{ "cells": [ { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "# Numerical calculations for \"Cosmology ...\"\n", "\n", "This SageMath notebook performs numerical calculations \n", "for the note *Calculations for \"Cosmology ...\"* \n", "which supplements \n", "the paper *Cosmology from the two-dimensional renormalization group acting as the Ricci flow*.\n", "\n", "This notebook contains the calculations related to the fixed point equation of the Ricci flow.\n", "\n", "Notation and section numbering are as in the note *Calculations ...*.\n", "\n", "The unit of time is the Hubble time $t_H=H_0^{-1}$ estimated to be $t_H =4.55\\times 10^{17}\\mathrm{s}=1.44 \\times 10^{10}\\mathrm{y}$.\n", "\n", "The present deceleration parameter is estimated to be $q_0 = -0.60$." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "t_{H}= 4.55e17 's' = 1.44e10 'y'" ] }, "execution_count": 1, "metadata": { }, "output_type": "execute_result" }, { "data": { "text/html": [ "" ], "text/plain": [ "q_0= -0.60" ] }, "execution_count": 1, "metadata": { }, "output_type": "execute_result" } ], "source": [ "%display latex\n", "LE = lambda latex_string: LatexExpr(latex_string)\n", "#\n", "t_H_in_secs = 4.55e17\n", "t_H_in_years = 1.44e10\n", "q_0 = -0.6\n", "pretty_print(LE(\"t_{H}=\"),t_H_in_secs.n(digits=3),\"s\",\n", " LE(\"=\"),t_H_in_years.n(digits=3),\"y\")\n", "pretty_print(LE(\"q_0=\"),q_0.n(digits=2))" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "## 7 The cosmological parameters" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "### 7.1 Formulas for $H$, $q$, $w$, and $\\Omega$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "T = var('T')\n", "#\n", "incomplete_beta(p,q,x)=(x^p/p)*hypergeometric([p,1-q],[p+1],x)\n", "beta(p,q)=incomplete_beta(p,q,1)\n", "#\n", "sqrt3 = sqrt(3)\n", "nu = sqrt3/2 -1/2\n", "#\n", "f_T(T) = ((cos(T))^2+nu)/(sin(T)*cos(T))\n", "v_T(T) = (-sqrt3/2)/(sin(T)*cos(T))\n", "a_dimless(T) = (sin(T))^(1+nu)*(cos(T))^(-nu)\n", "t_dimless(T) = (1/2)*incomplete_beta(1+nu/2,1/2-nu/2,(sin(T))^2)\n", "#\n", "H_dimless(T) = f_T(T)/a_dimless(T)\n", "q(T) = (sqrt3*(cos(T))^2-nu)/((cos(T))^2+nu)^2\n", "w(T) = 1+(4/3)*(f_T(T)*v_T(T))/(f_T(T)^2+1)\n", "Omega(T) = 1 + 1/f_T(T)^2\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "consistency check of the formula for q(T)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 3, "metadata": { }, "output_type": "execute_result" } ], "source": [ "qder(T) = -f_T^(-2)*f_T.derivative(T)\n", "plot(q-qder,(T,0,pi/2))" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "### 7.2 Estimate $t_0$, $t_0'$, and $z$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "\\nu= 0.366025 \\qquad\\sqrt{3}= 1.73205 \\qquad1/\\sqrt{3}= 0.577350" ] }, "execution_count": 4, "metadata": { }, "output_type": "execute_result" }, { "data": { "text/html": [ "" ], "text/plain": [ "T_0= 1.2 = 0.77 \\,\\frac{\\pi}{2} \\qquad t_0'= 1.1 \\,t_H \\qquad t_0= 0.73 \\,t_H" ] }, "execution_count": 4, "metadata": { }, "output_type": "execute_result" }, { "data": { "text/html": [ "" ], "text/plain": [ "a_0= 1.5 \\,t_H \\qquad w_0= -0.61 \\qquad \\Omega_0= 1.5" ] }, "execution_count": 4, "metadata": { }, "output_type": "execute_result" }, { "data": { "text/html": [ "" ], "text/plain": [ "t_{\\max}= 1.6 \\,t_H" ] }, "execution_count": 4, "metadata": { }, "output_type": "execute_result" }, { "data": { "text/html": [ "" ], "text/plain": [ "'at ' \\;\\;q=0: \\quad z= 0.18 \\qquad T= 1.09314 = 0.695913 \\frac{\\pi}{2}" ] }, "execution_count": 4, "metadata": { }, "output_type": "execute_result" }, { "data": { "text/html": [ "" ], "text/plain": [ "'at ' \\;\\;T=\\frac12 T_0:\\quad z= 1.7" ] }, "execution_count": 4, "metadata": { }, "output_type": "execute_result" } ], "source": [ "Tx = var('Tx')\n", "T_0 = N(find_root(q(Tx)==q_0,0,pi/2))\n", "tprime_0 = H_dimless(T_0) # in units of t_H\n", "#\n", "a(T) = tprime_0*a_dimless(T)\n", "H(T) = H_dimless(T)/tprime_0\n", "t(T) = tprime_0*t_dimless(T)\n", "#\n", "z(T) = a(T_0)/a(T) - 1\n", "#\n", "t_0 = t(T_0)\n", "t_max = t(pi/2)\n", "a_0 = a(T_0)\n", "#\n", "w_0 =w(T_0)\n", "Omega_0 =Omega(T_0)\n", "#\n", "T_qeq0 = pi/2-atan(sqrt(2))/2\n", "z_qeq0 = z(T_qeq0)\n", "z_half_T_0 = z(T_0/2)\n", "#\n", "sig = lambda x: x.n(digits=2)\n", "exact = lambda x: x.n(digits=6)\n", "#\n", "pretty_print(LE(r\"\\nu=\"),exact(nu),LE(r\"\\qquad\\sqrt{3}=\"),exact(sqrt3),\n", " LE(r\"\\qquad1/\\sqrt{3}=\"),exact(1/sqrt3))\n", "#\n", "pretty_print(LE(r\"T_0=\"),sig(T_0),LE(\"=\"),sig(T_0/(pi/2)),LE(r\"\\,\\frac{\\pi}{2}\"),\n", " LE(r\"\\qquad t_0'=\"),sig(tprime_0),LE(r\"\\,t_H\"),\n", " LE(r\"\\qquad t_0=\"),sig(t_0),LE(r\"\\,t_H\"))\n", "pretty_print(LE(r\"a_0=\"),sig(a_0),LE(r\"\\,t_H\"),\n", " LE(r\"\\qquad w_0=\"),sig(w_0),\n", " LE(r\"\\qquad \\Omega_0=\"),sig(Omega_0))\n", "pretty_print(LE(r\"t_{\\max}=\"),sig(t_max),LE(r\"\\,t_H\"))\n", "#\n", "pretty_print(r\"at \", LE(r\"\\;\\;q=0:\"),\n", " LE(\"\\quad z=\"),sig(z_qeq0),\n", " LE(\"\\qquad T=\"),exact(T_qeq0),LE(\"=\"), exact(T_qeq0/(pi/2)), LE(r\"\\frac{\\pi}{2}\"))\n", "pretty_print(\"at \", LE(r\"\\;\\;T=\\frac12 T_0:\\quad z=\"),sig(z_half_T_0))" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "### 7.3 The limit $T\\rightarrow 0$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "\\frac{t'_0}{2+\\nu}= 0.47 \\qquad t'_0\\left(\\frac{2+\\nu}{t'_0}\\right)^{1/\\sqrt{3}}= 1.7 \\qquad\\frac{a_0}{t'_0}\\left(\\frac{2+\\nu}{t'_0}\\right)^{-1/\\sqrt{3}}= 0.86 \\qquad\\left(\\frac{a_0}{t'_0}\\right)^{\\sqrt{3}}\\left(\\frac{2+\\nu}{t'_0}\\right)^{-1}= 0.77 \\qquad\\left(\\frac{a_0}{t'_0}\\right)^{-\\sqrt{3}}\\left(\\frac{1+\\nu}{t'_0}\\right)= 0.75" ] }, "execution_count": 5, "metadata": { }, "output_type": "execute_result" } ], "source": [ "coefftT = (tprime_0/(2+nu))\n", "coeffat = tprime_0 * coefftT^(-1/sqrt3)\n", "coeffzt = a_0/coeffat\n", "coefftz = coeffzt^(sqrt3)\n", "coeffHz = ((1+nu)/(2+nu))/coefftz\n", "#\n", "pretty_print(LE(r\"\\frac{t'_0}{2+\\nu}=\"),sig(coefftT),\n", " LE(r\"\\qquad t'_0\\left(\\frac{2+\\nu}{t'_0}\\right)^{1/\\sqrt{3}}=\"),sig(coeffat),\n", " LE(r\"\\qquad\\frac{a_0}{t'_0}\\left(\\frac{2+\\nu}{t'_0}\\right)^{-1/\\sqrt{3}}=\"),sig(coeffzt),\n", " LE(r\"\\qquad\\left(\\frac{a_0}{t'_0}\\right)^{\\sqrt{3}}\\left(\\frac{2+\\nu}{t'_0}\\right)^{-1}=\"),sig(coefftz),\n", " LE(r\"\\qquad\\left(\\frac{a_0}{t'_0}\\right)^{-\\sqrt{3}}\\left(\\frac{1+\\nu}{t'_0}\\right)=\"),sig(coeffHz),)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "Calculate and plot the cosmological parameters $H/H_1$, $q$, $w$, $\\Omega$ as functions of $z = a(t_0)/a(t) -1$." ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "### 7.5 Table of parameters for selected z values" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1000, 100, 10, 1.68628376855095, 1, 0.176297241220437, 0]\n" ] } ], "source": [ "#\n", "Tx = var('Tx')\n", "zlist = [1000,100,10,N(z_half_T_0),1,N(z_qeq0),0]\n", "print zlist\n", "z_params={}\n", "for z_val in zlist:\n", " T_val=RR(find_root(z(Tx)==z_val,0,pi/2))\n", " z_params[z_val] = {\"z\": latex(sig(z_val))}\n", " z_params[z_val][\"T\"]= sig(T_val)\n", " z_params[z_val][\"T_normalized\"]= sig(T_val/(pi/2))\n", " z_params[z_val][\"H_normalized\"]=sig(H(T_val)/H(T_0))\n", " z_params[z_val][\"q\"]=sig(sig(q(T_val)))\n", " z_params[z_val][\"w\"]=sig(w(T_val))\n", " z_params[z_val][\"Omega\"]=sig(Omega(T_val))\n", " t_val = sig(t(T_val))\n", " z_params[z_val][\"t_in_t_H\"]= sig(t_val)\n", " z_params[z_val][\"t_in_secs\"]=sig(t_val*t_H_in_secs)\n", " z_params[z_val][\"t_in_years\"]=sig(t_val*t_H_in_years)\n", " z_params[z_val][\"label\"]=\"\"\n", "z_params[N(z_half_T_0)][\"label\"]=r\"$T=\\frac12 T_0$\"\n", "z_params[N(z_qeq0)][\"label\"]=r\"$q=0$\"\n", "z_params[0][\"label\"]=r\"$t=t_0$\"" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, 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" ], "text/plain": [ " $z$ $H/H_0$ $q$ $w$ $\\Omega$\n", " $z\\gg 1$ $\\gg 1$ 0.75 $z^{1.7}$ 0.73 0.16 1.0\n", " 1000. 120000. 0.73 0.16 1.0\n", " 100. 2200. 0.73 0.15 1.0\n", " 10. 48. 0.74 0.15 1.0\n", " $T=\\frac12 T_0$ 1.7 4.1 0.74 0.079 1.2\n", " 1.0 2.4 0.69 0.021 1.3\n", " $q=0$ 0.18 1.1 0.00 -0.33 1.5\n", " $t=t_0$ 0.00 1.0 -0.60 -0.61 1.5" ] }, "execution_count": 7, "metadata": { }, "output_type": "execute_result" } ], "source": [ "param_names = [\"label\", \"z\", \"H_normalized\", \"q\", \"w\", \"Omega\"]\n", "param_table=[[r\"\",r\"$z$\",r\"$H/H_0$\",r\"$q$\",r\"$w$\",r\"$\\Omega$\"]]\n", "param_table.append([r\"$z\\gg 1$\",r\"$\\gg 1$\", str(sig(coeffHz))+r\" $z^{1.7}$\", sig(q(0)), sig(w(0.001)), sig(Omega(0.001))])\n", "for zkey in zlist:\n", " p=z_params[zkey]\n", " row=[]\n", " for name in param_names:\n", " row.append(p[name])\n", " param_table.append(row)\n", "the_table=table(param_table, header_row=False, frame=False,align='center')\n", "the_table" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "\\begin{tabular}{cccccc}\n", " & $z$ & $H/H_0$ & $q$ & $w$ & $\\Omega$ \\\\\n", "$z\\gg 1$ & $\\gg 1$ & 0.75 $z^{1.7}$ & $0.73$ & $0.16$ & $1.0$ \\\\\n", " & 1000. & $120000.$ & $0.73$ & $0.16$ & $1.0$ \\\\\n", " & 100. & $2200.$ & $0.73$ & $0.15$ & $1.0$ \\\\\n", " & 10. & $48.$ & $0.74$ & $0.15$ & $1.0$ \\\\\n", "$T=\\frac12 T_0$ & 1.7 & $4.1$ & $0.74$ & $0.079$ & $1.2$ \\\\\n", " & 1.0 & $2.4$ & $0.69$ & $0.021$ & $1.3$ \\\\\n", "$q=0$ & 0.18 & $1.1$ & $0.00$ & $-0.33$ & $1.5$ \\\\\n", "$t=t_0$ & 0.00 & $1.0$ & $-0.60$ & $-0.61$ & $1.5$ \\\\\n", "\\end{tabular}" ] }, "execution_count": 8, "metadata": { }, "output_type": "execute_result" } ], "source": [ "latex(the_table)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "### 7.6 Plot of the cosmological parameters" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 14 graphics primitives" ] }, "execution_count": 9, "metadata": { }, "output_type": "execute_result" } ], "source": [ "my_ymin = N(-1/nu-.01)\n", "my_ymax= 2.0\n", "#my_ymin = -1/nu-.1\n", "#my_ymax= 2.01387\n", "parts=[]\n", "# plot z\n", "parts.append(parametric_plot((lambda T: t(T), z(T)), (T, 0.3*pi/2, T_0)))\n", "parts.append(text(\"$z$\",(0.1,1.9),color=\"black\"))\n", "# plot q\n", "parts.append(parametric_plot((lambda T: t(T), q(T)), (T, 0, pi/2)))\n", "parts.append(text(\"$q$\",(0.05,0.86),color=\"black\"))\n", "# plot w\n", "parts.append(parametric_plot( (lambda T: t(T), w(T)), (T, 0, pi/2)))\n", "parts.append(text(\"$w$\",(0.05,0.22),color=\"black\"))\n", "# plot Omega\n", "parts.append(parametric_plot( (lambda T: t(T), Omega(T)), (T, 0, pi/2)))\n", "parts.append(text(r\"$\\Omega$\",(0.05,1.2),color=\"black\"))\n", "# plot H\n", "parts.append(parametric_plot((lambda T: t(T), H(T)), (T, 0.52*pi/2, 0.9625*pi/2)))\n", "parts.append(text(r\"$\\frac{H}{H_0}$\",(0.25,1.95),color=\"black\"))\n", "#parts.append(text(r\"$\\frac{H}{H_0}$\",(1.42,1.95),color=\"black\"))\n", "# draw