{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "9de40674", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "IPython console for SymPy 1.10.1 (Python 3.9.12-64-bit) (ground types: python)\n", "\n", "These commands were executed:\n", ">>> from sympy import *\n", ">>> x, y, z, t = symbols('x y z t')\n", ">>> k, m, n = symbols('k m n', integer=True)\n", ">>> f, g, h = symbols('f g h', cls=Function)\n", ">>> init_printing()\n", "\n", "Documentation can be found at https://docs.sympy.org/1.10.1/\n", "\n" ] } ], "source": [ "from sympy import init_session\n", "init_session()" ] }, { "cell_type": "code", "execution_count": 2, "id": "3c6e4c5e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "['Abs',\n", " 'AccumBounds',\n", " 'Add',\n", " 'Adjoint',\n", " 'AlgebraicField',\n", " 'AlgebraicNumber',\n", " 'And',\n", " 'AppliedPredicate',\n", " 'Array',\n", " 'AssumptionsContext',\n", " 'Atom',\n", " 'AtomicExpr',\n", " 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" 'pycode',\n", " 'python',\n", " 'quadratic_congruence',\n", " 'quadratic_residues',\n", " 'quo',\n", " 'rad',\n", " 'radsimp',\n", " 'randMatrix',\n", " 'random_poly',\n", " 'randprime',\n", " 'rational_interpolate',\n", " 'ratsimp',\n", " 'ratsimpmodprime',\n", " 'rcode',\n", " 'rcollect',\n", " 're',\n", " 'real_root',\n", " 'real_roots',\n", " 'reduce_abs_inequalities',\n", " 'reduce_abs_inequality',\n", " 'reduce_inequalities',\n", " 'reduced',\n", " 'reduced_totient',\n", " 'refine',\n", " 'refine_root',\n", " 'register_handler',\n", " 'release',\n", " 'rem',\n", " 'remove_handler',\n", " 'reshape',\n", " 'residue',\n", " 'resultant',\n", " 'rf',\n", " 'riemann_xi',\n", " 'ring',\n", " 'root',\n", " 'rootof',\n", " 'roots',\n", " 'rot_axis1',\n", " 'rot_axis2',\n", " 'rot_axis3',\n", " 'rotations',\n", " 'round_two',\n", " 'rsolve',\n", " 'rsolve_hyper',\n", " 'rsolve_poly',\n", " 'rsolve_ratio',\n", " 'rust_code',\n", " 'satisfiable',\n", " 'sec',\n", " 'sech',\n", " 'separatevars',\n", " 'sequence',\n", " 'series',\n", " 'seterr',\n", " 'sets',\n", " 'sfield',\n", " 'shape',\n", " 'sieve',\n", " 'sift',\n", " 'sign',\n", " 'signsimp',\n", " 'simplify',\n", " 'simplify_logic',\n", " 'sin',\n", " 'sinc',\n", " 'sine_transform',\n", " 'singularities',\n", " 'singularityintegrate',\n", " 'sinh',\n", " 'solve',\n", " 'solve_linear',\n", " 'solve_linear_system',\n", " 'solve_linear_system_LU',\n", " 'solve_poly_inequality',\n", " 'solve_poly_system',\n", " 'solve_rational_inequalities',\n", " 'solve_triangulated',\n", " 'solve_undetermined_coeffs',\n", " 'solve_univariate_inequality',\n", " 'solvers',\n", " 'solveset',\n", " 'source',\n", " 'sqf',\n", " 'sqf_list',\n", " 'sqf_norm',\n", " 'sqf_part',\n", " 'sqrt',\n", " 'sqrt_mod',\n", " 'sqrt_mod_iter',\n", " 'sqrtdenest',\n", " 