Untitled.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# nbi:hide_in\n",
    "#%matplotlib notebook\n",
    "from __future__ import print_function\n",
    "from ipywidgets import interact, interactive, fixed, interact_manual\n",
    "import ipywidgets as widgets\n",
    "import nbinteract as nbi\n",
    "from IPython.display import display\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from matplotlib.pyplot import figure, savefig\n",
    "import sys \n",
    "sys.path.append('/home/nico/.local/lib/python3.8/site-packages')\n",
    "from lcapy import Circuit\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "4cfc2d435e184ec0b31167f3a324d4ca",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=1, description='R', max=10, min=1), SelectMultiple(description='Toleranc…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#interact(R=(1,10,1))\n",
    "#interact(tol=(0.0,0.1,0.005))\n",
    "\n",
    "a = widgets.IntSlider(min=1, max=10, step=1)\n",
    "'''\n",
    "b = widgets.FloatText(\n",
    "    value=0.0,\n",
    "     min=0,\n",
    "    max=0.1,\n",
    "    step=0.01,\n",
    "    description='Tolerncia',\n",
    "    disabled=False\n",
    ")\n",
    "'''\n",
    "b = widgets.SelectMultiple(\n",
    "    options={'0%':0.0, '0.05%':0.005, '0.1%':0.001, '0.25%':0.0025, '0.5%':0.005, \n",
    "             '1%':0.01, '2%':0.02, '5%':0.05, '10%':0.1, '20%':0.2},\n",
    "    value=[0],\n",
    "    #rows=10,\n",
    "    description='Tolerancia de la resisitencia',\n",
    "    disabled=False\n",
    ")\n",
    "\n",
    "def response(R,tol):\n",
    "    \n",
    "    tol = tol[0]\n",
    "    tol = (np.random.uniform(low=-tol, high=tol, size=1)).item(0) \n",
    "    #tol = (np.random.normal(0, np.sqrt(tol), size=1)).item(0) \n",
    "   \n",
    "    R = (1 + tol) * R \n",
    "    \n",
    "    cct = Circuit()\n",
    " \n",
    "    cct.add('V 0_1 0 step 10;down')\n",
    "    cct.add('L 0_1 0_2 1e-3;right')\n",
    "    cct.add('C 0_2 1 1e-4;right')\n",
    "    cct.add('R 1 0_4 {R};down'.format(R=R))\n",
    "    cct.add('W 0_4 0; left')\n",
    "        \n",
    "    t = np.linspace(0, 0.01, 1000)\n",
    "    vr = cct.R.v.evaluate(t)\n",
    " \n",
    "    fig = figure()\n",
    "    #Note that we can add Greek symbols from LaTex into the figure text\n",
    "    ax = fig.add_subplot(111, title='Resistor voltage (R={:1.4f}$\\Omega$)'.format(R))\n",
    "    ax.plot(t, vr, linewidth=2)\n",
    "    ax.set_xlabel('Time (s)')\n",
    "    ax.set_ylabel('Resistor voltage (V)')\n",
    "    ax.grid(True)\n",
    "     \n",
