{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Ordinary differential equations\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction \n", "\n", "Engineering systems are often represented as differential equations. ``sympy`` has robust support for the following types of ordinary differential equations (ODEs):\n", "\n", "- 1st order separable differential equations\n", "- 1st order differential equations whose coefficients or dx and dy are functions homogeneous of the same order.\n", "- 1st order exact differential equations.\n", "- 1st order linear differential equations\n", "- 1st order Bernoulli differential equations.\n", "- 2nd order Liouville differential equations.\n", "- nth order linear homogeneous differential equation with constant coefficients.\n", "- nth order linear inhomogeneous differential equation with constant coefficients using the method of undetermined coefficients.\n", "- nth order linear inhomogeneous differential equation with constant coefficients using the method of variation of parameters.\n", "\n", "In addition to ODE support, sympy can even solve separable (either multiplicative or additive) partial differential equations (PDEs).\n", "\n", "The main functionality for ODE solving in sympy is the ``sympy.dsolve`` function. The call signature for this function is ``sympy.dsolve(eq, goal, **kwargs)``, where ``eq`` is the differential equation, ``goal`` is the function you want to end up with, and ``**kwargs`` is a placeholder for other arguments that could be passed to the function to help it out a bit. For more detail on what ``**kwargs`` could be, see the documentation." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sympy import *" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "IPython console for SymPy 1.0 (Python 2.7.13-64-bit) (ground types: python)\n", "\n", "These commands were executed:\n", ">>> from __future__ import division\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 http://docs.sympy.org/1.0/\n" ] } ], "source": [ "init_session()\n", "plt.style.use(u\"seaborn-notebook\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To solve differential equations, use dsolve. First, create an undefined function by passing cls=Function to the symbols function." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "f, g = symbols('f g', cls=Function)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Derivatives of f(x) are unevaluated." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAADcAAAAhCAYAAAB9VDPAAAAABHNCSVQICAgIfAhkiAAAA1RJREFU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\n7AAAAABJRU5ErkJggg==\n", "text/latex": [ "$$\\frac{d}{d x} f{\\left (x \\right )}$$" ], "text/plain": [ "d \n", "──(f(x))\n", "dx " ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(x).diff(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To represent the differential equation $f′′(x)−2f′(x)+f(x)=sin(x)$, we would use" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "ode = Eq(f(x).diff(x, x) - 2*f(x).diff(x) + f(x), sin(x))" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAASUAAAAmCAYAAACChI1tAAAABHNCSVQICAgIfAhkiAAAB2RJREFU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\nURRFSYX/ASik7MwIt41UAAAAAElFTkSuQmCC\n", "text/latex": [ "$$f{\\left (x \\right )} - 2 \\frac{d}{d x} f{\\left (x \\right )} + \\frac{d^{2}}{d x^{2}} f{\\left (x \\right )} = \\sin{\\left (x \\right )}$$" ], "text/plain": [ " 2 \n", " d d \n", "f(x) - 2⋅──(f(x)) + ───(f(x)) = sin(x)\n", " dx 2 \n", " dx " ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ode" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To solve the ODE, pass it and the function to solve for to ``dsolve``." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAR4AAAAYCAYAAAAs55J/AAAABHNCSVQICAgIfAhkiAAACHZJREFU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\nmZCI9AAAAABJRU5ErkJggg==\n", "text/latex": [ "$$f{\\left (x \\right )} = \\left(C_{1} + C_{2} x\\right) e^{x} + \\frac{1}{2} \\cos{\\left (x \\right )}$$" ], "text/plain": [ " x cos(x)\n", "f(x) = (C₁ + C₂⋅x)⋅ℯ + ──────\n", " 2 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sol = dsolve(ode, f(x))\n", "display(sol)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "``dsolve`` returns an instance of ``Eq``. This is because in general, solutions to differential equations cannot be solved explicitly for the function." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAL8AAAAXCAYAAABapZ6FAAAABHNCSVQICAgIfAhkiAAABglJREFU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\n/wLp8VPqcD3guwAAAABJRU5ErkJggg==\n", "text/latex": [ "$$f{\\left (x \\right )} + \\cos{\\left (f{\\left (x \\right )} \\right )} = C_{1}$$" ], "text/plain": [ "f(x) + cos(f(x)) = C₁" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dsolve(f(x).diff(x)*(1 - sin(f(x))), f(x))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The arbitrary constants in the solutions from ``dsolve`` are symbols of the form $C_1, C_2, C_3$, and so on." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Applying Boundary conditions\n", "\n", "This isn't implemented yet in ``dsolve`` stable version, but it will be available in the next release (probably!).\n", "\n", "For now, solve for contants on your own. For example, if\n", "\n", "$$f(0)=1\\quad \\left.\\frac{d f}{d x}\\right\\vert_{x=0}=0,$$\n", "\n", "solve the following equations:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAALAAAAAfCAYAAABH/UdlAAAABHNCSVQICAgIfAhkiAAABGFJREFU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\n", "text/latex": [ "$$\\left \\{ C_{1} : \\frac{1}{2}, \\quad C_{2} : - \\frac{1}{2}\\right \\}$$" ], "text/plain": [ "{C₁: 1/2, C₂: -1/2}" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "constants = solve([sol.rhs.subs(x,0) - 1, sol.rhs.diff(x,1).subs(x,0)- 0])\n", "constants" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAASEAAAAfCAYAAACoGntyAAAABHNCSVQICAgIfAhkiAAACRxJREFU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\nAAAASUVORK5CYII=\n", "text/latex": [ "$$f{\\left (x \\right )} = \\left(- \\frac{x}{2} + \\frac{1}{2}\\right) e^{x} + \\frac{1}{2} \\cos{\\left (x \\right )}$$" ], "text/plain": [ " ⎛ x 1⎞ x cos(x)\n", "f(x) = ⎜- ─ + ─⎟⋅ℯ + ──────\n", " ⎝ 2 2⎠ 2 " ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "C1, C2 = symbols('C1,C2')\n", "sol = sol.subs(constants)\n", "sol" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Systems of equations" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": true }, "outputs": [], "source": [ "g1, g2 = symbols('g1 g2', cls=Function)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": true }, "outputs": [], "source": [ "eq1 = g1(x).diff(x) - 2*g1(x) - g2(x)\n", "eq2 = g2(x).diff(x) - 3*g1(x) - 4*g2(x)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAd0AAAAaCAYAAADyp4bWAAAABHNCSVQICAgIfAhkiAAAChJJREFU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\nHo/H4/F4HOH/h+PAJg/hYWwAAAAASUVORK5CYII=\n", "text/latex": [ "$$\\left [ \\operatorname{g_{1}}{\\left (x \\right )} = C_{1} e^{x} + C_{2} e^{5 x}, \\quad \\operatorname{g_{2}}{\\left (x \\right )} = - C_{1} e^{x} + 3 C_{2} e^{5 x}\\right ]$$" ], "text/plain": [ "⎡ x 5⋅x x 5⋅x⎤\n", "⎣g₁(x) = C₁⋅ℯ + C₂⋅ℯ , g₂(x) = - C₁⋅ℯ + 3⋅C₂⋅ℯ ⎦" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dsolve((eq1, eq2), fun=(g1(x), g2(x)))" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## Vector field" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The '''Lotka–Volterra equations''', also known as the '''predator–prey equations''', are a pair of first-order, nonlinear, differential equations frequently used to describe the dynamics of biological systems in which two species interact, one as a predator and the other as prey. The populations change through time according to the pair of equations:\n", "\n", "\\begin{align}\n", "\\frac{dx}{dt} & = \\alpha x - \\beta x y \\\\[6pt]\n", "\\frac{dy}{dt} & = \\delta x y - \\gamma y\n", "\\end{align}\n", "\n", "where\n", "\n", "* $x$ is the number of prey (for example, rabbits);\n", "* $y$ is the number of some predator (for example, foxes);\n", "* $\\tfrac{dy}{dt}$ and $\\tfrac{dx}{dt}$ represent the growth rates of the two populations over time;\n", "* $t$ represents time; and\n", "* $α, β, γ, δ$ are positive real parameters describing the interaction of the two species." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": true }, "outputs": [], "source": [ "y, x = np.mgrid[0:2.5:100j, 0:4:100j]" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": true }, "outputs": [], "source": [ "alpha = 2/3\n", "beta = 4/3\n", "gamma = 1\n", "delta = 1\n", "dxdt = alpha*x - beta*x*y\n", "dydt = delta*x*y - gamma*y\n", "speed = np.sqrt(dxdt**2 + dydt**2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the first case we just plot the velocity field." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$$\\left ( 0, \\quad 2.5\\right )$$" ], "text/plain": [ "(0, 2.5)" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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EdqWGnJpOsmraya7uILe2k+o2JcJZl0aIp1OvA+DLyGjfazog6T+NDqWWdadq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\n08KZkxbOnLQwjxWDUt37xzH6B8qbWfTceoL89Gx5+MwTxs1mdTj5cm8Fb20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onCSoRl9F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\nioqKispJwv8D/IYRQq80n+YAAAAASUVORK5CYII=\n", "text/plain": [ "<matplotlib.figure.Figure at 0x7fe941a94d90>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig0 = plt.figure(figsize=(8,5))\n", "strm = plt.streamplot(x, y, dxdt, dydt, linewidth=2)\n", "plt.xlabel(\"Preys\")\n", "plt.ylabel(\"Predators\")\n", "plt.xlim(0,4)\n", "plt.ylim(0,2.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this example we change the color of the line according to the magnitude of the\n", "_speed_ at each point." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFsAAAAVCAYAAAApZJKFAAAABHNCSVQICAgIfAhkiAAAA3BJREFU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\nh5QDKbuYKegXR1lvZ2nMYhbThX8BMnnYeGZ/tRoAAAAASUVORK5CYII=\n", "text/latex": [ "$$\\left ( 0, \\quad 2.5\\right )$$" ], "text/plain": [ "(0, 2.5)" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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RdYBG+9/LfjKjUpmYPZIJvUaQFNH9mw8hBMcbj/PFuVVUW6oBiDPGMbtgFmMyx6AJIfFJ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\nr1za7EPIhDEesPfRVYIigzHW1iM5J5M2z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31j1nUYySjPTqhLJOx8cIFehxfzKjWu1HFv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af+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"text/plain": [ "<matplotlib.figure.Figure at 0x7fe9407338d0>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig1 = plt.figure(figsize=(8,5))\n", "strm = plt.streamplot(x, y, dxdt, dydt, color=speed, linewidth=2, cmap=\"summer\")\n", "plt.colorbar(strm.lines)\n", "plt.xlabel(\"Preys\")\n", "plt.ylabel(\"Predators\")\n", "plt.xlim(0,4)\n", "plt.ylim(0,2.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this case the densities in $x$ and $y$ directions are different." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$$\\left ( 0, \\quad 2.5\\right )$$" ], "text/plain": [ "(0, 2.5)" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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soWS/boOZV374Mct/TnY4S+ZkXHLGPu/vqkIug9+Ni+dEfRf3f51PSYuaSD93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\nAAAAAElFTkSuQmCC\n", "text/plain": [ "<matplotlib.figure.Figure at 0x7fe9404b8d10>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig2 = plt.figure(figsize=(8,5))\n", "plt.streamplot(x, y, dxdt, dydt, density=[0.5, 1])\n", "plt.xlabel(\"Preys\")\n", "plt.ylabel(\"Predators\")\n", "plt.xlim(0,4)\n", "plt.ylim(0,2.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this last case we vary the width of the lines according to the magnitude\n", "of the _speed_ at each point." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$$\\left ( 0, \\quad 2.5\\right )$$" ], "text/plain": [ "(0, 2.5)" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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GpbsWFWU35u7du+jevbvUwN2/f/8KsXtx9epVNG3aVEp/MzMzBAcHc2JxURal4XeyHPF0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\n+owxxliE4KDPGGOMRQgO+owxxliE+P+ukH2hExRsBAAAAABJRU5ErkJggg==\n", "text/plain": [ "<matplotlib.figure.Figure at 0x7fe940f01ed0>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig3 = plt.figure(figsize=(8,5))\n", "lw = 5*speed / speed.max()\n", "plt.streamplot(x, y, dxdt, dydt, density=0.6, color='k', linewidth=lw)\n", "plt.xlabel(\"Preys\")\n", "plt.ylabel(\"Predators\")\n", "plt.xlim(0,4)\n", "plt.ylim(0,2.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Power series approximation" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def picard_iteration(f, t, y0, n):\n", " y = y0\n", " for cont in range(n):\n", " y = y0 + f(t, y, n).integrate((t, 0, t))\n", "\n", " return y" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def fun(t, y, n):\n", " return Matrix([y[1], t*y[0]])" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "x0, x1 = symbols(\"x0 x1\")\n", "y = Matrix([airyai(0), airyaiprime(0)])\n", "y_approx = picard_iteration(fun, t, y, 10)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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xf/9+MMZw+fJltG/fnqY3iEqiOWg5qK6uxqlTp2BgYNDo08FUjUQiwbZt2/DB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\nffWVwscjhJDm4rru55w5c6C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"text/plain": [ "<matplotlib.figure.Figure at 0x7fe941ab1750>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "<matplotlib.figure.Figure at 0x7fe940ec7510>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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KCeWhH8/R5d4PmbTwDb7ZuLtNP1hMzS9n5tu7ScgsYdbgjoyL0n7kldVa0ADh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\nVVU5U+GKuaqcOTHWGV4nhBA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"text/plain": [ "<matplotlib.figure.Figure at 0x7fe94156c510>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "p0 = plot(airyai(t), (t, -4, 4), line_color=\"black\");\n", "p1 = plot(N(y_approx[0]), (t, -4, 4));\n", "p0.extend(p1);\n", "p0.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", "1. SymPy Development Team (2016). [Sympy Tutorial: Matrices](http://docs.sympy.org/latest/tutorial/matrices.html)\n", "2. Ivan Savov (2016). [Taming math and physics using SymPy](https://minireference.com/static/tutorials/sympy_tutorial.pdf)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following cell change the style of the notebook." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "<link href='http://fonts.googleapis.com/css?family=Fenix' rel='stylesheet' type='text/css'>\n", "<link href='http://fonts.googleapis.com/css?family=Alegreya+Sans:100,300,400,500,700,800,900,100italic,300italic,400italic,500italic,700italic,800italic,900italic' rel='stylesheet' type='text/css'>\n", "<link href='http://fonts.googleapis.com/css?family=Source+Code+Pro:300,400' rel='stylesheet' type='text/css'>\n", "<style>\n", "/* Based on Lorena Barba template available at: https://github.com/barbagroup/AeroPython/blob/master/styles/custom.css*/\n", "@font-face {\n", "font-family: \"Computer Modern\";\n", "src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunss.otf');\n", "}\n", "div.cell{\n", "width:800px;\n", "margin-left:16% !important;\n", "margin-right:auto;\n", "}\n", "h1 {\n", "font-family: 'Alegreya Sans', sans-serif;\n", "}\n", "h2 {\n", "font-family: 'Fenix', serif;\n", "}\n", "h3{\n", "font-family: 'Fenix', serif;\n", "margin-top:12px;\n", "margin-bottom: 3px;\n", "}\n", "h4{\n", "font-family: 'Fenix', serif;\n", "}\n", "h5 {\n", "font-family: 'Alegreya Sans', sans-serif;\n", "}\t\n", "div.text_cell_render{\n", "font-family: 'Alegreya Sans',Computer Modern, \"Helvetica Neue\", Arial, Helvetica, Geneva, sans-serif;\n", "line-height: 135%;\n", "font-size: 120%;\n", "width:600px;\n", "margin-left:auto;\n", "margin-right:auto;\n", "}\n", ".CodeMirror{\n", "font-family: \"Source Code Pro\";\n", "font-size: 90%;\n", "}\n", "/* .prompt{\n", "display: None;\n", "}*/\n", ".text_cell_render h1 {\n", "font-weight: 200;\n", "font-size: 50pt;\n", "line-height: 100%;\n", "color:#CD2305;\n", "margin-bottom: 0.5em;\n", "margin-top: 0.5em;\n", "display: block;\n", "}\t\n", ".text_cell_render h5 {\n", "font-weight: 300;\n", "font-size: 16pt;\n", "color: #CD2305;\n", "font-style: italic;\n", "margin-bottom: .5em;\n", "margin-top: 0.5em;\n", "display: block;\n", "}\n", ".warning{\n", "color: rgb( 240, 20, 20 )\n", "}\n", "</style>\n", "<script>\n", "MathJax.Hub.Config({\n", "TeX: {\n", "extensions: [\"AMSmath.js\"]\n", "},\n", "tex2jax: {\n", "inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n", "displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n", "},\n", "displayAlign: 'center', // Change this to 'center' to center equations.\n", "\"HTML-CSS\": {\n", "styles: {'.MathJax_Display': {\"margin\": 4}}\n", "}\n", "});\n", "</script>\n", "\n", "\n" ], "text/plain": [ "<IPython.core.display.HTML object>" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.core.display import HTML\n", "def css_styling():\n", " styles = open('./styles/custom_barba.css', 'r').read()\n", " return HTML(styles)\n", "css_styling()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3 (Spyder)", "language": "python3", "name": "julia-0.6" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.8" } }, "nbformat": 4, "nbformat_minor": 1 }