'srepr',\n", " 'sring',\n", " 'sstr',\n", " 'sstrrepr',\n", " 'stationary_points',\n", " 'stieltjes',\n", " 'strategies',\n", " 'sturm',\n", " 'subfactorial',\n", " 'subresultants',\n", " 'subsets',\n", " 'substitution',\n", " 'summation',\n", " 'swinnerton_dyer_poly',\n", " 'symarray',\n", " 'symbols',\n", " 'symmetric_poly',\n", " 'symmetrize',\n", " 'sympify',\n", " 'take',\n", " 'tan',\n", " 'tanh',\n", " 'tensor',\n", " 'tensorcontraction',\n", " 'tensordiagonal',\n", " 'tensorproduct',\n", " 'terms_gcd',\n", " 'test',\n", " 'testing',\n", " 'textplot',\n", " 'threaded',\n", " 'timed',\n", " 'to_cnf',\n", " 'to_dnf',\n", " 'to_nnf',\n", " 'to_number_field',\n", " 'together',\n", " 'topological_sort',\n", " 'total_degree',\n", " 'totient',\n", " 'trace',\n", " 'trailing',\n", " 'transpose',\n", " 'tribonacci',\n", " 'trigamma',\n", " 'trigsimp',\n", " 'true',\n", " 'trunc',\n", " 'unbranched_argument',\n", " 'unflatten',\n", " 'unpolarify',\n", " 'uppergamma',\n", " 'use',\n", " 'utilities',\n", " 'var',\n", " 'variations',\n", " 'vectorize',\n", " 'vfield',\n", " 'viete',\n", " 'vring',\n", " 'wronskian',\n", " 'xfield',\n", " 'xring',\n", " 'xthreaded',\n", " 'yn',\n", " 'zeros',\n", " 'zeta',\n", " 'zoo']" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import sympy\n", "dir(sympy)" ] }, { "cell_type": "code", "execution_count": null, "id": "8ff4b7f2", "metadata": {}, "outputs": [], "source": [ "#Solving Equations and Working With Math Functions" ] }, { "cell_type": "code", "execution_count": 3, "id": "2194a51b", "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAADkAAAATCAYAAAAqL6XVAAAACXBIWXMAAA7EAAAOxAGVKw4bAAACOUlEQVRYCdWW7U0bQRCG7YgCDFSA6SB2OjAdEFEB0IEtftn/IuiAUAKUQCoA0kHcQeA6cJ5nNbs6W44SLsE+RhrN7Kx3d96bL3cXi0XntTSbzXqcuYhz/ZCn2KvX3rWJ3+80fOQSQOf5LPo1+hN8mG1tkh8aOnMGsFHt7CV6H9vHmq01alOQRvGxNSj+4Ei3SU2u3kkEjeQxspXp2rQmC85I0WMMg2LcgoIf9oVMeyilEf5TJLnYzurln9G30ll5105v07tGv0J2kPaGb/AAfd60Jr1IgBPkEVy5DhvmjdINr+3xdgLoy+jfEfaMFN1G6RpgvECQuaPajCbwpslSEdQqaRvjX68RSA6bHjlNyuVcWGZnMb6hIoC4/nnNMz/DNiwg48BZbHxCnsKm5EnYHvjNnTpyN2xbFfhhmeiDjWaV9sPQr9ek/2KuZDYfYHN9xNoU9Is5JtpIfniDsUq5jHoJJECMYB1Exdpc/xon/VL1/TC3QphxHTCMsjfoAhSDNE8jRCNcihfdpjJE/tfZx31mhK1d+bfkeCq+rTsU9xqEH7BpaiYaXW2DtXOSQy9sfkGWtsz6XRG+C3AM76Z0rXvPpmH3S6cm4x62nqz+jsiUvcfvaiecv8Vg47lHOgbsWnNkpgvW25iB+f3fSvyyd9gkD9Arf4g0IAYrlZuRdCE/x+bSzMHmnjneVrL2lnxmbdDO8T3Vcnc6nYo6F22HDceIX+cIdugLvqQu69YR/um/JBbpFptZmegXDInJimMvxbcAAAAASUVORK5CYII=\n", "text/latex": [ "$\\displaystyle x^{2} - 9$" ], "text/plain": [ " 2 \n", "x - 9" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f = x**2 - 9" ] }, { "cell_type": "code", "execution_count": null, "id": "967bf1d6", "metadata": {}, "outputs": [], "source": [ "f" ] }, { "cell_type": "code", "execution_count": 4, "id": "c6cacbd0", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\left[ -3, \\ 3\\right]$" ], "text/plain": [ "[-3, 3]" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solve(f,x)" ] }, { "cell_type": "code", "execution_count": null, "id": "79afd1a3", "metadata": {}, "outputs": [], "source": [ "#Factorization " ] }, { "cell_type": "code", "execution_count": 5, "id": "cfdd3125", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\left(x - 3\\right) \\left(x + 3\\right)$" ], "text/plain": [ "(x - 3)⋅(x + 3)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "factor(f)" ] }, { "cell_type": "code", "execution_count": null, "id": "41fea251", "metadata": {}, "outputs": [], "source": [ "#Graph function " ] }, { "cell_type": "code", "execution_count": 6, "id": "e8a6c68d", "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "p = plot(f, xlim=(-8, 8),show=False, \n", " title=\"Plot of x squared minus 9\")\n" ] }, { "cell_type": "code", "execution_count": 7, "id": "b1b08f1c", "metadata": {}, "outputs": [ { "data": { "image/png": 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WPRdCiBpu9d5zfBF9kodvacztrXwrpc0qvR/US/1a08rPjX99vYtz6blVeSghhBAGiUvLZvI3u2gb6MGkPq0qrd0qDSgne1tm39+R3IIi/vnVDgrlfJQQQtQohUXFPPXVToo1fDC8Aw52lRcrVX5H3Wa+rrwxMIwtx1P5YO3Rqj6cEEKIavT+r0eIOZnGm4PCaOTtUqltV8st3wd3DGRop0BmrT3CxqPJ1XFIIYQQVWzj0WRm/3aUezsFMqB9QKW3Xy0BBfDagFCaeLvw5JKdJGXmVddhhRBCVIGUC3k8tWQnjb1deHVAaJUco9oCqo6DHR+O7EhGTgHPfL2T4mJZCkkIIaxRcbHm6a93cT6ngNkjOpZ7KaPrqbaAAmjl584r/UP580gyc34/Vp2HFkIIUUlm/3aUPw4n8fI9rWndwL3KjlOtAQUwvHMQ97RrwLu/HGbridTqPrwQQogKWH8kmZlrDjOoQwD3dwmu0mNVe0AppZg6KIzAus5MXLSD5AtyPkoIIazBufRcnvxqB818XHlzUNgN3R23PKo9oADcnOz58P6OpGbn8+RXOyiS81FCCGFqBUXFTFy8nZyCIuaMqrrzTpczJKAAwgI8eH1AKBuOpsit4oUQwuT+76dDbD2RxrQhbWnm61Ytx6z6CLyG+zoHE3MijVlrj9IxuG6lrd8kBEBiYiIbNmzg7NmzODs7ExYWRnh4ODY2hn0uE8Iq/bTvHHP/iOWBrg3p365BtR3X8P+prw8MI8TfnaeW7OR0arbR5Yga4LfffqNPnz7cfffd/Pjjj8THx7N//37eeOMN2rRpw8svv0xGRobRZQphFU6lZPPs0pJ19l7sV75bt5eXquCt2Svl5NGJ5Czumb2ext4uLH30JhztbCujWVFLTZo0iYkTJxIc/PcZRoWFhaxcuZKioiKGDBlSZTWEh4cTExNTZe0LUR1yC4oYMmcjcWk5rJzYnSCvOpXVdJlmV5gioAB+3neO8V9sY2REMG8OalNZzQphCAkoURM8990eFm85xSeR4fQMqV+ZTZcpoAwf4ruod6gfj9zWhC83n+K77XFGlyNqgAceeID09PRLX584cYKePXsaWJEQ1mPJ1lMs3nKKCT2aVnY4lZlpAgpgUu+WRDT24vn/7WHf2fTr7yDENXTv3p2IiAh++OEH5s2bR+/evXnqqaeuu19RUREdOnSgX79+AKSmptKrVy+aN29Or169SEtLq+LKhTDW9lNpvLRsH7c09+bZ3i0Nq8M0Q3wXJWXm0X/2emyU4vuJ3fFycajsQ4haZP369dx+++14e3uzY8cO/Pz8rrvPu+++S0xMDBkZGaxcuZLJkyfj5eXFlClTmDZtGmlpabz99tvXbEOG+IS1SszM5Z5Z63Gws+H7J7rjWadK3oOta4jvIh83Rz4a1YmkC3lMXLxdbnIoyu2LL75gzJgxfP755zz00EPcdddd7Nq165r7xMXFsWrVKsaNG3fpe8uXLycyMhKAyMhIli1bVpVlC2GY/MJiHlu4nYycQuY+EF5V4VRmpgsogHZBnrw5MIwNR1N4e/VBo8sRVurbb79l/fr1jBgxgrfeeouPPvqIhx566Jr7PPXUU0yfPv0v10olJCTg7+8PgL+/P4mJiVVZthCGeW3lPmJOpvH20LaE+FfdIrBlZcqAArg3PIgHb2rIvD+Ps3znGaPLEVZo2bJl+Pr+/4u/u3TpwubNm6+6/cqVK/H19aVTp07lOt7cuXMJDw8nPDycpKSkcrUhhFGWbD3FwuhTPHJrk2q9GPdaTBtQAC/1a02XRl78+9vdMmlClNkbb7xBamrpK+U7ODiwdu1aVq5c+bfHNmzYwIoVK2jUqBHDhw9n7dq1jBo1ivr16xMfHw9AfHz8X0LvcuPHjycmJoaYmBh8fHwq7wkJUcV2WCZFdG/mzaQ+xk2KuJLpJklcKSkzj3tmrcfOVvH9E92pK5MmxHUsX76c6dOn4+TkRMeOHfHx8SE3N5cjR46wc+dO7rzzTp5//vlrhsi6det45513WLlyJZMmTaJevXqXJkmkpqYyffr0a9YgkySEtUjMzKX/rA3V/R5rnZMkruTj5shHD3QiMTOPiYt3yKQJcV3ffPMNGzZsoE+fPoSGhlJUVIS7uzujRo1iy5YtzJw584Z6OFOmTOGXX36hefPm/PLLL0yZMqUKqxei+uQXFvP4l9s5n5PP3AfCTdcBMH0P6qKvY04z+ZvdjOvemBf7ta6uwwor1Lp1a3788Uf69+/Pb7/99rfHvby8qrwG6UEJa/DSsr18EX2S94e3Z0D7gOo8dJl6UIauZn4jhoUHse9MOvPXH6dFfTeGdQ4yuiRhUo8++ih9+/YlNjaW8PDwS9/XWqOUIjY21sDqhDCHJVtP8UX0SR6+pXF1h1OZWU0PCqCwqJjRn20lOjaFhWMjiGhSrzoPL6zMhAkTmDNnjiHHlh6UMLPNsSmM+mQzEY3r8dnoztjZVv/N1cu0kTUFFEB6TgGD/ruBtKx8lj/eneB6lba6rhCVRgJKmNXJlCwGfriBunUc+N9jN+NRx96IMmrGJIkreTjb82lkZ4o1jI3aSkZugdElCSGEVcjILWBsVAzFGj55qLNR4VRmVhdQAI28XZgzqiPHk7OYuEhm9gkhxPUUFhXzxKIdnEjOYs6ojjT2djG6pOuyyoAC6NbUm9cHhvH74SSm/iDLIQkhxLW8seoAfxxO4vWBYXRr6m10OWViNbP4SjOiSzBHEi7w6YbjNPN15f6Iv99BVQgharuF0Sf5bOMJxtzcmBFdrOd90mp7UBc9f1crerT04T/L97LxWLLR5QghhKlsPJrMyyv2cXtLH164O8Tocm6I1QeUna0NH4zoQGNvFyYs3M6J5CyjSxJCCFOITbrAowu30dTHhQ9GdMDWpkyT50zD6gMKwN3Jnk8iO2OjSmb2pWfLzD4hRO2WlpXPuKgY7Gxt+CSyM25O5p6xV5oaEVAAwfXq8NGoTpxOzWH8FzHkFRYZXZIQQhgit6CIhz+PIe58Dh8/0IkgL+u8XrTGBBRARJN6/N+9bdl8PJVnl+6muLjaryMWQghDFRdr/vX1LmJOpvHusHZ0blT1a09WFauexVeaAe0DiE/PZdqPB2ng4cRzd1nXSUEhhKiIt348wKo98bxwVwj92prjxoPlVeMCCuCRW5twJi2Hj/+IJaCuMw/e1MjokoQQosp9tuE48/48zkPdGjHulsZGl1NhNTKglFK80j+U+PRcXl6xj/ruTvQJ9TO6LCGEqDKr957j1ZX76d26Pi/1a41S1jVjrzQ16hzU5WxtFLNGdKBtoCf/XLyD7afSjC5JCCGqxPZTaTz51Q7aB3ny/nDrm05+NTU2oACcHWz5JDIcPw8nxkXFyDVSQoga50RyFuOiYvD3cGL+g+E4O9gaXVKlqdEBBeDt6shno7sAELlgCykX8gyuSAghKkfKhTwiF2wB4LPRXajn6mhwRZWrxgcUQGNvF+ZHhnMuPZcxUTHk5Ms1UkII63Yhr5Axn23lXHou8yPDaWQFq5PfqFoRUAAdg+vywYgO7I47z4Qvt5FfKLfoEEJYp7zCIh79Yht7z2Yw+/6OdAyua3RJVaLWBBRAn1A/pg5qw7pDSTy7dJdcyCuEsDpFxZpnluxi/dFk3h7Sll6t6xtdUpWpkdPMr2VEl2DSsvOZvvoQnnXsebV/aI2YjimEqPm01ry0fC+r9sTz4t0hDO0UaHRJVarWBRTAhNuakpaVz7w/j+NZx4FnerUwuiQhhLiuGT8fZtHmUzzWoynjbmlidDlVrlYGlFKK5+8K4Xx2AR/8eoS6dewZfbP1X3UthKi55v8Zy+zfjjKiSxCT+rQ0upxqUSsDCkpC6q3BbUjPKeDV7/fj4WzP4I41u7sshLBO326L441VB/hHmB9vDGxTa05L1KpJEle6eLPDm5rUY9I3u1mzP8HokoQQ4i/W7E9g8re7ublZPd4b3r7GrBJRFrU6oACc7G2Z+2AnWvu78/ii7WyOTTG6JCGEAGDD0WQeX7SdsAbufPxAOI52NWeViLKo9QEF4OZkz2ejOxNY15kxn22VdfuEEIaLjk1hbNRWGnu7sGB0F1wda98ZGQkoi3qujnw5rivebo5EfrqFPXHpRpckhKilYk6kMuazrQTWrcPCcRF4uTgYXZIhJKAu4+fhxKKHu+LuZM8Dn27mQHyG0SUJIWqZHafSeGjBVvzcnVg0LgLvGra+3o2QgLpCgKczix/uirO9LaPmb+ZIQqbRJQkhaok9cek8+OkW6rk6sOjhrvi6OxldkqEkoEoRXK8OX46LwMZGcf/8zRyX23QIIarY/rMZjPpkMx7O9ix6uCt+HrU7nEAC6qqa+LiyaFwExcWa++dFczo12+iShBA11KFzmYz6ZDN1HGxZ/HBXAjydjS7JFCSgrqF5fTcWjosgp6CIEfOiOXM+x+iShBA1zNHEC4ycH42djWLxw10J8qpjdEmmIQF1HSH+7iwcG0F6TgHD526SnpQQotIcT87i/nnRgGLRw11r5D2dKkICqgzCAjz4clwEGTmFDJ8bzakUCSkhRMWcSsnm/nnRFBZrFj0cQTNfV6NLMh0JqDJqG+jJl+MiyMovZPjcTZyQiRM1zunTp7n99tsJCQkhNDSU999/H4DU1FR69epF8+bN6dWrF2lpciG3qJgTyVmMmBdNTkERC8dG0KK+m9ElmZIE1A0IC/Bg0biu5BYWc9/cTcQmXTC6JFGJ7OzsmDFjBgcOHCA6OpoPP/yQ/fv3M23aNHr27MmRI0fo2bMn06ZNM7pUYcWOJGQy7ONNZOcXsnBsBK0buBtdkmlJQN2g1g3cWfxwVwqLNPfNjeZoooRUTeHv70/Hjh0BcHNzIyQkhDNnzrB8+XIiIyMBiIyMZNmyZQZWKazZ3jPp3Dc3Gg0seeQmwgI8jC7J1CSgyqGlnxtfje+K1jB87iYOy8W8Nc6JEyfYsWMHERERJCQk4O/vD5SEWGJiYqn7zJ07l/DwcMLDw0lKSqrOcoUV2HEqjfvnReNkZ8PXj9wkw3plIAFVTs3ru7Hkka7Y2iju+3gTu06fN7okUUkuXLjAkCFDeO+993B3L/vwy/jx44mJiSEmJgYfH58qrFBYm+jYFEbN30xdFwe+fvQmGstsvTKRgKqApj6uLH2kG65Odtw/L5pNx+RWHdauoKCAIUOGMHLkSAYPHgxA/fr1iY+PByA+Ph5fX18jSxRW5vfDSTy0YAv+ns58/chNBNaV65zKSgKqgoLr1eGbR7vRwNOZyAVb5KaHVkxrzdixYwkJCeGZZ5659P3+/fsTFRUFQFRUFAMGDDCqRGFlft53joejYmjs7cqS8V2pX8vX1rtRSmtdkf0rtHNNkpaVz0MLtrD3bAbv3NuWQR3k9vHWZv369dxyyy20adMGG5uSz25Tp04lIiKCYcOGcerUKYKDg1m6dCleXl7XbCs8PJyYmJjqKFuY1IpdZ3l6yU7aBHgQNboLHnXsjS7JTMp0W2AJqEp0Ia+Qh6Ni2BSbwmsDQnnwpkZGlyQMIgFVuy2MPsl/lu8lvJEXnz7UuVbebPA6yhRQMsRXiVwd7VgwujN3htTnP8v3MXvtESr4AUAIYUW01rz78yFeXLaXHi19iaqld8KtLBJQlczJ3pY5ozoyqEMA7/x8mKk/HKC4WEJKiJqusKiYKd/u4YO1RxkWHsjcBzrh7GBrdFlWTaK9Ctjb2jDj3na4O9kx78/jJGbmMX1oWxzt5JdViJooJ7+IJxZt59eDiUy8oxnP9GqBUmUaxRLXIAFVRWxsFK/0D8XX3Yn/++kQSZl5fPRAJ9yd5ESpEDVJalY+Y6O2svP0eV4fGMYDXRsaXVKNIUN8VUgpxeO3N2PGve3YcjyVYR9t4lx6rtFlCSEqyenUbIZ+tJF9ZzOYM7KThFMlk4CqBkM6BfLpQ505nZrNoP9ukKWRhKgB9p/NYPCcjSRn5vHluAj6hvkZXVKNIwFVTW5t4cOSR26isFgzZM5GomNl1QkhrNXGY8nc9/Em7GwU30zoRudG174uTpSPBFQ1Cgvw4LsJ3fB1c+SBTzbzzbY4o0sSQtygr7eeJvLTLfh7OvHdY91k0dcqJAFVzYK86vDdhJvp3MiLZ5fu4u3VB2UauhBWoKhYM/WHA0z+djddm9Rj6aPd8PdwNrqsGk0CygAedeyJGtOFEV2CmbPuGBO+3EZ2fqHRZQkhriIzt4Dxn8cw949YHurWiAUPdcbDWWbkVjUJKIPY29owdVAYL/VrzS/7E7hXZvgJYUqnU7MZOmcT6w4n8frAMF7pH4qdrbx1Vgf5KRtIKcXY7o2ZHxnOieQs+s9ez+6480aXJYSwiDmRysAPNxCfnkPU6C4yjbyaSUCZwB2t6vPtY92wt7Vh2MebWLU73uiShKj1vt0Wx/3zNuPubM//Hr+Z7s29jS6p1pGAMolWfu4sf+JmWvu78/ii7bz14wEKi4qNLkuIWqeoWDPtx4P8a+kuOjWsy/8e60ZTH1ejy6qVJKBMxNvVkcXjuzIyIpiPf48lcsEWUi7kGV2WELVGquW+bh/9foz7I4L5fGwXPOs4GF1WrSUBZTKOdra8OagN04e2ZeuJNO6ZJeelhKgOu06f555Z69l8PJVpg9swdVAb7GUyhKHkp29Sw8KD+PbRbiilGPrRJr7eetrokoSokbTWLN5yins/2gTAN4/exPAuwQZXJUACytTaBHrw/cTudGnkxeRvd/Pcd3vIKywyuiwhaozcgiL+bfm/FdHEi+8ndqdtoKfRZQkLud2GyXm5OBA1pgszfj7Ef9cdY398BnNGdqSBp1zBLkRFnE7N5tGF29h3NoN/3tGMJ+9sga2N3MPJTKQHZQVsbRST+7bio1EdOZqQSb9Z61l7MMHosoSwWr8dTKTfrPWcSs3mk8hwnundUsLJhCSgrEjfMH9WTOxOfXcnxnwWw2vf75chPyFuQF5hEa9+v4/Rn22lgaczKyd2p2dIfaPLElehtK7QQqWyyqkBcguKmPbjQT7beIKwAHdmjehIY28Xo8sSlwkPDycmJsboMsRljiZmMnHxTg7EZ/BQt0ZM+UcrnOxtjS6rtipTd1UCyor9vO8ck7/dTUFhMa8PDGNwx0CjSxIWElDmUTJL7zSvrdxHHQc7/m9oW+k1Ga9MASWTJKxY71A/2gR68ORXO3nm6138eSSZ1weG4eooL6sQAOez85ny7R5W7zvHLc29mXFvO3zdnYwuS5SR9KBqgKJizay1R/jg1yMEe9XhveEdaB/kaXRZtZr0oIy36VgKTy/ZSUpWHpP6tGRc9ybYyEQIsyjTCyGTJGoAWxvFU3e2YPHDXckvLGbwfzfwfz8dlAkUolYqKCrmnZ8Ocf/8aJwdbPluws2Mv7WphJMVkh5UDZORW8Dr3+9n6bY4Wvm5MWNYO0IbeBhdVq0jPShjHIjP4Nmlu9h3NoN7OwXySv9QXGTI24xkkkRt9uuBBKZ8t4e0rHz+2bM5E3o0lXXFqpEEVPUqKCrmv78dY/ZvR/Bwtuf1AWH8o42/0WWJq5OAqu3SsvJ5ecU+Vuw6S9tAD2bc247m9d2MLqtWkICqPvvOpjNp6W72x2fQv10DXukfipeLrEBuchJQosQPe+J5cdleLuQV8vSdLRh3S2PpTVUxCaiql19YzOzfjvLf347iWceBNwaG0TfMz+iyRNlIQIn/LykzjxeX7eGnfQm08nPjrcFt6BBc1+iyaiwJqKq1Jy6dSd/s4uC5TAZ1COA//VpTV3pN1kQCSvzdT/vO8fLyfSRk5vJA14Y826cl7k72RpdV40hAVY30nALe/fkQX0SfpJ6rI1MHtaFXa7no1gpJQInSZeYWMOPnw0RtOoGPqyOv9A/lH2F+KCXTcCuLBFTl0lqzfOdZ3lh1gNSsPB7o2pBnerfEw1k+XFkpCShxbbtOn+f5/+1h39kM7mjly6v9QwnyqmN0WTWCBFTlOZqYyUvL9rEpNoV2gR68MbANbQLl0gkrJwElrq+wqJjPNp5gxs+HKdKa8bc0YUKPpnLtSAVJQFVcTn4Rs9YeYd6fsTjb2zK5bytGdAmW22LUDBJQouzOns9h+uqDLNt5Fh83Ryb1acnQjoFy9X05SUCVn9aaVXvieeuHg5w5n8OQjoE8d1crvF0djS5NVB5Z6kiUXQNPZ94b3oHvHutGgKczk7/ZTf8P17M5NsXo0kxj9erVtGzZkmbNmjFt2jSjy6mRtp1MY8icjTyxaAduTnYsGd+VGcPaSTjVUtKDEn+jtWbFrrO8/eNBzqbnclcbP577R0itPj9VVFREixYt+OWXXwgMDKRz584sXryY1q1bl7q99KBuzOnUbKatPsiq3fElPfjeLRnSKVCG82ouud2GKB+lFAPaB9C7tR/z/oxlzrpjrNmfyJjujXns9qa1clr6li1baNasGU2aNAFg+PDhLF++/KoBJcomPaeA//52lAUbTmBjA//s2ZxHbm0i50AFUMEeVGhoqHZ2dq7EcoyRlJSEj4+P0WVUWFU9j4IiTUJGLmnZ+dgqhbebI96uDthU0bR0M74eaWlpZGRk0LBhQwBSUlLIysoiODj40jZJSUkkJycDkJeXR/v27Y0otVJV1WtRrDXJF/JJzsyjSGvq1nGgvrtjla1wYsbfqfKoKc9j27Zt+7TWYdfbrkIfU5ydnWvEMEZNGY6p6uex90w67605zJoDieg69oy7rSkP3tSQOg6V+2nXjK/H0qVL+emnn5g/fz4AX3zxBVu2bGHWrFmlbu/i4mK651Aelf1a5BYUsTD6JHPWHcMmK5/hrXx5plcLwgKqdtq4GX+nyqOmPA+lVG5ZtpN+tCizsAAP5kd2Ztfp88xcc5hpPx5k/p+xPHpbU0ZGNMTZwdboEqtMYGAgp0+fvvR1XFwcDRo0MLAi65JfWMySmNPMXnuEhIw8bm5Wj2d6taRTQ1luS1ydBJS4Ye2CPPlsdBe2nUxl5i9HeGPVAT7+I5bHejRlRJdgnOxrXlB17tyZI0eOcPz4cQICAvjqq69YtGiR0WWZXlZeIYu3nGL+n8c5l5FLeMO6vHdfB25qWs/o0oQVqFBAjR8/vrLqMJQ8j/Lp1NCLheMi2Bybwru/HObV7/fz4W9HGdW1IaO6Niz31GAzvh52dnbMnj2bPn36UFRUxJgxYwgNDb3q9t7e3tVYXdUp72uRciGPqI0niNp0kvScAro28WL60Lbc0tzbkCW1zPg7VR415XkAc8uykUwzF5VCa82m2BTm/RHLb4eScLCzYVD7AMbe0pgWtfAeVDXlXMGNikvLZv6fx/lq6ylyC4rpE1qfR29rKivniyvJShLCGEcTL/DphuN8tz2O3IJibmnuzdjujbmthU+tWZC2NgWU1prtp9L4fNNJVu6Ox0bBwPYBPHJbE5r51r4PJ6JMJKCEsdKy8lm05RRRG0+QmJlHM19XxnZvzKAOATXyPNXlakNAZeUVsnznWb6IPsmB+AzcHO0Y1jmIsd0b08DT+i8/EVWq6pc62rlzJ127dqV9+/aEh4ezZcuWijRnqFmzZtGyZUtCQ0OZPHmy0eVUyDvvvINS6tI1OUap6+LA47c3Y/2/72Dmfe1wtLPhue/20G3aWt5efZCjiRdK3W/SpEm0atWKtm3bMmjQIM6fP1+9hVfQ6tWr2bt3r1UviXT69Gluv/12QkJCCA0N5f3337/02NHETF5ZsY+uU3/l+f/tAeCtwW3Y/EJPXurX2pThVFRURIcOHejXr5/RpZTb+fPnGTp0KK1atSIkJIRNmzYZXVK5zJw5E6XUPqXUXqXUYqWU01U31lqX+0+vXr30Dz/8oLXWetWqVfq2227T1mjt2rW6Z8+eOjc3V2utdUJCgsEVld+pU6d07969dXBwsE5KSjK6nL8oLi7Wm44l63FRW3WT51bphv9eqQfMXq8/33RCn8/Kv7TdTz/9pAsKCrTWWk+ePFlPnjzZqJJvWGFhoW7SpIkOCwvTeXl5um3btnrfvn1Gl3XDzp49q7dt26a11jojI0M3CwnTH6yI1iPmbtIN/71SN3/+B/3k4u065kSKLi4uNrja65sxY4YeMWKEvvvuu40updwefPBBPW/ePK211nl5eTotLc3YgsohLi5ON2rUSAPOumT07mvgIX2VjKlQD0opRUZGBgDp6elWe13InDlzmDJlCo6OJbPOfH19Da6o/J5++mmmT59uynM9Sim6NqnHvAfD2fTcHbxwVwi5BUW8tGwvnd9cw2NfbmPtwQTu6HkndnYlE0y7du1KXFycwZWX3cUlkRwdHXFwcLi0JJK18ff3p0279vx6IIHnVx6lsN8bzNiQzKnUbCb1acnG5+7gveEd6NTQy5S/a5eLi4tj1apVjBs3zuhSyi0jI4M//viDsWPHAuDg4ICnp6exRZVTYWEhgLNSyg6oA5y92rYVmmb+3nvv0adPH5599lmKi4vZuHFjRZozzOHDh/nzzz954YUXcHJy4p133qFz585Gl3XDVqxYQUBAAO3atTO6lOvydXPi4VubMO6Wxuw7m8E32+JYsessP+w5h7erIwPbN2BIp0A+/fRT7rvvPqPLLbMzZ84QFBRESkrJKvCBgYFs3rzZ4KrKTlsmPCzbcZaVu8+Sll2Au6Mtxcc2EvXaE9waYn23YHnqqaeYPn06mZmZRpdSbrGxsfj4+DB69Gh27dpFp06deP/993FxcTG6tBsSEBDAs88+y1NPPXUKyAF+1lr/fLXtrxtQSqk1gF8pD70wceJEZs6cyZAhQ/j6668ZO3Ysa9asKX/1VejOO+/k3Llzf/v+m2++SWFhIWlpaURHR7N161aGDRtGbGysKT8ZXut5TJ06lZ9/vuprbSqlPQ+tbBn3zOuctvMkatMJ5q8/jmPz4Zz26si2k6l0CKpr+jdHXcqkIzP+Hl2uuFiz+0w6a/YnsHzXGU6n5uBoZ0Ov1vXp28qL/4wfxsznp9AjNMjoUm/YypUr8fX1pVOnTqxbt87ocsqtsLCQ7du3M2vWLCIiInjyySeZNm0ar7/+utGl3ZC0tLSLIwqNgfPAUqXUKK31wtK2v25Aaa3vvNpjHh4el06e3nvvvabuQl8rOOfMmcPgwYNRStGlSxdsbGxITk425aKMV3see/bs4fjx45d6T3FxcXTs2JEtW7bg51fa5wtjXe+DzH8/+ZyPVm2mTd+RfLL+OB//EYu3qyN3hvjSO7Q+3Zp6m3ImoLUsiZSRW8Cfh5NZezCR3w8nknwhHxsFNzfz5qmeLegT5oejjaZfv36Mun84gwcPNrrkctmwYQMrVqzghx9+IDc3l4yMDEaNGsXChaW+H5pWYGAggYGBREREADB06FCrnICzZs0aGjduzNq1a5MAlFLfAd2A8gXUtTRo0IDff/+dHj16sHbtWpo3b16R5gwzcOBA1q5dS48ePTh8+DD5+flWtxJAmzZtSExMvPR1o0aNiImJsbrnASWz4GbPmMbvv/+Oj48P6TkFrDuUyC/7E1i5O56vtp6mjoMt3Zp6c1PTenRrWo+W9d1M0bu6uCSSi4sL+fn5plkSSWvNsaQLrD2YyNqDicScSKOwWOPhbM9tLXy4o5Uvt7Xwoa6Lw6XtIyMjCQkJ4ZlnnjG4+vJ76623eOuttwBYt24d77zzjtWFE4Cfnx9BQUEcOnSIli1b8uuvv1rlrV6Cg4OJjo5GKVWHkiG+nsBVr8eoUEDNmzePJ598ksLCQpycnJg7t0yrV5jOmDFjGDNmDGFhYTg4OBAVFWX6YZma7IknniAvL49evXoBJRMlPvroIwa0DyCvsIhNx1L4ZX8C648ms+ZAAgBeLg50beLFTU3qcVNTb5r6uBjyGl5cEmnw4MGEhIRcd0mkqqK15mRKNpuPp7D5eCqbY1M5cz4HgFZ+bjx8axPuaOVLhyBP7Eq5xcWGDRv44osvaNOmzaXbhkydOpW77rqrOp+GuMysWbMYOXIk+fn5NGnShAULFhhd0g2LiIhg6NChvPbaa9uBQmAH11j2SC7UFVbtzPkcNh1LYeOxZKKPpXA2vWQVf183Rzo39qJDkCftgzwJbeBRrautV/eFupm5Bew5k87uuHR2x51n28k0EjLyAKjn4kCXxl7c3Myb21v5EmDC65RErSMrSYja5WKvYVNsCpuOpbDtZNqlXoOtjaKZjyutG7jT2t+dEH93mvm6Ut/dsUp6WlUVUFpr4tNzOZSQyeFzmRw6l8nuM+kcS7rAxf/KQV7OtA+qS0RjLyIae9HM11VGBITZSEAJkZiZy+7T6eyKO8/+sxnsj88gPv3/3yvN1dGOpj4uNPVxpWE9FxrWq0NAXWcCPJ3xdXMsdfirLCoSUIVFxSRm5nHmfA6nU7M5nZrDiZQsYpOziE28QGZe4aVt67s7EtbAg7aBnrQLKvnby3IeSQgTk4ASojSpWfkcPJfBscQLHEvK4mjiBY4lXfhLcAHYKPBxc8TXzQlvVwe8XBzxcrHHw7nkj6uTHXUc7HC2t8XRzgYHOxvsbGywsYH7/tGDJT+uo7gYCoqLKSgsJq+wmOz8IrLzC7mQV0hmbiHns/NJyy4g5UIeyRfySczMJSkzj+Ir/mc18HCisY8LTbxdaennRks/N1r4uuFRx74af3JCVBoJKCFuRG5BEXFp2cSl5XDmfA7n0nM5l55L0oU8kjLzSMvKJzU7n9yC4uu2FR/1FP6R7113Oyd7G+rWcaCeqwM+ro54uzri5+GEn4cTgXXrEGjpzZlxSr0QFSABJURVyC0oIjO3pBeUlVdIbkEReYXF5BcWU1BUTLGGf97Xhw+W/IStjcLOVuFga4OjnQ1O9ra4ONrh5mSHq6OdBI+orcoUUHLLdyFukJO9LU72tvi4Xf2Owe7O9vQNM98F0kJYkwotFiuEEEJUFQkoISrR1q1badu2LVprsrKyCA0NZe/evUaXJYRVkoASohJ17tyZ/v37c+bMGSZPnsyoUaMICwszuiwhrJJMkhCikuXn5+Pp6UmbNm3YuHEjtrYyEUKIK1T9Ld+FEH+XmppKUVERmZmZ5ObmXn8HIUSpJKCEqGTjx48nICCAkSNH8u9//9vocoSwWhJQQlSizz//HDs7O7y8vJgyZQpbt25l7dq1RpclhFWSc1BCVIHqXs1cCCsj56CEEEJYr4r2oIQQpVBKrdZa9zW6DiGsmQSUEEIIU5IhPiGEEKYkASWEEMKUJKCEEEKYkgSUEEIIU5KAEkIIYUr/D37y0ltgbvAoAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "p.show()" ] }, { "cell_type": "code", "execution_count": 