vertical dashed line at t_0\n", "parts.append(line([(t_0,0.00),(t_0,my_ymax-.001)],linestyle=\"dashed\"))\n", "parts.append(line([(t_0,my_ymin+.001),(t_0,-0.22)],linestyle=\"dashed\"))\n", "parts.append(text(r\"$t_0$\",(t_0,-0.12),color=\"black\",horizontal_alignment=\"center\"))\n", "# draw vertical solid line at t_max\n", "parts.append(line([(t_max,my_ymin+.001),(t_max,my_ymax-.001)]))\n", "param_plot=sum(parts)\n", "show(param_plot,ymin=my_ymin,ymax=my_ymax,xmax=t_max+.001,dpi=200,aspect_ratio=0.25,axes_labels=[r\"$\\frac{t}{t_H}$\",\"\"],axes_pad=0)\n", "plot(param_plot).save('parameter_plot.pdf',ymin=my_ymin,ymax=my_ymax,dpi=200,aspect_ratio=0.25,axes_labels=[r\"$\\frac{t}{t_H}$\",\"\"],axes_pad=0)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "### 7.7 Plot the conformal diagram" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 15 graphics primitives" ] }, "execution_count": 10, "metadata": { }, "output_type": "execute_result" } ], "source": [ "parts = [line([(T_0,0),(T_0,pi)],linestyle=\"dashed\")]\n", "parts.append(line([(T_0,0),(0,T_0)],linestyle=\"dotted\"))\n", "parts.append(line([(0,0),(T_0,T_0)],linestyle=\"dotted\"))\n", "parts.append(line([(0,0), (pi/2,0), (pi/2,pi),(0,pi),(0,0)],\n", " color=\"black\",axes=False))\n", "parts.append(line([(T_0/2,0),(T_0/2,T_0/2)],linestyle=\"dashed\",\n", " thickness=0.5))\n", "parts.append(text(\"$T$\",(0.25*pi,-.2),color=\"black\"))\n", "parts.append(text(\"$T_0$\",(T_0,-.07),color=\"black\",fontsize=6))\n", "parts.append(text(\"$0$\",(0,-.07),color=\"black\",fontsize=6))\n", "parts.append(text(r\"$\\frac{\\pi}{2}$\",(pi/2,-.07),\n", " color=\"black\",fontsize=6))\n", "zstr = r\"$z{=}\"+str(sig(z_half_T_0)) +\"$\"\n", "parts.append(text(zstr,(T_0/2,-.07),color=\"black\",fontsize=6))\n", "parts.append(text(\"$R$\",(-.2,pi/2),color=\"black\"))\n", "parts.append(text(\"$0$\",(-.07,0),color=\"black\",fontsize=6))\n", "parts.append(text(r\"$\\frac{T_0}{2}$\",(-.07,T_0/2),color=\"black\",fontsize=6))\n", "parts.append(text(\"$T_0$\",(-.07,T_0),color=\"black\",fontsize=6))\n", "parts.append(text(\"$\\pi$\",(-.07,pi),color=\"black\",fontsize=6))\n", "diagram = sum(parts)\n", "show(diagram,dpi=200,aspect_ratio=1,axes=False,axes_pad=0,\n", " ticks=[[],[]])\n", "plot(diagram).save('conformal_diagram.pdf',dpi=200,aspect_ratio=1,axes=False,axes_pad=0,\n", " ticks=[[],[]])" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "## 8 Analysis of the real-time ode continued" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "### 8.1 Real-time phase portrait" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "solver_step_size = 0.01 # step_size in T for the trajectories returned by the ode solver\n", "hmax=10.0 # cutoff on h values" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "#### Trajectories to plot \n", " traj is a dictionary of trajectories. \n", " The dictionary key is the initial condition $(h_{-},h_{+})_{T=0}$ of the trajectory. \n", " e.g., traj[(-1,1)] is the trajectory that passes through $(-1,1)$ at $T=0$. \n", " traj[key] is itself a dictionary with keys \n", " \"end_points\" = [$T_i$, $T_f$] the initial and final values of $T$ \n", " \"arrow_pos\" = where on the trajectory to put the arrow (as a fraction of \n", " the number of points in the trajectory\n", " \"dot_size\"\n", " \"dot_color\"\n", " \n", " " ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "traj= {}\n", "traj[(1,-1)] = {\"end_points\": [-0.55,0.65],\"arrow_pos\": 0.99, \"dot_size\":5, \"dot_color\":\"red\"}\n", "traj[(-1,1)] = {\"end_points\": [-0.65,0.55],\"arrow_pos\": 0.005, \"dot_size\":5, \"dot_color\":\"red\"}\n", "traj[(0,0)] = {\"end_points\": [-1.3,1.3]}\n", "traj[(2,0)] = {\"end_points\": [-0.2,2.3], \"arrow_pos\":0.23}\n", "traj[(-2,0)] = {\"end_points\": [-2.3,0.2], \"arrow_pos\":0.77}\n", "traj[(4,0)] = {\"end_points\": [-0.016,2.3], \"arrow_pos\":0.153}\n", "traj[(-4,0)] = {\"end_points\": [-2.3,0.016], \"arrow_pos\":0.847}\n", "traj[(-1.4168,-6)] = {\"end_points\": [-0.3,1.2], \"arrow_pos\":0.999}\n", "traj[(1.4168,6)] = {\"end_points\": [-1.2,0.3], \"arrow_pos\":0.001}\n", "traj[(-.75,-4)] = {\"end_points\": [-2,0.53], \"arrow_pos\":0.99}\n", "traj[(.75,4)] = {\"end_points\": [-0.53,2], \"arrow_pos\":0.01}\n", "#traj[(-.45,-4)] = {\"end_points\": [-1.65,0.236], \"arrow_pos\":0.98}\n", "#traj[(.45,4)] = {\"end_points\": [-0.236,1.65], \"arrow_pos\":0.02}\n", "traj[(-.15,-4)] = {\"end_points\": [-1.2,0.16], \"arrow_pos\":0.972}\n", "traj[(.15,4)] = {\"end_points\": [-0.16,1.2], \"arrow_pos\":0.028}\n", "traj[(1.5,-1.5)] = {\"end_points\": [-0.3,0.23], \"arrow_pos\":0.94}\n", "traj[(-1.5,1.5)] = {\"end_points\": [-0.23,0.3], \"arrow_pos\":0.06}\n", "traj[(2,-2)] = {\"end_points\": [-0.2,0.118], \"arrow_pos\":0.9}\n", "traj[(-2,2)] = {\"end_points\": [-0.118,0.2], \"arrow_pos\":0.1}\n", "traj[(2.5,-2.5)] = {\"end_points\": [-0.12,0.06], \"arrow_pos\":0.8}\n", "traj[(-2.5,2.5)] = {\"end_points\": [-0.06,0.12], \"arrow_pos\":0.2}\n", "traj[(-3,-5)] = {\"end_points\": [-2.0,0.14], \"arrow_pos\":0.925}\n", "traj[(3,5)] = {\"end_points\": [-0.14,2.0], \"arrow_pos\":0.075}" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "#### Define a function that Integrates the ode numerically for given initial conditions and plots the trajectory\n", "\n", "The function make_traj takes as argument a key of the traj dictionary. \n", " It adds to traj[key] 