 1, 6, 8, 5, 7, 2, 3]\n[0, 5, 7, 2, 1, 6, 8, 3]\n[0, 5, 7, 2, 1, 6, 9, 4, 3]\n[0, 1, 6, 8, 5, 7, 9, 4, 3]\n[0, 4, 9, 6, 8, 5, 7, 2, 3]\n[0, 4, 9, 7, 2, 1, 6, 8, 3]\n[0, 1, 2, 7, 5, 8, 6, 9, 4, 3]\n[0, 5, 8, 6, 1, 2, 7, 9, 4, 3]\n[0, 4, 9, 7, 5, 8, 6, 1, 2, 3]\n[0, 4, 9, 6, 1, 2, 7, 5, 8, 3]\n" | |
} | |
] | |
}, | |
{ | |
"metadata": {}, | |
"id": "86b931c1", | |
"cell_type": "markdown", | |
"source": "Compute a Hamiltonian cycle" | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "1b5e1ed3", | |
"cell_type": "code", | |
"source": "G = graphs.DodecahedralGraph()\nH = G.hamiltonian_cycle()\nG.plot(edge_colors={'red': H.edges()})", | |
"execution_count": 54, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": "Graphics object consisting of 51 graphics primitives" | |
}, | |
"execution_count": 54, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
] | |
}, | |
{ | |
"metadata": {}, | |
"id": "fd8ae733", | |
"cell_type": "markdown", | |
"source": "Check isomorphisms between graphs" | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "9948896e", | |
"cell_type": "code", | |
"source": "G = graphs.Grid2dGraph(3, 4)\nH = G.relabel(inplace=False) # relabel the vertices 0..n-1\nG.is_isomorphic(H)", | |
"execution_count": 55, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": "True" | |
}, | |
"execution_count": 55, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
] | |
}, | |
{ | |
"metadata": {}, | |
"id": "233f04d8", | |
"cell_type": "markdown", | |
"source": "Search for a subgraph isomorphic to a given graph" | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "18e09e16", | |
"cell_type": "code", | |
"source": "G = graphs.EuropeMap()\nB = graphs.BullGraph()\nG.subgraph_search(B).show()", | |
"execution_count": 60, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": "Graphics object consisting of 11 graphics primitives" | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
] | |
}, | |
{ | |
"metadata": {}, | |
"id": "968d3cd4", | |
"cell_type": "markdown", | |
"source": "Display all graphs or order 5 (may require optional package `nauty`, which gives more options)" | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "98b12622", | |
"cell_type": "code", | |
"source": "glist= [g for g in graphs(5)]\ngraphs_list.show_graphs(glist)", | |
"execution_count": 61, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": "Graphics Array of size 5 x 4" | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
] | |
}, | |
{ | |
"metadata": {}, | |
"id": "69275d20", | |
"cell_type": "markdown", | |
"source": "## Linear programming\n[https://doc.sagemath.org/html/en/thematic_tutorials/linear_programming.html]\n[https://doc.sagemath.org/html/en/reference/numerical/sage/numerical/mip.html]\n\nSimple interface for `glpk`, `PPL`, `cbc`, `cplex`, `gurobi`." | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "45f60dcc", | |
"cell_type": "code", | |
"source": "def dominating_set(G):\n \"\"\"\n Return a minimum dominating set of ``G``\n \"\"\"\n from sage.numerical.mip import MixedIntegerLinearProgram\n p = MixedIntegerLinearProgram(maximization=False)\n b = p.new_variable(binary=True, name='b')\n for u in G:\n # Either u in D or a neighbor of u is in D\n p.add_constraint(b[u] + p.sum(b[v] for v in G.neighbors(u)) >= 1)\n # We want to maximize the size of the dominating set\n p.set_objective(p.sum(b[u] for u in G))\n p.solve()\n b_val = p.get_values(b)\n return [v for v in G if b_val[v]]\n\nG = graphs.RandomUnitDiskGraph(100, radius=.2, seed=0)\ndom = dominating_set(G)\nprint(dom)\nG.plot(vertex_colors={'red':dom})", | |
