Fix 'Custom Display Logic' example notebook for Python 3

IPython/core/display.py

@@ -1,556 +1,558 b''
 # -*- coding: utf-8 -*-
 """Top-level display functions for displaying object in different formats.
 
 Authors:
 
 * Brian Granger
 """
 
 #-----------------------------------------------------------------------------
 #       Copyright (C) 2008-2011 The IPython Development Team
 #
 #  Distributed under the terms of the BSD License.  The full license is in
 #  the file COPYING, distributed as part of this software.
 #-----------------------------------------------------------------------------
 
 #-----------------------------------------------------------------------------
 # Imports
 #-----------------------------------------------------------------------------
 
 from __future__ import print_function
 
 from xml.dom import minidom
 
 from .displaypub import (
     publish_pretty, publish_html,
     publish_latex, publish_svg,
     publish_png, publish_json,
     publish_javascript, publish_jpeg
 )
 
+from IPython.utils.py3compat import string_types
+
 #-----------------------------------------------------------------------------
 # Main functions
 #-----------------------------------------------------------------------------
 
 def display(*objs, **kwargs):
     """Display a Python object in all frontends.
 
     By default all representations will be computed and sent to the frontends.
     Frontends can decide which representation is used and how.
 
     Parameters
     ----------
     objs : tuple of objects
         The Python objects to display.
     include : list or tuple, optional
         A list of format type strings (MIME types) to include in the
         format data dict. If this is set *only* the format types included
         in this list will be computed.
     exclude : list or tuple, optional
         A list of format type string (MIME types) to exclue in the format
         data dict. If this is set all format types will be computed,
         except for those included in this argument.
     """
     include = kwargs.get('include')
     exclude = kwargs.get('exclude')
 
     from IPython.core.interactiveshell import InteractiveShell
     inst = InteractiveShell.instance()
     format = inst.display_formatter.format
     publish = inst.display_pub.publish
 
     for obj in objs:
         format_dict = format(obj, include=include, exclude=exclude)
         publish('IPython.core.display.display', format_dict)
 
 
 def display_pretty(*objs, **kwargs):
     """Display the pretty (default) representation of an object.
 
     Parameters
     ----------
     objs : tuple of objects
         The Python objects to display, or if raw=True raw text data to
         display.
     raw : bool
         Are the data objects raw data or Python objects that need to be
         formatted before display? [default: False]
     """
     raw = kwargs.pop('raw',False)
     if raw:
         for obj in objs:
             publish_pretty(obj)
     else:
         display(*objs, include=['text/plain'])
 
 
 def display_html(*objs, **kwargs):
     """Display the HTML representation of an object.
 
     Parameters
     ----------
     objs : tuple of objects
         The Python objects to display, or if raw=True raw HTML data to
         display.
     raw : bool
         Are the data objects raw data or Python objects that need to be
         formatted before display? [default: False]
     """
     raw = kwargs.pop('raw',False)
     if raw:
         for obj in objs:
             publish_html(obj)
     else:
         display(*objs, include=['text/plain','text/html'])
 
 
 def display_svg(*objs, **kwargs):
     """Display the SVG representation of an object.
 
     Parameters
     ----------
     objs : tuple of objects
         The Python objects to display, or if raw=True raw svg data to
         display.
     raw : bool
         Are the data objects raw data or Python objects that need to be
         formatted before display? [default: False]
     """
     raw = kwargs.pop('raw',False)
     if raw:
         for obj in objs:
             publish_svg(obj)
     else:
         display(*objs, include=['text/plain','image/svg+xml'])
 
 
 def display_png(*objs, **kwargs):
     """Display the PNG representation of an object.
 
     Parameters
     ----------
     objs : tuple of objects
         The Python objects to display, or if raw=True raw png data to
         display.
     raw : bool
         Are the data objects raw data or Python objects that need to be
         formatted before display? [default: False]
     """
     raw = kwargs.pop('raw',False)
     if raw:
         for obj in objs:
             publish_png(obj)
     else:
         display(*objs, include=['text/plain','image/png'])
 
 
 def display_jpeg(*objs, **kwargs):
     """Display the JPEG representation of an object.
 