5 dictionary items \n", " traj[key][\"calculated\"] = output from the ode solver \n", " traj[key][\"chopped\"] = list of points $(h_{-},h_{+})$ to plot \n", " traj[key][\"chopped_fv\"] = list of points $(f_{T},v_{T})$ to plot \n", " traj[key][\"plotted\"] = $(h_{-},h_{+})$ trajectory plotted \n", " traj[key][\"plotted_fv\"] = $(f_{T},v_{T})$ trajectory plotted \n", " \n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "from sage.calculus.desolvers import desolve_system_rk4\n", "sqrt3=N(sqrt(3))\n", "lambdaplus = 2+sqrt3\n", "lambdaminus = 2-sqrt3\n", "betaplus=1+sqrt3/3\n", "betaminus=1-sqrt3/3\n", "#dot_color = var('dot_color')\n", "def make_traj(key):\n", " my_arrow = lambda p1,p2: arrow(p1,p2,arrowsize=2.0,width=0.1,color=dot_color)\n", " hplus,hminus,T=var('hplus hminus T')\n", " ode_function=[-1-hminus^2+lambdaminus*(hplus*hminus+1),-1-hplus^2+lambdaplus*(hplus*hminus+1)]\n", " traj_solved=desolve_system_rk4(ode_function,[hminus,hplus],ics=[0]+list(key),\n", " ivar=T,end_points=traj[key][\"end_points\"],step=solver_step_size)\n", " traj[key][\"calculated\"]=traj_solved\n", " traj_list = []\n", " traj_list_fv = []\n", " for T,hminus,hplus in traj_solved:\n", " if abs(hplus) <= hmax and abs(hminus) <= hmax:\n", " traj_list.append([hminus,hplus])\n", " f_T = (sqrt3/2)*(betaplus*hminus-betaminus*hplus)\n", " v_T = (sqrt3/2)*(hplus-hminus)\n", " traj_list_fv.append([f_T,v_T])\n", " traj[key][\"chopped\"]=traj_list\n", " traj[key][\"chopped_fv\"]=traj_list_fv\n", " dot_size = 1\n", " if \"dot_size\" in traj[key]:\n", " dot_size = traj[key][\"dot_size\"]\n", " dot_color=\"blue\"\n", " if \"dot_color\" in traj[key]:\n", " dot_color = traj[key][\"dot_color\"]\n", " traj[key][\"plotted\"]=list_plot(traj_list,size=dot_size,color=dot_color)\n", " traj[key][\"plotted_fv\"]=list_plot(traj_list_fv,size=dot_size,color=dot_color)\n", " Npoints = len(traj_list)\n", " arrow_index=int(Npoints/2)\n", " Npoints_fv = len(traj_list_fv)\n", " arrow_index_fv=int(Npoints_fv/2)\n", " if \"arrow_pos\" in traj[key]:\n", " arrow_index = int(traj[key][\"arrow_pos\"]*Npoints)\n", " arrow_index_fv = int(traj[key][\"arrow_pos\"]*Npoints_fv)\n", " arrow_index = min(Npoints-2,arrow_index)\n", " arrow_index_fv = min(Npoints_fv-2,arrow_index_fv)\n", " arrow_p1 = traj_list[arrow_index]\n", " arrow_p2 = traj_list[arrow_index+1]\n", " traj[key][\"plotted\"]+=my_arrow(arrow_p1,arrow_p2)\n", " arrow_p1 = traj_list_fv[arrow_index_fv]\n", " arrow_p2 = traj_list_fv[arrow_index_fv+1]\n", " traj[key][\"plotted_fv\"]+=my_arrow(arrow_p1,arrow_p2)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "#### Integrate and plot the individual trajectories" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "for key in traj:\n", " make_traj(key)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "#### Construct the two phase portraits and save as pdf files" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 49 graphics primitives" ] }, "execution_count": 15, "metadata": { }, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 49 graphics primitives" ] }, "execution_count": 15, "metadata": { }, "output_type": "execute_result" } ], "source": [ "LP = sum(traj[key][\"plotted_fv\"] for key in traj)\n", "my_font_size='small'\n", "LP+= text(r\"$C{=}0$\",(3.1,-6.8),fontsize=my_font_size,color=\"red\")\n", "LP+= text(r\"$C{=}0'$\",(-3.1,6.8),fontsize=my_font_size,color=\"red\")\n", "LP+= text(r\"$C{<}0'$\",(-5.5,5),fontsize=my_font_size)\n", "LP+= text(r\"$C{<}0$\",(5.5,-5),fontsize=my_font_size)\n", "LP+= text(r\"$C{>}0$\",(4,4),fontsize=my_font_size)\n", "LP+= text(r\"${S}$\",(0.19,-6.2),fontsize=my_font_size)\n", "LP+= text(r\"${S'}$\",(-0.19,6.2),fontsize=my_font_size)\n", "LP.fontsize(4)\n", "plot(LP).save('phase_portrait_fv.pdf',dpi=200,aspect_ratio=0.75,\n", " axes_labels=['$f_T$','$v_T$'],axes_labels_size=2)\n", "show(LP,aspect_ratio=0.75,dpi=200,axes_labels=['$f_T$','$v_T$'],\n", " axes_labels_size=2)\n", "LP = sum(traj[key][\"plotted\"] for key in traj)\n", "LP+= text(r\"$C{=}0$\",(0.55,-7.8),fontsize=my_font_size,color=\"red\")\n", "LP+= text(r\"$C{=}0'$\",(-0.55,7.8),fontsize=my_font_size,color=\"red\")\n", "LP+= text(r\"$C{<}0$\",(4,-4),fontsize=my_font_size)\n", "LP+= text(r\"$C{<}0'$\",(-4,4),fontsize=my_font_size)\n", "LP+= text(r\"$C{>}0$\",(4,4),fontsize=my_font_size)\n", "LP+= text(r\"${S}$\",(-2.6,-9.7),fontsize=my_font_size)\n", "LP+= text(r\"${S'}$\",(2.6,9.7),fontsize=my_font_size)\n", "LP.fontsize(4)\n", "plot(LP).save('phase_portrait_hh.pdf',dpi=200,aspect_ratio=0.5,\n", " axes_labels=[r\"$h_-$\",r\"$h_+$\"],axes_labels_size=2)\n", "show(LP,dpi=200,aspect_ratio=0.5,axes_labels=[r\"$h_-$\",r\"$h_+$\"],\n", " axes_labels_size=2)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "### 8.4 Asymptotic behavior of the separatrices $S$, $S'$" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "$\n", "T\\rightarrow \\pm \\infty\n", "\\qquad\n", "f_{T} = \\sum_{m=0} f_{m} T^{-2m-1}\n", "\\qquad\n", "v_{T} = -T+\\sum_{m'=0} v_{m'} T^{-2m'-1}\n", "\\qquad\n", "f_{0}=1\n", "$\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "calculate $\\quad\\tilde f_m = f_m/m! \\qquad\\tilde v_m = v_m/m!$" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "N_tilde_coeffs =2000\n", "f_tilde_coeffs = [1.0]\n", "v_tilde_coeffs = []\n", "for m_tilde in range(N_tilde_coeffs+1):\n", " ff_sum=sum(f_tilde_coeffs[mp]*f_tilde_coeffs[m_tilde-mp]/binomial(m_tilde,mp) for mp in range(m_tilde+1))\n", " v_tilde_coeffs.append(-2*f_tilde_coeffs[m_tilde] + ff_sum/(2*m_tilde+1))\n", " fv_sum=sum(f_tilde_coeffs[mp]*v_tilde_coeffs[m_tilde-mp]/binomial(m_tilde,mp) for mp in range(m_tilde+1))\n", " f_tilde_coeffs.append(-(m_tilde+1/2)*f_tilde_coeffs[m_tilde]/(m_tilde+1)+(ff_sum+fv_sum)/(m_tilde+1))\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "plot $m \\ln\\left(\\frac{-\\tilde f_m}{\\tilde f_{m-1}}\\right)$\n", "and $m \\ln\\left(\\frac{-\\tilde v_m}{\\tilde v_{m-1}}\\right)$" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 17, "metadata": { }, "output_type": "execute_result" } ], "source": [ "f_ratios = [[mm,mm*ln(((-f_tilde_coeffs[mm]/f_tilde_coeffs[mm-1])).n())] for mm in range(int(0.1*N_tilde_coeffs),N_tilde_coeffs)]\n", "v_ratios = [[mm,mm*ln(((-v_tilde_coeffs[mm]/v_tilde_coeffs[mm-1])).n())] for mm in range(int(0.1*N_tilde_coeffs),N_tilde_coeffs)]\n", "show(list_plot(f_ratios)); show(list_plot(v_ratios))" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "Plot the expansions in the $(f_T,v_T)$ plane" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ "Ry. = RR[]\n", "f_poly = 0*y\n", "v_poly = 0*y\n", "for mm in range(N_tilde_coeffs):\n", " f_poly += f_tilde_coeffs[mm]*factorial(mm) *y^(2*mm+1)\n", " v_poly += v_tilde_coeffs[mm]*factorial(mm) *y^(2*mm+1)\n", "def fv_plot(T_i,T_f,T_int):\n", " point_list=[]\n", " N_plot = int((T_f-T_i)/T_int)\n", " for k in range(N_plot):\n", " T_val = T_i+k*T_int\n", " y_val = 1.0/T_val\n", " f_T_val = f_poly(y=y_val)\n", " v_T_val = -T_val + v_poly(y=y_val)\n", " point_list.append([f_T_val,v_T_val])\n", " show(list_plot(point_list))" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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", 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lS5bg559/xooVK7Bp0ybMmjWr1bEJIVBZWQmu/EJERETWavO15HJychAXF4dTp04hLCys0fc6nQ49e/bE3LlzkZKS0urrrl27Fg8++CCuXLkCFxeXFo+vrKyEj4+PxasRExEREV2r5czDQhqNBiqVCr6+vma/z8jIQEVFBWbMmGHxdb29vZtMlrRaLbRaraFcWVlp0fWJiIiImtKmg75ramqwYMECPPDAA0226qSmpmLcuHEIDQ1t9XXPnz+PV155BXPmzGnymMWLF8PHx8ewWXJ9IiIiouZY1CWXnp5ukrR89913GDFiBACpq23q1KkoLi5Gdna22YSppKQEvXr1wpdffol77723VfesrKzE2LFj0bVrV2RkZMDV1dXsceZamEJDQ9utS04IQKVq88sSERGRDbKoSy4hIQFDhw41lENCQgBIyVJSUhKKioqQmZnZZIKSlpYGf39/k0HhzamqqsL48ePh6emJr7/+uslkCQDc3d3h7u5uwa+5fkuXAvPnAy4uwAcfANOnd8htiYiISCZWD/puSJYKCgqQlZWFgIAAs8cJIdCnTx/8+c9/xpIlS1q8bmVlJcaNGwd3d3ds3LgRXbp0sSiu9hr0XVQE9OkjtTABgJsb8NtvAMeVExERKZdVY5jq6uqQmJiI3NxcpKenQ6/Xo7y8HOXl5aitrTU5NjMzE0VFRWanBigtLUVERAT27t0LQGpZGjt2LK5cuYLU1FRUVlYarqvX660J2WqXLhmTJQCorQWuXJEvHiIiImp/Vr0lV1JSgoyMDABAbGysyXdZWVkYNWqUoZyamor4+HhERkY2uo5Op0N+fj6qq6sBAPv27cOePXsAAH379jU5tqioCOHh4daEbZUBA4CxY4Hvv5fKDzwABAXJFg4RERF1gDafh8lWtOc8THV1wObNgKsrMGYMB38TEREpXZvPw+QIXFyAiRPljoKIiNrb778Dv/4K9OwJNDFElxyE4hbfVavViIqKwpAhQ+QOhYiI7NhvvwEDBwKDBgG9ewPbtskdEcmJXXJERERmvPYa8MILxvKwYcCuXfLFQ/JSXAsTERFRW3B2Ni23YhlTUjAmTERERGY8/jhwyy3SZz8/4K235I2H5MWEiYiIyAwfH2DPHmnC4tOngVtvlTsiZTh2DIiPB3r1Al56Se5oWo9jmIiIiKjDDB0K/DFPNQDg22+BCRPki6e12MJEREREHaa4uPmyrWLCRERERB3m4YeNn7t1s595DRWXMHEeJiIiItv1xhvA+vXA0qVAbi4QGnp91zl1ShoL5e8PzJ4NtPdSsxzDRERERHZn4kRg40Zj+cMPgccea7/7Ka6FiYiIiJSvrMy0fOZM+96PCRMRERHZnatbk3x8gHvuAXS69rsf5y0lIiIiu/P440D//tK8TkeOSOv+ubhIXXMzZrT9/TiGiYiIiOzW0aNAVJSx7OoKXLwIeHi07X3YJUdERER26/Jl07JOB9TUtP19FJcwcVoBIiIix3HLLcDttxvLTz4pTTXQ1tglR0RERHbrsceA5culzzNmAGlp7XMfJkxERERkl44cAW6+2XTf2bNA9+5tfy/FdckRERGRY3C6JotRqRrva7N7tc9liYiIiNpXRQWQkCB9VqmAV1+V1qdrD5yHiYiIiOzOwoXSunSANK3AN98AN9zQfvdjCxMRERHZFSGAd981ln/5Bfj55/a9JxMmIiIisisqFeDra7qva9f2vafiEibOw0RERKRcej2wYgVw992Anx/g5gb8/e+mczG1B04rQERERHZjxgzg00+lz4GBQF4eEBTU/vdVXAsTERERKdeaNcbP5eXA9u0dc18mTERERGQ3evduvtxerEqYdDod5s+fj+joaHh4eCA4OBjJyckoKyszHJOdnQ2VSmV2y8nJafLac+bMQZ8+fdC5c2cEBARgypQp+PXXX60Jl4iIiOxUZSXwf/8HxMRIW0QEoFYDcXEdc3+rxjBpNBokJiZi9uzZiImJwcWLFzFv3jzU1dUhNzcXAFBbW4sLFy6YnJeSkoKtW7eisLAQKpXK7LU/+ugjREREICwsDBcuXMCiRYtw4MABFBUVwdnZucXYOIaJiIhIOUaPBjIzpc9eXtI0Ar16ddz923zQd05ODuLi4nDq1CmEhYU1+l6n06Fnz56YO3cuUlJSWn3dQ4cOISYmBsePH0efPn1aPJ4JExERkTIIAbi4APX1xn3r1gH33ttxMbT5TN8ajQYqlQq+106Q8IeMjAxUVFRgxowZrb7mlStXkJaWht69eyM0NNTsMVqtFlqt1lCurKy0KG4iIiKyTSoVMGgQ8EfnFdzcGi+6297adNB3TU0NFixYgAceeKDJVp3U1FSMGzeuycTnasuWLYOnpyc8PT2xadMmbNmyBW5ubmaPXbx4MXx8fAxba65PREREtq2wUGpJ6txZ6pabPFlaBqVfv46Nw6IuufT0dMyZM8dQ/u677zBixAgAUlfb1KlTUVxcjOzsbLMJU0lJCXr16oUvv/wS97aiHU2j0eDcuXM4c+YMlixZgtLSUuzcuROdOnVqdKy5FqbQ0FB2yREREdmxiAggP1/67O4OHDkCtGJkTpuzKGGqqqrC2bNnDeWQkBB07twZOp0OSUlJKCwsRGZmJvz9/c2e/8orr2Dp0qUoLS2Fq6urRYHW1taia9eu+Pjjj3H//fe3eDzHMBEREdk3rRa4to1kwwZg4sSOj8WiMUxeXl7w8vIy2deQLBUUFCArK6vJZEkIgbS0NCQnJ1ucLF19jatbkYiIiEi53N2BUaOA7Gyp7O8P3HKLPLFYNYaprq4OiYmJyM3NRXp6OvR6PcrLy1FeXo7a2lqTYzMzM1FUVIRZs2Y1uk5paSkiIiKwd+9eAEBhYSEWL16Mffv2obi4GLt370ZSUhI6d+6MCRMmWBMyERER2YEff5QGdhcVAVOmAE8/Le0LDJQnHqvekispKUFGRgYAIDY21uS7rKwsjBo1ylBOTU1FfHw8IiMjG11Hp9MhPz8f1dXVAIBOnTphx44d+Ne//oWLFy+iR48euP3227Fr1y50797dmpCJiIjIxtXXS4vrnj8vlU+fBn75peMHel+Ni+8SERGRTamqAq79p3vbNuCOO+SJB+BackRERGRjunSRuuEaRER03BIoTVFcwqRWqxEVFYUhQ4bIHQoRERFZaNUqaemTDRuk+ZeWLQN27QI8PeWNi11yREREZBOqq4GuXYGr3xs7cgSIipIvpgaKa2EiIiIi+6TVmiZLgDSeyRYwYSIiIiKboNEAV89NPW4cMHiwfPFcjQkTERERye4f/wB69wY+/1wa8L11qzSOydlZ7sgkHMNEREREsvrtN+DaaRYPHwb695cnHnPYwkRERESyUqmk7dp9tkRxCROnFSAiIrIf9fVAXh7w0EPGfX/5i228GXc1dskRERGRbJKSgLVrpc9jxgAffQSEh8saklmKa2EiIiIi+3DypDFZAoAtW6S5mGwREyYiIiKShacn4OJiLDs5NV5DzlYwYSIiIqIOV1UFrFkD3Hcf0LmztL3/PtCzp9yRmefS8iFEREREbUenA0aPBnJypPLQocCOHYCrq7xxNYctTERERNShCgqMyRIA7NkDFBXJF09rMGEiIiKiDtWjB9Cli7Hs4dF44kpbo7iEifMwERER2a6TJ4GXXwbGjgX69QOio4H16wFfX7kjax7nYSIiIqIOcfmytNxJcbFUvukmaQkUWx671EBxLUxERERkmwoKjMkSABw7BpSUyBePJZgwERERUYcIDwf8/IzloCBpswecVoCIiIja3c6dwKuvAjffDDg7S4nTSy8BnTrJHVnrMGEiIiKidvXbb8CECUBlpVQODpamEXBzkzcuS7BLjoiIiNpVYaExWQKAsjIpibInTJiIiIioXUVFAaGhxnJ0NBAYKF8810NxCRPnYSIiIrIdq1cDAwdKa8VNnQosWABkZkrjmOwJ52EiIiKidnHyJHDjjUBdnVT28QHOnbOvsUsNFNfCRERERLahrMyYLAGARmM6lsmeMGEiIiKidnHzzdLW4K67gG7d5IvHGlYlTDqdDvPnz0d0dDQ8PDwQHByM5ORklJWVGY7Jzs6GSqUyu+VcvVRxE4QQuOuuu6BSqfDf//7XmnCJiIiog7z8sjTXUlERMGsW8MkngD3/M25VwlRdXY28vDykpKQgLy8P69evx7Fjx5CQkGA4Jj4+HmfOnDHZHn30UYSHh2Pw4MEt3uNf//oXVCqVNWESERFRBzp0CHjxRUCvB65cAdLTgenT7XPsUgOrJq708fHBli1bTPYtXboUcXFxKC4uRlhYGNzc3BB41buDOp0OGRkZmDt3bouJ0MGDB/Huu+8iJycHQS3Mna7VaqHVag3lSnvtJCUiIrJz1/4TXFMDaLX2nTC1+RgmjUYDlUoFX19fs99nZGSgoqICM2bMaPY61dXVuP/++/H++++bJFxNWbx4MXx8fAxb6NUTPhAREVGH8fMDhg0zlufOBby85IunLbTptAI1NTUYPnw4IiIisGrVKrPHTJgwAQCwcePGZq81Z84c6PV6fPzxx1KgKhW+/vpr3H333WaPN9fCFBoaymkFiIiIOogQwAMPAGvWACoV8NhjwEMPAbfdJndk1rOohSk9PR2enp6GbceOHYbvdDodpk2bhvr6eixbtszs+SUlJdi8eTNmzZrV7H0yMjKQmZmJf/3rX62Ozd3dHd7e3iYbERERdZydO6VkCZCSp48/BloxXNkuWDSGKSEhAUOHDjWUQ0JCAEjJUlJSEoqKipCZmdlkspKWlgZ/f3+TQeHmZGZm4sSJE4269e69916MGDEC2dnZloRNREREHeDaockqVeN99sqihMnLywte13RCNiRLBQUFyMrKgr+/v9lzhRBIS0tDcnIyXF1dm73PggUL8Oijj5rsi46Oxj//+U9MnjzZkpCJiIioA9TUABcvAmPHAt9/Dzg5Ae++a98Dva9m1VtydXV1SExMRF5eHjZs2AC9Xo/y8nIAgJ+fH9yuqqXMzEwUFRWZ7Y4rLS3F6NGjsXLlSsTFxSEwMNDsQO+wsDD07t3bmpCJiIiojWm1wJ/+BPz0k1R+5BHgtdfsb4Hd5lj1llxJSQkyMjJQUlKC2NhYBAUFGbZdu3aZHJuamor4+HhERkY2uo5Op0N+fj6qq6utCYeIiIhk8MMPxmQJAFaskN6UUxIuvktERERWyckB4uKMZS8vad04pYxfAhS4lpxarUZUVBSGDBkidyhERESKd/as9HZcQgLg7Az4+kozeyspWQLYwkRERETX6eJFYOBA4NQpqZyUBHzxhbwxtRfFtTARERFRx/jxR2OyBABr1wJ1dfLF056YMBEREdF16dXLtOstJARwser9e9ul0J9FRERE7engQWD5cmDCBODoUcDfH/jPf+SOqv0wYSIiIiKLnD4N3H47UFkple+4A9i2Td6Y2hu75IiIiMgiubnGZAkAsrKA+nr54ukITJiIiIjIIv37my55EhMjLYWiZIrrklOr1VCr1dDr9XKHQkREpDgbNgBLlwLDhkkDvoODgTfflDuq9sd5mIiIiKhVfvkFiI0FdDqpPGgQsG+fvDF1FIU3oBEREVFbOXLEmCwB0ptyymx2aYwJExEREbXK0KHA1Z02d96pvCVQmqK4MUxERETU9v79b+C994DQUGDAAKBfP+DZZ+WOquMwYSIiIqJm/fQT8Ne/Gsu1tcDq1fLFIwd2yREREVGziotNy1evH+comDARERFRs0aMkNaJa/Dgg/LFIhfFJUxqtRpRUVEYMmSI3KEQERHZvblzgZ49gStXgCeeANLTpTXkHA3nYSIiIiKzvv8eGDfOWA4OBkpL5YtHToprYSIiIqK2cemSaVmjkScOW8CEiYiIiBqprwf69gUiI437FiyQLx65cVoBIiIiMqHTAQkJwKZNgKurNN9SUhLgyMODOYaJiIiITKxfD9x7r7Hs5wecPy9fPLaAXXJERERk4trlThxl+ZPmKC5h4rQCRERE1+/yZcDZGRg2TCq7ukpLojg6dskRERERAKCqCoiPBw4flsrPPAPMnw8EBMgbly1QXAsTERERXZ8NG4zJEgB8/DGTpQZMmIiIiAgA4ONjWvbqPJyaAAAgAElEQVT1lScOW2RVwqTT6TB//nxER0fDw8MDwcHBSE5ORllZmeGY7OxsqFQqs1tOTk6T1x41alSj46dNm2ZNuERERNSE06eBY8eAO++UBnl36wasWCF3VLbDqjFMGo0GiYmJmD17NmJiYnDx4kXMmzcPdXV1yM3NBQDU1tbiwoULJuelpKRg69atKCwshKqJofejRo3CTTfdhJdfftmwr3PnzvC5Nv1tAscwERERtc6ZM8DAgcDZs1J5zhzgP/+RNyZbY9XElT4+PtiyZYvJvqVLlyIuLg7FxcUICwuDm5sbAgMDDd/rdDpkZGRg7ty5TSZLDbp06WJyLhEREbW9LVuMyRIArF7NhOlabT6GSaPRQKVSwbeJjs+MjAxUVFRgxowZLV4rPT0d3bp1Q//+/fHss8+iqqqqyWO1Wi0qKytNNiIiImpZeLhpuVcvWcKwaW06rUBNTQ2GDx+OiIgIrFq1yuwxEyZMAABs3Lix2WstX74cvXv3RmBgIA4fPoyFCxeib9++jVq0GixatAgvvfRSo/3skiMiImpaTg7w6afA8eNAfj4QGAikpgJRUXJHZlssSpjS09MxZ84cQ/m7777DiBEjAEhdbVOnTkVxcTGys7PNJiklJSXo1asXvvzyS9x79ZzrrbBv3z4MHjwY+/btw6BBgxp9r9VqodVqDeXKykqEhoYyYSIiImpCQQEQGwtUV0vle+6RlkWhxiwaw5SQkIChQ4cayiEhIQCkZCkpKQlFRUXIzMxsMkFJS0uDv78/EhISLA500KBBcHV1RUFBgdmEyd3dHe7u7hZfl4iIyFHt2mVMlgBpLBOZZ1HC5OXlBS8vL5N9DclSQUEBsrKy4O/vb/ZcIQTS0tKQnJwMV1dXiwM9cuQIdDodgoKCLD6XiIiIGouOlpZB0eulspn2CPqDVW/J1dXVITExEXl5ediwYQP0ej3Ky8sBAH5+fnBzczMcm5mZiaKiIsyaNavRdUpLSzF69GisXLkScXFxOHHiBNLT0zFhwgR069YNv/zyC5555hkMHDgQt912mzUhExEREYCvvwY+/BAYMQIQAggLA95+W+6obJdVCVNJSQkyMjIAALGxsSbfZWVlYdSoUYZyamoq4uPjERkZ2eg6Op0O+fn5qP6jXdDNzQ3btm3De++9h8uXLyM0NBQTJ07Eiy++CGdnZ2tCJiIicnj79wNTpxpblm6/HVi5Ut6YbB0X3yUiInIwK1YAM2cay15eAGfjaR7XkiMiInIwt90GdOliLN95p3yx2AuruuRskVqthlqthr6hnZGIiIgM3nkHWLYM6NMHuPlmICICeO45uaOyfeySIyIichDZ2cCf/mQsDxgAHDwoWzh2hV1yREREDuLUKdPyyZOyhGGXmDARERE5iDvuALp3N5anT5cvFnvDhImIiEjhhAAef1xaZLe+Hpg7F1i9GlCr5Y7MfnAMExERkcJt2ABMnmws9+4NFBbKF489YgsTERGRwl261HyZWsaEiYiISMHq64H+/YGbbjLumz9fvnjsFedhIiIiUiidDpg0Cfj+e8DNDfj734HERGDIELkjsz8cw0RERKRQa9cCSUnGco8eQHm5fPHYM3bJEREROQhlNpF0DCZMRERECnTlCuDuDsTFSWVXV+Cf/5Q3JnumuDFMREREjq6yUlpg9/BhqfzMM9L4pasnrSTLsIWJiIhIYTZsMCZLAJCaymTJWkyYiIiIFMbHp/kyWU5xCZNarUZUVBSG8J1JIiJyQKWlwPHj0rpxKhXg7w+kpckdlf3jtAJEREQKcfYsMHAgcOaMVH7sMeDDD+WNSSkU18JERETkqLZuNSZLgLTALrUNJkxEREQKERbWfJmuH6cVICIiUoD9+6WZvceNA44eBYKCpLfjqG0wYSIiIrJzhYXA7bcDly9L5SlTgP/+V96YlIZdckRERHZu925jsgRIi+1S22LCREREZOduvhlwdjaWY2Pli0WpFNclp1aroVarodfr5Q6FiIio3W3YACxbBowYAej1QGgo8PbbckelPJyHiYiIyE4dPizNu1RXJ5VvvVXqnqO2xy45IiIiO/Xzz8ZkCQDy8uSLRemYMBEREdmpoUMBDw9jefRo+WJROqsSJp1Oh/nz5yM6OhoeHh4IDg5GcnIyysrKDMdkZ2dDpVKZ3XJycpq9/u7du3HHHXfAw8MDvr6+GDVqFH7//XdrQiYiIlKEZcuA8eOBG24A7rsPSEkBvvxS7qiUy6oxTBqNBomJiZg9ezZiYmJw8eJFzJs3D3V1dcjNzQUA1NbW4sKFCybnpaSkYOvWrSgsLIRKpTJ77d27d2P8+PFYuHAhJk+eDDc3Nxw8eBCTJ0+Gu7t7i7FxDBMRESnV3r1S61KDm24C8vPli8cRtPmg75ycHMTFxeHUqVMIMzMnu06nQ8+ePTF37lykpKQ0eZ1bb70VY8aMwSuvvHJdcTBhIiIipfryS6lVqYGbG6DVyhePI2jzMUwajQYqlQq+vr5mv8/IyEBFRQVmzJjR5DXOnTuHPXv2oHv37oiPj0ePHj0wcuRI/Pjjj02eo9VqUVlZabIREREp0e23A8HBxvL998sXi6No04SppqYGCxYswAMPPNBkq05qairGjRuH0NDQJq9TWFgIAFi0aBFmz56NTZs2YdCgQRg9ejQKCgrMnrN48WL4+PgYtuauT0REZK+ee06aa+n334E5c4CVK4FPPpE7KuWzKGFKT0+Hp6enYduxY4fhO51Oh2nTpqG+vh7Lli0ze35JSQk2b96MWbNmNXuf+vp6AMCcOXMwc+ZMDBw4EP/85z/Rr18/fNLEU7Fw4UJoNBrDdvr0aUt+GhERkc374QdgyRJpKoGLF4GvvwYeeghw4jvv7c6imb4TEhIw9KpRZiEhIQCkZCkpKQlFRUXIzMxssnUpLS0N/v7+SEhIaPY+QUFBAICoqCiT/ZGRkSguLjZ7jru7e6sGgxMREdmrixdNyxoNIATQxPtT1IYsSpi8vLzg5eVlsq8hWSooKEBWVhb8/f3NniuEQFpaGpKTk+Hq6trsfcLDwxEcHIz8a4b8Hzt2DHfddZclIRMRESmCEEDfvtK6cYcPS/ueeYbJUkexqhGvrq4OiYmJyM3NRXp6OvR6PcrLy1FeXo7a2lqTYzMzM1FUVGS2O660tBQRERHYu3cvAEClUuG5557Dv//9b6xbtw7Hjx9HSkoKfv311xa784iIiJSmvh5ISgKio4FffwWeegr48UfgtdfkjsxxWLX4bklJCTIyMgAAsdcsjZyVlYVRo0YZyqmpqYiPj0dkZGSj6+h0OuTn56O6utqwb968eaipqcHTTz+NCxcuICYmBlu2bEGfPn2sCZmIiMjubN0KrFsnfa6rA1JTgffekzcmR8PFd4mIiGzc5s3SrN4NOncGrlxhd1xHUty4erVajaioKAwZMkTuUIiIiKym1UpdciNGSGUnJ+Ddd5ksdTS2MBEREdmomhrgT38CfvpJKj/2GPDii6aTVlLHUFwLExERkVJkZxuTJUAau9S9u2zhODQmTERERDbqmpl84OEBODvLE4ujY8JERERkg86fBw4eBCZMkMYreXkBn33GsUtysWpaASIiImp7lZXArbcCx49L5alTgTVruASKnFj1RERENmbXLmOyBABr1wLXzAdNHYwJExERkY3p2dO0661HD6BTJ/niIQUmTJyHiYiI7FlBAZCWJo1dCgsDBgwA/vc/uaMizsNERERkIyoqgP79gXPnpPKwYVL3HMlPcS1MRERE9mr/fmOyBAC7dwNVVfLFQ0ZMmIiIiGzETTeZjlW64YbGczGRPDitABERkQ3YuRN46y2pG662VprR+8035Y6KGjBhIiIikllZGTB+PHD5slTu0wfYsYOTVNoSdskRERHJ7NgxY7IEACdOAJcuyRcPNcaEiYiISGY33wwEBBjLAwcCXbvKFw81priEifMwERGRPVm3Dhg5UkqY7rkHeO45YMsWuaOia3EeJiIiIpmcOgXceCOg00llPz/gzBnAzU3euKgxxbUwERER2YvSUmOyBAAXLgAajXzxUNOYMBEREckkJgaIiDCW77zTdCwT2Q4mTERERDL497+Bbt2AkhLgwQeBDz4AvvlG7qioKRzDRERE1MEKC4G+fYGGf4Hd3KR15Dirt+1iCxMREVEHu3TJmCwB0szeV67IFw+1jAkTERFRB/P3B0aMMJanTwcCA+WLh1qmuISJ8zAREZEte+YZIDxcWvpk+nTg+++Bzz6TOypqCccwERERdZCCAuCmm0z3nTnD1iV7oLgWJiIiIltVX994nzKbLZSHCRMREVEHEAIoLwemTDHuW7AACAqSLyZqPasSJp1Oh/nz5yM6OhoeHh4IDg5GcnIyysrKDMdkZ2dDpVKZ3XJycsxe9+TJk02es3btWmtCJiIiksX99wOjRgH/+x8wcSJw/DiweLHcUVFrWTWGSaPRIDExEbNnz0ZMTAwuXryIefPmoa6uDrm5uQCA2tpaXLhwweS8lJQUbN26FYWFhVCpVI2uq9fr8dtvv5ns++ijj/DWW2+hvLwcnp6eLcbGMUxERGQrzI1dOn4c6NNHnnjIci7WnOzj44Mt1yypvHTpUsTFxaG4uBhhYWFwc3ND4FWj2XQ6HTIyMjB37lyzyRIAODs7m5wDAF9//TXuu+++JpMlrVYLrVZrKFdWVl7vzyIiImpTHh6Ak5NxDJOTk7SP7Eebj2HSaDRQqVTw9fU1+31GRgYqKiowY8aMVl9z3759OHDgAGbNmtXkMYsXL4aPj49hCw0NtTR0IiKiNldTA2zaBCQlAc7OgKurtCwK34yzL206rUBNTQ2GDx+OiIgIrFq1yuwxEyZMAABs3Lix1dd94oknkJ2djV9++aXJY8y1MIWGhrJLjoiIZFNfD4weDWRnS+W4OOlz585yRkXXw6IWpvT0dHh6ehq2HTt2GL7T6XSYNm0a6uvrsWzZMrPnl5SUYPPmzc22FF3r999/x+rVq1s8x93dHd7e3iYbERGRnE6eNCZLALB3rzR2ieyPRWOYEhISMHToUEM5JCQEgJQsJSUloaioCJmZmU0mK2lpafD390dCQkKr77lu3TpUV1cjOTnZklCJiIhk5+8PdOkCVFdLZXd3oHt3eWOi62NRwuTl5QWva5ZSbkiWCgoKkJWVBX9/f7PnCiGQlpaG5ORkuLq6tvqeqampSEhIQEBAgCWhEhERyer8eeDdd4G77gL27ZMGer/9NtCjh9yR0fWw6i25uro6JCYmIi8vDxs2bIBer0d5eTkAwM/PD25uboZjMzMzUVRUZLZrrbS0FKNHj8bKlSsRFxdn2H/8+HFs377dovFOREREctPrgTvuAA4dksq9egEHDwKtmBWHbJRVb8mVlJQgIyMDJSUliI2NRVBQkGHbtWuXybGpqamIj49HZGRko+vodDrk5+ejuqHN8g+ffPIJQkJCMHbsWGvCJCIi6lBlZcZkCQBOnQKOHpUvHrIeF98lIiJqY1otEB4uLYUCAN7e0mBvji6xX4pbS06tViMqKgpDhgyROxQiInJAJ04AM2YAUVFAfDwwZgzw7bdMluwdW5iIiIjaiF4P3HgjUFQklb29gWPHONBbCRTXwkRERCSX8+eNyRIAVFZK68iR/WPCRERE1Ea6dQOio43lHj2krjmyf0yYiIiI2kBuLjBsGFBbK8299PjjwPbtgJ+f3JFRW7BqHiYiIiKS1oybNAk4e1YqnzgB/PKLNJ6JlIEtTERERFa6csWYLAFAXR1QXCxfPNT2mDARERFZyctL6oZrcMMNAGe3URbFJUych4mIiDrS5s3SgrqZmcDEicCSJcDu3dKUAqQcnIeJiIjoOgkhDeq+dMm4b88e4KplUUkhFNfCRERE1FHq6qS5lq524YI8sVD7YsJERER0naqqgIcfNpYHDQJGjpQvHmo/TJiIiIiuw2efAYGBQFoacPvtwFdfATt2AJ07yx0ZtQcmTERERNfhyScBnU76vH27lCh16SJvTNR+mDARERFdh/p607JeL08c1DGYMBEREVno0CHg0UcBlUoqjx8vbaRcilsaRa1WQ61WQ89Un4iI2sE77wDPPit97t8f+OQTYPBgwIlNEIrGeZiIiIgs4OsLaDTG8uefA9OmyRcPdQzmw0RERBbw8mq+TMrEhImIiKiV/vc/4J57jEnSI48AEybIGxN1DMWNYSIiImoPCxYAb74pfe7RA8jLA/r2lTcm6jhsYSIiImqFTz4xfj57FsjOli0UkgETJiIiolbo2bP5Mimb4rrkOK0AERG1pbo64P33gQEDgN9/lxbbffRRzrvkaDitABERUTPmzAE++kj67O4O7N0rJU/kWNglR0RE1IyNG42ftVogK0u+WEg+TJiIiIiacW1rUnS0PHGQvKxKmHQ6HebPn4/o6Gh4eHggODgYycnJKCsrMxyTnZ0NlUpldsvJyWny2uXl5XjooYcQGBgIDw8PDBo0COvWrbMmXCIiola7fBmYN08awxQfD9x+O7B8OXDHHXJHRnKwagyTRqNBYmIiZs+ejZiYGFy8eBHz5s1DXV0dcnNzAQC1tbW4cOGCyXkpKSnYunUrCgsLoWpYufAaY8aMgUajwfvvv49u3bph9erVePHFF5Gbm4uBAwe2GBvHMBERkTUefBBITzeWv/8eGDNGvnhIXm0+6DsnJwdxcXE4deoUwsLCGn2v0+nQs2dPzJ07FykpKU1ex9PTEx988AEeeughwz5/f3+89dZbmDVrVotxMGEiIiJr9OsHHDtmLL/+OrBwoXzxkLzafAyTRqOBSqWCr6+v2e8zMjJQUVGBGTNmNHud4cOH44svvsCFCxdQX1+PNWvWQKvVYtSoUWaP12q1qKysNNmIiIiu19X/3Dg5SV1y5LjatIWppqYGw4cPR0REBFatWmX2mAl/LLqz8erXDszQaDS47777sHnzZri4uKBLly5Yt24dxjTRHrpo0SK89NJLZq/DFiYiImqt334DHnsMOHpUWgLlhhuApCTgrrvkjozkZFELU3p6Ojw9PQ3bjh07DN/pdDpMmzYN9fX1WLZsmdnzS0pKsHnz5lZ1qb3wwgu4ePEitm7ditzcXPztb3/D1KlT8fPPP5s9fuHChdBoNIbt9OnTlvw0IiIiAMCTTwL//S+Qnw9s3y61NDFZIotm+k5ISMDQoUMN5ZCQEABSspSUlISioiJkZmY22aKTlpYGf39/JCQkNHufEydO4P3338fhw4fRv39/AEBMTAx27NgBtVqN//znP43OcXd3h7u7uyU/h4iIqJHjx03LJ07IEwfZFosSJi8vL3h5eZnsa0iWCgoKkJWVBX9/f7PnCiGQlpaG5ORkuLq6Nnuf6upqAICTk2kDmLOzM+rr6y0JmYiIyCL33Qfs3y99dncHpkyRNx6yDVYN+q6rq0NiYiJyc3ORnp4OvV6P8vJylJeXo7a21uTYzMxMFBUVme2OKy0tRUREBPbu3QsAiIiIQN++fTFnzhzs3bsXJ06cwDvvvIMtW7bg7rvvtiZkIiIis06dAmJjgRdeAAYPBhYtAnbvBm65Re7IyBZYlTCVlJQgIyMDJSUliI2NRVBQkGHbtWuXybGpqamIj49HZGRko+vodDrk5+cbWpZcXV2xceNGBAQEYPLkyRgwYABWrlyJTz/91DBonIiIqC09/TRw8KA0UWVuLtCpE9CKaf/IQXDxXSIiIgAjR0qDvBs89xzw1lvyxUO2hWvJERGRw6upkcYuNQyd9fUFWpgukByM4hImtVqNqKgoDBkyRO5QiIjIDhw5Is219OSTQK9ewEcfAT//DERFyR0Z2RJ2yRERkUP785+Br782lp95BliyRL54yDYproWJiIjIEnq9abmuTp44yLYxYSIiIodVVgaMHQv4+EjlsDDpbTmia1k0cSUREZFS7NkDjBkDVFVJCdOaNcDEiYCnp9yRkS1iCxMRETmkd9+VkiUA0GiAzZuZLFHTmDAREZFDujY5YrJEzVFcwsRpBYiIqCUHDgB9+gC9e0vlmBhpSRSipnBaASIicijbtgF33QXodICzM5CeLk1aSdQcxbUwERERNWflSilZAqQpBb78Ut54yD4wYSIiIocSEtJ8mcgcTitAREQO47vvgMuXgSFDgFOngKFDgVdekTsqsgdMmIiIyCF88w2QkGAsv/suJ6mk1mOXHBEROYSNG5svEzWHCRMRETmE6GjT8s03yxMH2SfFdcmp1Wqo1Wror11NkYiIHNby5cCmTcDw4dLiuoMHA6+/LndUZE84DxMRESna2rVAUpKx/Je/AO+9J188ZJ/YJUdERIq2d2/zZaLWYMJERESKNnJk82Wi1lDcGCYiIqIGixZJXXKDBwM33CD9929/kzsqskdMmIiISJE+/xx46SVjuWdP4Lnn5IuH7Bu75IiISJGOH2++TGQJJkxERKRIkycDnToZy4mJ8sVC9k9xXXKch4mIyLHV1wOPPQasWgX06CEthzJihOnUAkSW4jxMRESkKKtXA9OnG8tDhnAqAbIeu+SIiEhRKipMy+fPyxMHKQsTJiIiUgwhgNtuA4KCjPv+8hf54iHlsCph0ul0mD9/PqKjo+Hh4YHg4GAkJyejrKzMcEx2djZUKpXZLScnp8lrnzhxAvfccw8CAgLg7e2NpKQknD171ppwiYhIwerqpIHegwcDly5JUwjs3g389a9yR0ZKYFXCVF1djby8PKSkpCAvLw/r16/HsWPHkJCQYDgmPj4eZ86cMdkeffRRhIeHY/DgwWave+XKFYwdOxYqlQqZmZnYuXMnamtrMXnyZNTX11sTMhERKdRXXwHffit9/v13YM0a4NZb5Y2JlMOqt+R8fHywZcsWk31Lly5FXFwciouLERYWBjc3NwQGBhq+1+l0yMjIwNy5c6FSqcxed+fOnTh58iT2799vGLCdlpYGPz8/ZGZm4s4777QmbCIiUiCdrvkykTXafAyTRqOBSqWCr6+v2e8zMjJQUVGBGTNmNHkNrVYLlUoFd3d3w75OnTrByckJP/74Y5PnVFZWmmxEROQYtFqge3cgJkYqu7gAb70lb0ykLG2aMNXU1GDBggV44IEHmnyVPzU1FePGjUNoaGiT17n11lvh4eGB+fPno7q6GleuXMFzzz2H+vp6nDlzxuw5ixcvho+Pj2Fr7vpERKQcNTXAqFHAuHHAwYPSIO/CQuChh+SOjJTEooQpPT0dnp6ehm3Hjh2G73Q6HaZNm4b6+nosW7bM7PklJSXYvHkzZs2a1ex9AgICsHbtWnzzzTfw9PQ0zKc0aNAgODs7mz1n4cKF0Gg0hu306dOW/DQiIrJTmzYBP/1kLC9fDvD/M1Nbs2gMU0JCAoYOHWooh4SEAJCSpaSkJBQVFSEzM7PJ1qW0tDT4+/ubDApvytixY3HixAlUVFTAxcUFvr6+CAwMRO/evc0e7+7ubtKFR0REjsHDo/kyUVuwKGHy8vKCl5eXyb6GZKmgoABZWVnw9/c3e64QAmlpaUhOToarq2ur79mtWzcAQGZmJs6dO9eqZIuIiByDRgOcPg2MHg1s2yYlS598IndUpERWvSVXV1eHxMRE5OXlYcOGDdDr9SgvLwcA+Pn5wc3NzXBsZmYmioqKzHbHlZaWYvTo0Vi5ciXi4uIASK1RkZGRCAgIwO7du/HXv/4VTz/9NPr162dNyEREpBCXLwPx8cAvv0jl++6T1o9zUdwqqWQLrHqsSkpKkJGRAQCIjY01+S4rKwujRo0ylFNTUxEfH4/IyMhG19HpdMjPz0d1dbVhX35+PhYuXIgLFy4gPDwczz//PJ5++mlrwiUiIgXZtcuYLAHAF18AK1YwYaL2wcV3iYjILv38szSNQMO/Yv7+wG+/AU1M8UdkFcWtJadWqxEVFYUhQ4bIHQoREbWTkhKpRWnCBKBHD+Cmm4D165ksUfthCxMREdmVqiogOho4dUoqDx4M7NkDOCmuCYBsCR8vIiKyK4cPG5MlAMjNBc6dky8ecgxMmIiIyK6EhwNduhjLgYHS+CWi9sR3CYiIyG788gvw6qvAsGFAZSXg5yetGWfB9H5E14UJExER2YXLl6UJKv+Y7g/BwUB2tmlrE1F7YZccERHZhVOnjMkSAJSVSbN8E3UEJkxERGQXevc2XVS3Vy8gLEy+eMixKC5h4jxMRETKs3u31B3n4wOMHw/MmSN1x3XuLHdk5Cg4DxMREdm0mhogJAS4cEEqd+oEFBYCQUHyxkWORXEtTEREpCznzxuTJUBKoEpK5IuHHBMTJiIismlBQUB8vLHcrx/Qv7988ZBjYsJEREQ2a9MmqTvu0CFg0iTgjTeAH3/kVALU8TiGiYiIbJJeL01MWVlp3HfgABATI19M5LjYwkRERDapttY0WQKAigp5YiFiwkRERDaprg6YPt1YvuUW07FMRB1JcQkT52EiIrJ/a9YAAQFAejowcqRU3r6d8y6RfDiGiYiIbE7XrsClS8byd99JE1YSyUVxLUxERGT/dDrTcm2tPHEQNWDCRERENiU/H3j0UWN59Gjgrrvki4cIAFzkDoCIiKjB8uXA//t/QH09EBkJfPghMGwY4MJ/rUhmbGEiIiKb8eKLUrIEAEePAidOMFki28CEiYiIbMa1M3hzRm+yFUyYiIjIJmRmAlOmAF5eUjkxEbj3XnljImqguIZOtVoNtVoNvV4vdyhERNRK77wDPPus9Nnfn0ugkO3hPExERCS7m24CCgqM5bffNiZQRLaAXXJERCS74GDTclCQPHEQNUVxXXJERGRfVqyQWpjOnpUW1502DXjgAbmjIjLV4S1MOp0O8+fPR3R0NDw8PBAcHIzk5GSUlZWZHHfs2DFMmTIF3bp1g7e3N2677TZkZWV1dLhERNSOXn4ZmDlTmn+poAD46itg6VJApZI7MiJTHZ4wVVdXIy8vDykpKcjLy8P69UDJH+UAAAPiSURBVOtx7NgxJCQkmBw3ceJE1NXVITMzE/v27UNsbCwmTZqE8vLyjg6ZiIjayTffGD/r9dKacUS2yCYGfefk5CAuLg6nTp1CWFgYKioqEBAQgO3bt2PEiBEAgKqqKnh7e2Pr1q0YPXp0o2totVpotVpDubKyEqGhoRz0TURkw2bMAD791Fj+7DPgwQdlC4eoSTYx6Fuj0UClUsHX1xcA4O/vj8jISKxcuRJXrlxBXV0dPvzwQ/To0QO33HKL2WssXrwYPj4+hi00NLQjfwIREVlArwdefRU4fx649VZg6FDgtdeYLJHtkr2FqaamBsOHD0dERARWrVpl2F9aWoopU6YgLy8PTk5O6NGjB7799lvExsaavQ5bmIiI7MeLL0rjlxqkpUmtTUS2qt1bmNLT0+Hp6WnYduzYYfhOp9Nh2rRpqK+vx7Jlywz7hRB44okn0L17d+zYsQN79+7FlClTMGnSJJw5c8bsfdzd3eHt7W2yERGRbfrpJ9Py7t3yxEHUWu3ewlRVVYWzZ88ayiEhIejcuTN0Oh2SkpJQWFiIzMxM+Pv7G47Ztm0bxo4di4sXL5okPjfeeCNmzZqFBQsWtHhfTlxJRGS7XnkF+Mc/jOVVq4Dp0+WLh6gl7T4Pk5eXF7waFgb6Q0OyVFBQgKysLJNkCZDepAMAJyfTBjAnJyfUNyxjTUREdkerBebNA3buBIYNA3r1AsaOZbJEtq/DJ66sq6tDYmIi8vLysGHDBuj1esNUAX5+fnBzc8OwYcPQtWtXPPzww/jHP/6Bzp07Y/ny5SgqKsLEiRM7OmQiImojr78O/Oc/xvIdd0jzMBHZug5/S66kpAQZGRkoKSlBbGwsgoKCDNuuXbsAAN26dcOmTZtw+fJl3HHHHRg8eDB+/PFH/O9//0MMV2MkIrJbx441XyayVbK/JddeOIaJiMj2rF0LJCUZy59/Li2FQmTrFLeWnFqthlqthl6vlzsUIiL6Q3U1cP/9wJYtQGQkcNdd0tilcePkjoyoddjCRERE7e7ll6W5lxpMny69GUdkL2xipm8iIlK2334zLZ87J08cRNeLCRMREbW7mTMBDw/ps7Mz8Pjj8sZDZCnFjWEiIiLbM2gQcPCgNKN3dDTAF57J3jBhIiKiDtGnj7T9/3bu2AZgEIaioBmARegZlUkZgIzwm0hR0N0ELp9ky/BHVnIAAIFgAgAIrgumtVaNMWrO+fUoAMAl/GECAAiuDaZzTu29q/derbWvxwEAfuzaYAIAeMt1N0wAAG8TTAAAgWACAAgEEwBAIJgAAALBBAAQCCYAgEAwAQAEggkAIBBMAADBA6rbUgPkbyA7AAAAAElFTkSuQmCC", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 20, "metadata": { }, "output_type": "execute_result" } ], "source": [ "fv_plot(27.18,28.0,.01)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "Calculate the coefficients of $m^{1/2}$ in $\\tilde f_m$ and $\\tilde v_m$" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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", 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", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 21, "metadata": { }, "output_type": "execute_result" } ], "source": [ "f_norms = [[mm,(-1)^mm*f_tilde_coeffs[mm]/(mm^0.5)] for mm in range(int(0.5*N_tilde_coeffs),N_tilde_coeffs)]\n", "v_norms = [[mm,(-1)^(mm+1)*v_tilde_coeffs[mm]/(mm^0.5)] for mm in range(int(0.5*N_tilde_coeffs),N_tilde_coeffs)]\n", "show(list_plot(f_norms)); show(list_plot(v_norms))" ] }, { "cell_type": "code", "execution_count": 0, "metadata": { "collapsed": false }, "outputs": [ ], "source": [ ] } ], "metadata": { "kernelspec": { "display_name": "SageMath (system-wide)", "language": "sagemath", "metadata": { "cocalc": { "description": "Open-source mathematical software system", "priority": -1, "url": "https://www.sagemath.org/" } }, "name": "sagemath", "resource_dir": "/ext/jupyter/kernels/sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.15" } }, "nbformat": 4, "nbformat_minor": 4 }