    "    cct.draw()\n",
    "\n",
    "interact(response, R=a, tol=b);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n"
     },
     "metadata": {
      "image/png": {
       "height": 169,
       "width": 421
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support. ' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fcb779a7bd0>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#%matplotlib notebook\n",
    "from lcapy import R, C, L, s, j, Hs\n",
    "\n",
    "((R(1) + L(2)) | C(3)).draw()\n",
    "\n",
    "H = Hs((s - 2) * (s + 3) / (s * (s - 2 * j) * (s + 2 * j)))\n",
    "H.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n"
     },
     "metadata": {
      "image/png": {
       "height": 155,
       "width": 244
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\mathrm{R}(\\frac{10}{3})$"
      ],
      "text/plain": [
       "R(10/3)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#%%\n",
    "from lcapy import R\n",
    "Rtot = R(10) | R(5)\n",
    "Rtot.draw()\n",
    "Rtot\n",
    "Rtot = Rtot.simplify()\n",
    "Rtot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n"
     },
     "metadata": {
      "image/png": {
       "height": 264,
       "width": 362
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$$\\frac{1}{10 s + \\frac{1}{5} + \\frac{1}{20 s}}$$"
      ],
      "text/plain": [
       "       1       \n",
       "───────────────\n",
       "       1    1  \n",
       "10⋅s + ─ + ────\n",
       "       5   20⋅s"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#%%\n",
    "n = R(5) | L(20) | C(10)\n",
    "n.draw()\n",
    "n.Zs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n"
     },
     "metadata": {
      "image/png": {
       "height": 209,
       "width": 492
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{s + \\frac{1}{C R_{2}}}{s^{2} + \\frac{s \\left(C R_{1} R_{2} + L\\right)}{C L R_{2}} + \\frac{R_{1} + R_{2}}{C L R_{2}}} & - \\frac{1}{L \\left(s^{2} + \\frac{s \\left(C R_{1} R_{2} + L\\right)}{C L R_{2}} + \\frac{R_{1} + R_{2}}{C L R_{2}}\\right)}\\\\\\frac{1}{C \\left(s^{2} + \\frac{s \\left(C R_{1} R_{2} + L\\right)}{C L R_{2}} + \\frac{R_{1} + R_{2}}{C L R_{2}}\\right)} & \\frac{s + \\frac{R_{1}}{L}}{s^{2} + \\frac{s \\left(C R_{1} R_{2} + L\\right)}{C L R_{2}} + \\frac{R_{1} + R_{2}}{C L R_{2}}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡                  1                                                   ⎤\n",
       "⎢             s + ────                                                 ⎥\n",
       "⎢                 C⋅R₂                              -1                 ⎥\n",