     Parameters
     ----------
     objs : tuple of objects
         The Python objects to display, or if raw=True raw JPEG data to
         display.
     raw : bool
         Are the data objects raw data or Python objects that need to be
         formatted before display? [default: False]
     """
     raw = kwargs.pop('raw',False)
     if raw:
         for obj in objs:
             publish_jpeg(obj)
     else:
         display(*objs, include=['text/plain','image/jpeg'])
 
 
 def display_latex(*objs, **kwargs):
     """Display the LaTeX representation of an object.
 
     Parameters
     ----------
     objs : tuple of objects
         The Python objects to display, or if raw=True raw latex data to
         display.
     raw : bool
         Are the data objects raw data or Python objects that need to be
         formatted before display? [default: False]
     """
     raw = kwargs.pop('raw',False)
     if raw:
         for obj in objs:
             publish_latex(obj)
     else:
         display(*objs, include=['text/plain','text/latex'])
 
 
 def display_json(*objs, **kwargs):
     """Display the JSON representation of an object.
     
     Note that not many frontends support displaying JSON.
 
     Parameters
     ----------
     objs : tuple of objects
         The Python objects to display, or if raw=True raw json data to
         display.
     raw : bool
         Are the data objects raw data or Python objects that need to be
         formatted before display? [default: False]
     """
     raw = kwargs.pop('raw',False)
     if raw:
         for obj in objs:
             publish_json(obj)
     else:
         display(*objs, include=['text/plain','application/json'])
 
 
 def display_javascript(*objs, **kwargs):
     """Display the Javascript representation of an object.
 
     Parameters
     ----------
     objs : tuple of objects
         The Python objects to display, or if raw=True raw javascript data to
         display.
     raw : bool
         Are the data objects raw data or Python objects that need to be
         formatted before display? [default: False]
     """
     raw = kwargs.pop('raw',False)
     if raw:
         for obj in objs:
             publish_javascript(obj)
     else:
         display(*objs, include=['text/plain','application/javascript'])
 
 #-----------------------------------------------------------------------------
 # Smart classes
 #-----------------------------------------------------------------------------
 
 
 class DisplayObject(object):
     """An object that wraps data to be displayed."""
 
     _read_flags = 'r'
 
     def __init__(self, data=None, url=None, filename=None):
         """Create a display object given raw data.
 
         When this object is returned by an expression or passed to the
         display function, it will result in the data being displayed
         in the frontend. The MIME type of the data should match the
         subclasses used, so the Png subclass should be used for 'image/png'
         data. If the data is a URL, the data will first be downloaded
         and then displayed. If
 
         Parameters
         ----------
         data : unicode, str or bytes
             The raw data or a URL to download the data from.
         url : unicode
             A URL to download the data from.
         filename : unicode
             Path to a local file to load the data from.
         """
-        if data is not None and data.startswith('http'):
+        if data is not None and isinstance(data, string_types) and data.startswith('http'):
             self.url = data
             self.filename = None
             self.data = None
         else:
             self.data = data
             self.url = url
             self.filename = None if filename is None else unicode(filename)
         self.reload()
 
     def reload(self):
         """Reload the raw data from file or URL."""
         if self.filename is not None:
             with open(self.filename, self._read_flags) as f:
                 self.data = f.read()
         elif self.url is not None:
             try:
                 import urllib2
                 response = urllib2.urlopen(self.url)
                 self.data = response.read()
                 # extract encoding from header, if there is one:
                 encoding = None
                 for sub in response.headers['content-type'].split(';'):
                     sub = sub.strip()
                     if sub.startswith('charset'):
                         encoding = sub.split('=')[-1].strip()
                         break
                 # decode data, if an encoding was specified
                 if encoding:
                     self.data = self.data.decode(encoding, 'replace')
             except:
                 self.data = None
 
 class Pretty(DisplayObject):
 
     def _repr_pretty_(self):
         return self.data
 
 
 class HTML(DisplayObject):
 
     def _repr_html_(self):
         return self.data
 
 
 class Math(DisplayObject):
 
     def _repr_latex_(self):
         s = self.data.strip('$')
         return "$$%s$$" % s
 
 
 class Latex(DisplayObject):
 
     def _repr_latex_(self):
         return self.data
 
 
 class SVG(DisplayObject):
     