"execution_count": 74, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": "[0, 2, 8, 13, 22, 39, 51, 54, 62, 70]\n" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": "Graphics object consisting of 581 graphics primitives" | |
}, | |
"execution_count": 74, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
] | |
}, | |
{ | |
"metadata": {}, | |
"id": "24d82014", | |
"cell_type": "markdown", | |
"source": "To display a graph, we can also use the `d3.js` interface. It will display the graph in a new window of your web browser." | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "b78e6c15", | |
"cell_type": "code", | |
"source": "G = graphs.RandomTree(100)\nG.show(method='js')", | |
"execution_count": 1, | |
"outputs": [] | |
}, | |
{ | |
"metadata": {}, | |
"id": "e20288c9", | |
"cell_type": "markdown", | |
"source": "## Use Cython\n[https://cython.org]\n\nStatic compiler for Python and the extended Cython programming language.\n\nWith Cython, you can\n* Code functions using both Python and C/C++\n* Make interface with C/C++ code\n* Get better performances for critical functions\n* Used to interface external code (cliquer, bliss, nauty, gmp, etc.) \n\nSagemath uses extensively Cython ([https://cython.org]) to make interfaces with various C/C++ libraries and get better performances for various functions." | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "49e618e3", | |
"cell_type": "code", | |
"source": "def sum_py(n):\n s = 0\n for i in range(n):\n s += i\n return s", | |
"execution_count": 12, | |
"outputs": [] | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "21298fc4", | |
"cell_type": "code", | |
"source": "%%cython\ndef sum_cy(n):\n s = 0\n for i in range(n):\n s += i\n return s", | |
"execution_count": 13, | |
"outputs": [] | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "fd24bb7e", | |
"cell_type": "code", | |
"source": "%%cython\ndef sum_cy2(int n):\n cdef long s = 0\n cdef int i\n for i in range(n):\n s += i\n return s", | |
"execution_count": 14, | |
"outputs": [] | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "613ed8c3", | |
"cell_type": "code", | |
"source": "n = 10**7\nprint(timeit(\"sum_py(10**5)\"))\nprint(timeit(\"sum_cy(10**5)\"))\nprint(timeit(\"sum_cy2(10**5)\"))", | |
"execution_count": 15, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": "25 loops, best of 3: 36.8 ms per loop\n125 loops, best of 3: 4.72 ms per loop\n625 loops, best of 3: 478 ns per loop\n" | |
} | |
] | |
}, | |
{ | |
"metadata": {}, | |
"id": "e2399e3c", | |
"cell_type": "markdown", | |
"source": "and you can do much more with Cython outside of jupyter..." | |
}, | |
{ | |
"metadata": { | |
"trusted": false | |
}, | |
"id": "99e71bab", | |
"cell_type": "code", | |
"source": "", | |
"execution_count": null, | |
"outputs": [] | |
} | |
], | |
"metadata": { | |
"kernelspec": { | |
"display_name": "SageMath 9.6.beta5", | |
"language": "sage", | |
"name": "sagemath" | |
}, | |
"language_info": { | |
"codemirror_mode": { | |
"name": "ipython", | |
"version": 3 | |
}, | |
"file_extension": ".py", | |
"mimetype": "text/x-python", | |
"name": "python", | |
"nbconvert_exporter": "python", | |
"pygments_lexer": "ipython3", | |
"version": "3.9.10" | |
}, | |
"toc": { | |
"nav_menu": {}, | |
"number_sections": true, | |
"sideBar": true, | |
"skip_h1_title": false, | |
"base_numbering": 1, | |
"title_cell": "Table of Contents", | |
"title_sidebar": "Contents", | |
"toc_cell": false, | |
"toc_position": {}, | |
"toc_section_display": true, | |
"toc_window_display": false | |
}, | |
"gist": { | |
"id": "", | |
"data": { | |
"description": "Examples_sagemath.ipynb", | |
"public": true | |
} | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 5 | |
} |
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