       "⎢  ──────────────────────────────    ──────────────────────────────────⎥\n",
       "⎢   2   s⋅(C⋅R₁⋅R₂ + L)   R₁ + R₂      ⎛ 2   s⋅(C⋅R₁⋅R₂ + L)   R₁ + R₂⎞⎥\n",
       "⎢  s  + ─────────────── + ───────    L⋅⎜s  + ─────────────── + ───────⎟⎥\n",
       "⎢            C⋅L⋅R₂        C⋅L⋅R₂      ⎝          C⋅L⋅R₂        C⋅L⋅R₂⎠⎥\n",
       "⎢                                                                      ⎥\n",
       "⎢                                                      R₁              ⎥\n",
       "⎢                                                  s + ──              ⎥\n",
       "⎢                1                                     L               ⎥\n",
       "⎢──────────────────────────────────    ──────────────────────────────  ⎥\n",
       "⎢  ⎛ 2   s⋅(C⋅R₁⋅R₂ + L)   R₁ + R₂⎞     2   s⋅(C⋅R₁⋅R₂ + L)   R₁ + R₂  ⎥\n",
       "⎢C⋅⎜s  + ─────────────── + ───────⎟    s  + ─────────────── + ───────  ⎥\n",
       "⎣  ⎝          C⋅L⋅R₂        C⋅L⋅R₂⎠              C⋅L⋅R₂        C⋅L⋅R₂  ⎦"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from lcapy import Circuit\n",
    "a = Circuit(\"\"\"\n",
    "... V 1 0 {v(t)}; down\n",
    "... R1 1 2; right\n",
    "... L 2 3; right=1.5, i={i_L}\n",
    "... R2 3 0_3; down=1.5, i={i_{R2}}, v={v_{R2}}\n",
    "... W 0 0_3; right\n",
    "... W 3 3_a; right\n",
    "... C 3_a 0_4; down, i={i_C}, v={v_C}\n",
    "... W 0_3 0_4; right\"\"\")\n",
    "ss = a.ss\n",
    "a.draw()\n",
    "#ss.x      # The state variable vector is shown using the x attribute:\n",
    "#ss.x0     # The initial values of the state variable vector are shown using the x0 attribute:\n",
    "#ss.u      # The independent source vector is shown using the u attribute. In this example, there is a single independent source:\n",
    "#ss.y      # The output vector can either be the nodal voltages, the branch currents, or both. By default the nodal voltages are chosen. This vector is shown using the y attribute:\n",
    "#ss.state_equations()      # The state equations are shown using the state_equations method:\n",
    "#ss.output_equations()     # The output equations are shown using the output_equations method:\n",
    "#ss.A      # The A matrices are obtained using the attributes of the same name. For example,\n",
    "#ss.B      # The B matrices are obtained using the attributes of the same name. For example,\n",
    "#ss.C      # The C matrices are obtained using the attributes of the same name. For example,\n",
    "#ss.D      # The D matrices are obtained using the attributes of the same name. For example,\n",