     # wrap data in a property, which extracts the <svg> tag, discarding
     # document headers
     _data = None
     
     @property
     def data(self):
         return self._data
     
     @data.setter
     def data(self, svg):
         if svg is None:
             self._data = None
             return
         # parse into dom object
         x = minidom.parseString(svg)
         # get svg tag (should be 1)
         found_svg = x.getElementsByTagName('svg')
         if found_svg:
             svg = found_svg[0].toxml()
         else:
             # fallback on the input, trust the user
             # but this is probably an error.
             pass
         self._data = svg
     
     def _repr_svg_(self):
         return self.data
 
 
 class JSON(DisplayObject):
 
     def _repr_json_(self):
         return self.data
 
 css_t = """$("head").append($("<link/>").attr({
   rel:  "stylesheet",
   type: "text/css",
   href: "%s"
 }));
 """
 
 lib_t1 = """$.getScript("%s", function () {
 """
 lib_t2 = """});
 """
 
 class Javascript(DisplayObject):
 
     def __init__(self, data=None, url=None, filename=None, lib=None, css=None):
         """Create a Javascript display object given raw data.
 
         When this object is returned by an expression or passed to the
         display function, it will result in the data being displayed
         in the frontend. If the data is a URL, the data will first be
         downloaded and then displayed. 
         
         In the Notebook, the containing element will be available as `element`,
         and jQuery will be available.  The output area starts hidden, so if
         the js appends content to `element` that should be visible, then
         it must call `container.show()` to unhide the area.
 
         Parameters
         ----------
         data : unicode, str or bytes
             The Javascript source code or a URL to download it from.
         url : unicode
             A URL to download the data from.
         filename : unicode
             Path to a local file to load the data from.
         lib : list or str
             A sequence of Javascript library URLs to load asynchronously before
             running the source code. The full URLs of the libraries should
             be given. A single Javascript library URL can also be given as a
             string.
         css: : list or str
             A sequence of css files to load before running the source code.
             The full URLs of the css files should be give. A single css URL
             can also be given as a string.
         """
         if isinstance(lib, basestring):
             lib = [lib]
         elif lib is None:
             lib = []
         if isinstance(css, basestring):
             css = [css]
         elif css is None:
             css = []
         if not isinstance(lib, (list,tuple)):
             raise TypeError('expected sequence, got: %r' % lib)
         if not isinstance(css, (list,tuple)):
             raise TypeError('expected sequence, got: %r' % css)
         self.lib = lib
         self.css = css
         super(Javascript, self).__init__(data=data, url=url, filename=filename)
 
     def _repr_javascript_(self):
         r = ''
         for c in self.css:
             r += css_t % c
         for l in self.lib:
             r += lib_t1 % l
         r += self.data
         r += lib_t2*len(self.lib)
         return r
 
 
 class Image(DisplayObject):
 
     _read_flags = 'rb'
     _FMT_JPEG = u'jpeg'
     _FMT_PNG = u'png'
     _ACCEPTABLE_EMBEDDINGS = [_FMT_JPEG, _FMT_PNG]
 
     def __init__(self, data=None, url=None, filename=None, format=u'png', embed=None, width=None, height=None):
         """Create a display an PNG/JPEG image given raw data.
 
         When this object is returned by an expression or passed to the
         display function, it will result in the image being displayed
         in the frontend.
 
         Parameters
         ----------
         data : unicode, str or bytes
             The raw data or a URL to download the data from.
         url : unicode
             A URL to download the data from.
         filename : unicode
             Path to a local file to load the data from.
         format : unicode
             The format of the image data (png/jpeg/jpg). If a filename or URL is given
             for format will be inferred from the filename extension.
         embed : bool
             Should the image data be embedded using a data URI (True) or be
             loaded using an <img> tag. Set this to True if you want the image
             to be viewable later with no internet connection in the notebook.
 