8, "id": "4bcf3c60", "metadata": {}, "outputs": [], "source": [ "g = sqrt(x)/(1-x**2)" ] }, { "cell_type": "code", "execution_count": 9, "id": "e2b39674", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\frac{\\sqrt{x}}{1 - x^{2}}$" ], "text/plain": [ " √x \n", "──────\n", " 2\n", "1 - x " ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g" ] }, { "cell_type": "code", "execution_count": null, "id": "5733248c", "metadata": {}, "outputs": [], "source": [ "#Limits" ] }, { "cell_type": "code", "execution_count": 10, "id": "59d87e56", "metadata": {}, "outputs": [], "source": [ "k = (x**2 - 25)/(x**2 + 2 * x - 15)\n" ] }, { "cell_type": "code", "execution_count": 11, "id": "332f8c7c", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\frac{x^{2} - 25}{x^{2} + 2 x - 15}$" ], "text/plain": [ " 2 \n", " x - 25 \n", "─────────────\n", " 2 \n", "x + 2⋅x - 15" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "k" ] }, { "cell_type": "code", "execution_count": 12, "id": "fc729762", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\frac{5}{4}$" ], "text/plain": [ "5/4" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "limit(k,x,-5)" ] }, { "cell_type": "code", "execution_count": null, "id": "1af7ee22", "metadata": {}, "outputs": [], "source": [ "#Differition " ] }, { "cell_type": "code", "execution_count": 13, "id": "db17ea9a", "metadata": {}, "outputs": [], "source": [ "M= 4*x**3 + sin(x) - 19" ] }, { "cell_type": "code", "execution_count": 14, "id": "930a63ba", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle 12 x^{2} + \\cos{\\left(x \\right)}$" ], "text/plain": [ " 2 \n", "12⋅x + cos(x)" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "diff(M)" ] }, { "cell_type": "code", "execution_count": null, "id": "09b7831f", "metadata": {}, "outputs": [], "source": [ "#Integration" ] }, { "cell_type": "code", "execution_count": 15, "id": "f3086272", "metadata": {}, "outputs": [], "source": [ "N= 12 * x**2 + cos(x)" ] }, { "cell_type": "code", "execution_count": 16, "id": "520b74a0", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle 4 x^{3} + \\sin{\\left(x \\right)}$" ], "text/plain": [ " 3 \n", "4⋅x + sin(x)" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "integrate(N)" ] }, { "cell_type": "code", "execution_count": null, "id": "0b293467", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "64fd00a2", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.12" } }, "nbformat": 4, "nbformat_minor": 5 }