    "#ss.X      # The Laplace transforms of the state variable vector, the independent source vector, and the output vector are accessed using the X, U, and Y attributes: For example,\n",
    "#ss.Phi    # The s-domain state-transition matrix is given by the Phi attribute and the time-domain state-transition matrix is given by the phi attribute. For example,\n",
    "#ss.G      # The system transfer functions are given by the G attribute and the impulse responses are given by the g attributes, for example:\n",
    "#ss.P      # The characteristic polynomial (system polynomial) is given by the P attribute, for example,\n",
    "\n",
    "#The roots of this polynomial are the eigenvalues of the system. These are given by the eigenvalues attribute. The corresponding eigenvectors are the columns of the modal matrix given by the M attribute. A diagonal matrix of the eigenvalues is returned by the Lambda attribute.\n",
    "#ss.eigenvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{\\mathrm{j} \\omega + 3}{\\mathrm{j} \\omega - 4}$$"
      ],
      "text/plain": [
       "ⅉ⋅ω + 3\n",
       "───────\n",
       "ⅉ⋅ω - 4"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from lcapy import s, j, omega, \n",
    "A= (j * omega + 3) / (j * omega - 4)\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{\\omega^{2} - 7 \\mathrm{j} \\omega - 12}{\\omega^{2} + 16}$$"
      ],
      "text/plain": [
       " 2             \n",
       "ω  - 7⋅ⅉ⋅ω - 12\n",
       "───────────────\n",
       "     2         \n",
       "    ω  + 16    "
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.rationalize_denominator()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\begin{cases} \\frac{2 \\sqrt{3} e^{- \\frac{t}{2}} \\sin{\\left(\\frac{\\sqrt{3} t}{2} \\right)}}{3} & \\text{for}\\: t \\geq 0 \\end{cases}$$"
      ],
      "text/plain": [
       "⎧      -t                      \n",
       "⎪      ───                     \n",
       "⎪       2     ⎛√3⋅t⎞           \n",
       "⎨2⋅√3⋅ℯ   ⋅sin⎜────⎟           \n",
       "⎪             ⎝ 2  ⎠           \n",
       "⎪───────────────────  for t ≥ 0\n",
       "⎩         3                    "
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from lcapy import t,f\n",
    "V = 1 / (s**2 +  s + 1)\n",
    "V(t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$10 \\mathrm{j} \\omega + 4 - \\frac{\\mathrm{j}}{20 \\omega}$$"
      ],
      "text/plain": [
       "              ⅉ  \n",
       "10⋅ⅉ⋅ω + 4 - ────\n",
       "             20⋅ω"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = R(4) + L(10) + C(20)\n",
    "n\n",
    "n.Z(omega)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$10 s + 4 + \\frac{1}{20 s}$$"
      ],
      "text/plain": [
       "            1  \n",
       "10⋅s + 4 + ────\n",
       "           20⋅s"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n.Z(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{10 \\left(s - \\frac{\\sqrt{14}}{20} + \\frac{1}{5}\\right) \\left(s + \\frac{\\sqrt{14}}{20} + \\frac{1}{5}\\right)}{s}$$"
      ],
      "text/plain": [
       "   ⎛    √14   1⎞ ⎛    √14   1⎞\n",
       "10⋅⎜s - ─── + ─⎟⋅⎜s + ─── + ─⎟\n",
       "   ⎝     20   5⎠ ⎝     20   5⎠\n",
       "──────────────────────────────\n",
       "              s               "
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    " n.Z(s).ZPK()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAS8AAABYCAYAAACkjnEVAAAJMmlDQ1BkZWZhdWx0X3JnYi5pY2MAAEiJlZVnUJNZF8fv8zzphUASQodQQ5EqJYCUEFoo0quoQOidUEVsiLgCK4qINEWQRQEXXJUia0UUC4uCAhZ0gywCyrpxFVFBWXDfGZ33HT+8/5l7z2/+c+bec8/5cAEgiINlwct7YlK6wNvJjhkYFMwE3yiMn5bC8fR0A9/VuxEArcR7ut/P+a4IEZFp/OW4uLxy+SmCdACg7GXWzEpPWeGjy0wPj//CZ1dYsFzgMt9Y4eh/eexLzr8s+pLj681dfhUKABwp+hsO/4b/c++KVDiC9NioyGymT3JUelaYIJKZttIJHpfL9BQkR8UmRH5T8P+V/B2lR2anr0RucsomQWx0TDrzfw41MjA0BF9n8cbrS48hRv9/z2dFX73kegDYcwAg+7564ZUAdO4CQPrRV09tua+UfAA67vAzBJn/eqiVDQ0IgALoQAYoAlWgCXSBETADlsAWOAAX4AF8QRDYAPggBiQCAcgCuWAHKABFYB84CKpALWgATaAVnAad4Dy4Aq6D2+AuGAaPgRBMgpdABN6BBQiCsBAZokEykBKkDulARhAbsoYcIDfIGwqCQqFoKAnKgHKhnVARVApVQXVQE/QLdA66At2EBqGH0Dg0A/0NfYQRmATTYQVYA9aH2TAHdoV94fVwNJwK58D58F64Aq6HT8Id8BX4NjwMC+GX8BwCECLCQJQRXYSNcBEPJBiJQgTIVqQQKUfqkVakG+lD7iFCZBb5gMKgaCgmShdliXJG+aH4qFTUVlQxqgp1AtWB6kXdQ42jRKjPaDJaHq2DtkDz0IHoaHQWugBdjm5Et6OvoYfRk+h3GAyGgWFhzDDOmCBMHGYzphhzGNOGuYwZxExg5rBYrAxWB2uF9cCGYdOxBdhK7EnsJewQdhL7HkfEKeGMcI64YFwSLg9XjmvGXcQN4aZwC3hxvDreAu+Bj8BvwpfgG/Dd+Dv4SfwCQYLAIlgRfAlxhB2ECkIr4RphjPCGSCSqEM2JXsRY4nZiBfEU8QZxnPiBRCVpk7ikEFIGaS/pOOky6SHpDZlM1iDbkoPJ6eS95CbyVfJT8nsxmpieGE8sQmybWLVYh9iQ2CsKnqJO4VA2UHIo5ZQzlDuUWXG8uIY4VzxMfKt4tfg58VHxOQmahKGEh0SiRLFEs8RNiWkqlqpBdaBGUPOpx6hXqRM0hKZK49L4tJ20Bto12iQdQ2fRefQ4ehH9Z/oAXSRJlTSW9JfMlqyWvCApZCAMDQaPkcAoYZxmjDA+SilIcaQipfZItUoNSc1Ly0nbSkdKF0q3SQ9Lf5RhyjjIxMvsl+mUeSKLktWW9ZLNkj0ie012Vo4uZynHlyuUOy33SB6W15b3lt8sf0y+X35OQVHBSSFFoVLhqsKsIkPRVjFOsUzxouKMEk3JWilWqUzpktILpiSTw0xgVjB7mSJleWVn5QzlOuUB5QUVloqfSp5Km8oTVYIqWzVKtUy1R1WkpqTmrpar1qL2SB2vzlaPUT+k3qc+r8HSCNDYrdGpMc2SZvFYOawW1pgmWdNGM1WzXvO+FkaLrRWvdVjrrjasbaIdo12tfUcH1jHVidU5rDO4Cr3KfFXSqvpVo7okXY5upm6L7rgeQ89NL0+vU++Vvpp+sP5+/T79zwYmBgkGDQaPDamGLoZ5ht2GfxtpG/GNqo3uryavdly9bXXX6tfGOsaRxkeMH5jQTNxNdpv0mHwyNTMVmLaazpipmYWa1ZiNsulsT3Yx+4Y52tzOfJv5efMPFqYW6RanLf6y1LWMt2y2nF7DWhO5pmHNhJWKVZhVnZXQmmkdan3UWmijbBNmU2/zzFbVNsK20XaKo8WJ45zkvLIzsBPYtdvNcy24W7iX7RF7J/tC+wEHqoOfQ5XDU0cVx2jHFkeRk4nTZqfLzmhnV+f9zqM8BR6f18QTuZi5bHHpdSW5+rhWuT5z03YTuHW7w+4u7gfcx9aqr01a2+kBPHgeBzyeeLI8Uz1/9cJ4eXpVez33NvTO9e7zofls9Gn2eedr51vi+9hP0y/Dr8ef4h/i3+Q/H2AfUBogDNQP3BJ4O0g2KDaoKxgb7B/cGDy3zmHdwXWTISYhBSEj61nrs9ff3CC7IWHDhY2UjWEbz4SiQwNCm0MXwzzC6sPmwnnhNeEiPpd/iP8ywjaiLGIm0iqyNHIqyiqqNGo62ir6QPRMjE1MecxsLDe2KvZ1nHNcbdx8vEf88filhICEtkRcYmjiuSRqUnxSb7JicnbyYIpOSkGKMNUi9WCqSOAqaEyD0tandaXTlz/F/gzNjF0Z45nWmdWZ77P8s85kS2QnZfdv0t60Z9NUjmPOT5tRm/mbe3KVc3fkjm/hbKnbCm0N39qzTXVb/rbJ7U7bT+wg7Ijf8VueQV5p3tudATu78xXyt+dP7HLa1VIgViAoGN1tubv2B9QPsT8M7Fm9p3LP58KIwltFBkXlRYvF/OJbPxr+WPHj0t6ovQMlpiVH9mH2Je0b2W+z/0SpRGlO6cQB9wMdZcyywrK3BzcevFluXF57iHAo45Cwwq2iq1Ktcl/lYlVM1XC1XXVbjXzNnpr5wxGHh47YHmmtVagtqv14NPbogzqnuo56jfryY5hjmceeN/g39P3E/qmpUbaxqPHT8aTjwhPeJ3qbzJqamuWbS1rgloyWmZMhJ+/+bP9zV6tua10bo63oFDiVcerFL6G/jJx2Pd1zhn2m9az62Zp2WnthB9SxqUPUGdMp7ArqGjzncq6n27K7/Ve9X4+fVz5ffUHyQslFwsX8i0uXci7NXU65PHsl+spEz8aex1cDr97v9eoduOZ67cZ1x+tX+zh9l25Y3Th/0+LmuVvsW523TW939Jv0t/9m8lv7gOlAxx2zO113ze92D64ZvDhkM3Tlnv296/d5928Prx0eHPEbeTAaMip8EPFg+mHCw9ePMh8tPN4+hh4rfCL+pPyp/NP637V+bxOaCi+M24/3P/N59niCP/Hyj7Q/Fifzn5Ofl08pTTVNG02fn3Gcufti3YvJlykvF2YL/pT4s+aV5quzf9n+1S8KFE2+Frxe+rv4jcyb42+N3/bMec49fZf4bmG+8L3M+xMf2B/6PgZ8nFrIWsQuVnzS+tT92fXz2FLi0tI/QiyQvpTNDAsAAAAGYktHRAD/AP8A/6C9p5MAAAAJcEhZcwAAFxIAABcSAWef0lIAAAAddEVYdFNvZnR3YXJlAEdQTCBHaG9zdHNjcmlwdCA5LjUw/rJdRQAADgJJREFUeJztnUFvG8cVx/9P8UUOBJdqAAtWIqsK4kt7CEAfeopRgP4ECX1JrqU+QBFQ6bkIyPYTiAHyAaSbD7mIQNBbD2JP7qk1gQRGgACNmFaA0aKIpod5jztacZe7y13uzOr9gIUtaTlciqs///PmvTdkjEFTIaI2gC6ADoB2xodNAIwBjI0x46quTVGU1aCmiRcRiVh1AbRiP54AmPG/Lm0+Ny5wMwCnsEJ2Wv7VKopSlMaIFxF1ABwDOHC+LS7q1BgTF6ykcZLc2hTAoboxRfGD4MWLRasPKzaAFZkRrGBNVxz7AFbIeohEcQxgqCKmKPUSrHgRUQtWtPr8rRmsqAwrej55LpmKjgAcGWNmVTyfoijpBCleLFxnsNO6GayQDKsWEkcwe7AiNgHwVAVMUdZPcOLFMakzWPGYAniWNZ5V8jWcwE4lZ7ACttZrUJTbzkbdF5AHIuohEq4JgMd1iAY/52PY+FcLwDlfm6IoayIY58Vu55y/HBljDuu8HoGIjmGnkUBNYqoot5EgnJcT4wI8Ei4A4GuRRYIzXqFUFKVivHdeseD82BjztOZLWggRncGma2gQX1HWQAjOawArXFMAz2q+ljSewQpXGzZZVlGUCvHaeXEC6hkCWdGLrYQ+1URWRakO353XgP8d+S5cwHwVUuJf6r5uCUTUIaLjqlaciahNRAOu261i/A6P31l+tj9467z4RjgGMDXGvFv39eSBiF7C5oAdGmNGdV+PUi1OvBMA3l21LC1l/BmPX2o81blfg/pb89l5SdlPJeU+FSPX3OcFB6WhsFtxHUup7otDETJ+q4Lxu4jqdg9Cylf0Urz4FyifBME5F77mMexrCOZmUAohH7LSMqlX8geW3D+nsa/LHl/is5VMTavAS/FC9EkTousSRHSDiiMo2XFc1wzAIaKKi1IEhnMGZawj2BX30tyR4+pmsKvlMwCdUGJf3okXf2qJ+gfbANBpXtjRqWNjEdc14jiUfNiW5Y5knBHH0WT8styRO740OHC/7zfGGK8O2F+cAXBS97WU8FpO+LX06r4WPUp/bzv83l4AaDnff1nGew7r4C54rAPn+/K9zorjH/A48/GTntPXwzvnhah7ae4cKSLqsxUuHSI6KOCg5DUEYcOVXMRdl1CW+5K2S2NzffWyLHcUd3Xg1yEzhv7CR3mEd6kSRHQB+6blXnImogEq2jijyNgsdhcAZsaY7bKvSakHJ3l6CluMP4v9XO7hwonKTvrCtTH4nnqJgn8jy8bgONtLVJSWUSZeOS/+pbZgVxlLzZWpA37jJwBaWrDdKCR5OqkB5kruKLbafk38SnJHSa4O/PUp/9xr97UBAET0ZGdn55937969unv37tXDhw9fEdF+DdcjU77ghctBbm4VrwbAwtJGehrPEPZ97xb80BLRS1ptnwfuCy4GLRvfm8A9Ee2//fbbL7a3t38iIvPee+/9m4g+BYANIvr4zTff/PqDDz74+fPnz+n58+f06NGj3c3NzSkRPVnztcob7X0pUA7ktah4NYOlydOruCOekrZhQw0LxXEVd5Tm6pzxx+C0j7qTVu/fv//3nZ2dXx4fH2+cnZ3hww8/3ALwx4cPH36B/f39//T7fROn2+2avb292TpXD2DtuAEwWOHxK63ClD32qq9JD38ORCvhLzOcK6t511YjMzzuJMv9Ame1M+drOEeG1dA8r7WqY3d398X7779/ZWIMBgOzubl5RQDMxcUFWq3r7nMymeDx48fAehNFnwD4NWws4SjpJA6eL0Ja5yyKQ0zMChvHFl0McIK7fwHw56LPXwL3APyrxudfJ1W91kMAP0PGmlUiOoHNyUq9n53zcwXLnZrHrNczX2gwGWoYkxYNUs7/BPZv8L/Lzs3C/v7+7z777LM7vd5N8/fOO++YOwBuCBcAHBzMZzmVpB4ksJPxvKRfpGzKsWjaWfeqyQ7W+7uMswXgssbnXydVvda/AXgji1AwI0T7fi4VLzilRsuES86DFa8+ojhVGvFSo2WMYGcOfWRLXfoDgAcA/ooSfv937tzZWKRNAPDWW28BrVbrp8FgEHdmpt/vm/v37/9vnTYRzZw29lZ5TXqEfcA6nSzTtBZiSaMZx5ek2NR7EwWmsbietNpecm6haWzasbe396rb7Zo45+fnBoDZ2Nra+vLzzz83p6eRGA+HQwyHQ3z//fe/X007c1O3O6oCDdTfbrIG7l3XlWe1XRxXnvEz/Z2ZfCVD86TXLGNn4dtvv/34q6++MkdHkWmdTCb46KOPzKNHj/4BYwy2t7e/3tzcvNra2rra2tq62tzcvNrb2/uihk8pUe+zgo/30XlJALaS69LD/wMZ3BEKlv0ggztCQVfHj71RRpRyTq7FiYzP/+m9e/d+AmAePHhwBcDs7u6+MIbLg3744YffvH79euPy8rJ/eXnZf/369cY333zz27IUNAdNyu8SZNLeRFepZCPVHXE6giSN5loQMtncUVFXBz4/z/il3ufGmD/9+OOPbwD45LvvvusD+MWrV69+BfhZHmQAwBhDBR7rVXkQP67w61GaQawc58benqt23nVWKYEFJUOrlis5e6beWAV1SuAWPneVeFUexIyBeYfHvCSlSZTBCDmTZ53X0KSkWyUnae7I6WRauPFmmjtaxdU540+Q3KussKtbFW/FCwU6MRhjKtuowxgzLWCJ5TUE25dMKY25uMRKhsoKdLvju/kF8U6vRUnqllF6oD4rPoqX/JKDaUebgoqXAmCxO4p1Ml3pj3+ROyrD1TnjjxHr5FqGq1sF78SL32TpxBBsHyy+MeXGaeJChJKfuDuKdzItbfzYv2W5ongn17JcXSG8Ey8muM0AFpA3m1lpODF31EfJ4mJs+Zu4owFKcnXO+CNEfe4HqHmTHF/FS35JvRDdF7uu2mIBitfMt8Xjf0clO/NF45e5iBVP+6jt/vYuVUJgZe/Dzqef1n09eXAKZjMV5Cq3Cyc1AliQOlHC+JIaAZScvhBL+6i126qvzguIGroFsxUTcGM7rJC3blOqQ+6LcUWr4+KGynZ1kvYhoZCyXV0uvHVegN1QA7YsZ2GvcN/gT6Uz2O4R6roUpUK8Fi8AIKJzWDEYGWMO676eNIjoGDbWFYTYKkrI+DxtFA4RBe+TmhDWDrvEHnj3YRUuRakW750XME+2O+EvC9V/VUns+p6ZFTq2KoqSjRCcl+SvSPxoULDusRL4Wo75y6EKl6KshyDECwCMMUPYVZQWgBOeptUKX8MJ7DWNNECvKOsjGPECAA7YyzLzgIiOC+5btzIcnHc3H/V6MUFRmkYQMa84zlStBVsHebSuwlDO4xqA99bj5/YqBqfcXvjDXPZ+nMImw660c5avBClewLwE5wRRpvII1gFVUgTNbUzcerQZbHM37dWllAZvlyYdHCawIiQ7dKcKkLPiPeIwi4iZfP+wUSJWZr/pdR+wzmuAqIe3gXVkufp0L3mOA0S7Gkmf7gFK7tWthx7G2Ka7C46lO0/xfZ/YAx8N3MUqWOflssAVAfZTawzb4TFvB9Q2bEcLsd9Cpe5OUTgp2w2BLC3xcTaTPTXGPFsydhsF20H7xp26L6AM+M09JKIhrIh1EdntPhGJBZc20XExa8O6uAP+v9vpUmq5VLSUdTAz+Vet5UN72Yf0GPb+7iLbJrJe0wjxEkTEYIVMCqSlm2Se/ROnsIJVS4dIRcmJrLgvEy/5eSP2Em2UeLmw6IwBHPE0sIXIYbVjp08QObJZ3mmmopQJf/DKvTpD9u4Ny0RJ7vtGlK41VrxcHDFSF6X4Tht2wUlWC3sAzonoaUrYYgw7y1gmXuLQGvF30IiAvaI0BSLqxEMVHGifmYSmnE6DwKkx5nHK2C8BwBjzbomXXBtBZdgrStNJiLGOYZtyLnRWPKUcAmgnneNsCNOYEjYVL0XxBCJa1jU4cVrI08wxkjet6cKmUjQmSVXFS1H84QQ2XysXjts6RLJ4dfjnSHJnoaHipSj+MMHiad0BbMwrKdDeA6I9T+PixFPGsbNiGd/1OkhuxWqjogSCVIXMcQqt0zZzkV2sp3xIUbbQATDlKekBolXHoFHxUhRPMMYcEdGAndIU0ea080LrBKaIGmICVujc2JbUAAuNCNoHnSohFfNp5RT8ieTa6GFSwp+Tld+DfcPHsO1EjmLnubWUkkTYiBtCqR+ntnYKO93TsrQFBCdeLBwiLm0AbWMMJZx7DJv7Igl/0kYndWcfZ8Pb1H753L7kMGP2s6IoJRJiwH4G+2l0iJRMYXZcHdduc6b9Ka5b6EWIYCUGNtn1zVS4FKUeghMvY0zaqotLB9eDlsIEdhu1xKAl2/QxUpL+YIWtMTkzihIawYlXDrpYXGUvTilenB1HhCnJfbW144Si1EcjxSvjphxpmcyAFa8ZFogXx86084Si1EgjxQvLXdVSOJZ1CqC1YJ9InTIqSs00VbzKQgTqRsmFLl8rSr2oeKXAMa0pgK5MRXkVU6eMilIzjRSvjIH0rCkO8bSJdlrul6Io66GR4sXMkF7DldU9zaeOTanGV5Qm0GTxOsXi/kcdpFfoX4NjW6fgnYgQOTFFUWqkEeKVkBoxgu0+Gf9ZG/kFSISurZtzKIofBFfbCABEJA3bZIeV+e4/boE0B9e7sE3YZrDOqcWlRXmf8wK2qDutul9RlDURpHjlgeNU0sco9+7ZzjhdXG/opihKjTRevBRFaSaNiHkpinL7UPFSFCVIVLwURQkSFS9FUYJExUtRlCBR8VIUJUhUvBRFCRIVL0VRgkTFS1GUIPk/VSS5sEQUbQ0AAAAASUVORK5CYII=\n"
     },
     "metadata": {
      "image/png": {
       "height": 88,
       "width": 303
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n"
     },
     "metadata": {
      "image/png": {
       "height": 169,
       "width": 244
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\mathrm{G}(\\frac{1}{5}) | \\mathrm{I}(2)$"
      ],
      "text/plain": [
       "G(1/5) | I(2)"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T = Vdc(10) + R(5)\n",
    "T.draw()\n",
    "n = T.norton()\n",
    "n.draw()\n",
    "n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n"
     },
     "metadata": {
      "image/png": {
       "height": 168,
       "width": 244
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n"
     },
     "metadata": {
      "image/png": {
       "height": 88,
       "width": 303
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\mathrm{R}(5) + \\mathrm{V}(50)$"
      ],
      "text/plain": [
       "R(5) + V(50)"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = Idc(10) | R(5)\n",
    "n.draw()\n",
    "T = n.thevenin()\n",
    "T.draw()\n",
    "T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{3 s + 20}{s^{3}}$$"
      ],
      "text/plain": [
       "3⋅s + 20\n",
       "────────\n",
       "    3   \n",
       "   s    "
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = 10 * t ** 2 + 3 * t\n",
    "v\n",
    "V=v.laplace()\n",
    "V"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}