             Default is `True`, unless the keyword argument `url` is set, then
             default value is `False`.
 
             Note that QtConsole is not able to display images if `embed` is set to `False`
         width : int
             Width to which to constrain the image in html
         height : int
             Height to which to constrain the image in html
 
         Examples
         --------
         # embed implicitly True, works in qtconsole and notebook
         Image('http://www.google.fr/images/srpr/logo3w.png')
 
         # embed implicitly False, does not works in qtconsole but works in notebook if
         # internet connection available
         Image(url='http://www.google.fr/images/srpr/logo3w.png')
 
         """
         if filename is not None:
             ext = self._find_ext(filename)
         elif url is not None:
             ext = self._find_ext(url)
         elif data is None:
             raise ValueError("No image data found. Expecting filename, url, or data.")
-        elif data.startswith('http'):
+        elif isinstance(data, string_types) and data.startswith('http'):
             ext = self._find_ext(data)
         else:
             ext = None
 
         if ext is not None:
             format = ext.lower()
             if ext == u'jpg' or ext == u'jpeg':
                 format = self._FMT_JPEG
             if ext == u'png':
                 format = self._FMT_PNG
 
         self.format = unicode(format).lower()
         self.embed = embed if embed is not None else (url is None)
 
         if self.embed and self.format not in self._ACCEPTABLE_EMBEDDINGS:
             raise ValueError("Cannot embed the '%s' image format" % (self.format))
         self.width = width
         self.height = height
         super(Image, self).__init__(data=data, url=url, filename=filename)
 
     def reload(self):
         """Reload the raw data from file or URL."""
         if self.embed:
             super(Image,self).reload()
 
     def _repr_html_(self):
         if not self.embed:
             width = height = ''
             if self.width:
                 width = ' width="%d"' % self.width
             if self.height:
                 height = ' height="%d"' % self.height
             return u'<img src="%s"%s%s/>' % (self.url, width, height)
 
     def _repr_png_(self):
         if self.embed and self.format == u'png':
             return self.data
 
     def _repr_jpeg_(self):
         if self.embed and (self.format == u'jpeg' or self.format == u'jpg'):
             return self.data
 
     def _find_ext(self, s):
         return unicode(s.split('.')[-1].lower())
 
 
 def clear_output(stdout=True, stderr=True, other=True):
     """Clear the output of the current cell receiving output.
     
     Optionally, each of stdout/stderr or other non-stream data (e.g. anything
     produced by display()) can be excluded from the clear event.
     
     By default, everything is cleared.
     
     Parameters
     ----------
     stdout : bool [default: True]
         Whether to clear stdout.
     stderr : bool [default: True]
         Whether to clear stderr.
     other : bool [default: True]
         Whether to clear everything else that is not stdout/stderr
         (e.g. figures,images,HTML, any result of display()).
     """
     from IPython.core.interactiveshell import InteractiveShell
     if InteractiveShell.initialized():
         InteractiveShell.instance().display_pub.clear_output(
             stdout=stdout, stderr=stderr, other=other,
         )
     else:
         from IPython.utils import io
         if stdout:
             print('\033[2K\r', file=io.stdout, end='')
             io.stdout.flush()
         if stderr:
             print('\033[2K\r', file=io.stderr, end='')
             io.stderr.flush()
         

IPython/utils/py3compat.py

@@ -1,179 +1,183 b''
 # coding: utf-8
 """Compatibility tricks for Python 3. Mainly to do with unicode."""
 import __builtin__
 import functools
 import sys
 import re
 import types
 
 from .encoding import DEFAULT_ENCODING
 
 orig_open = open
 
 def no_code(x, encoding=None):
     return x
 
 def decode(s, encoding=None):
     encoding = encoding or DEFAULT_ENCODING
     return s.decode(encoding, "replace")
 
 def encode(u, encoding=None):
     encoding = encoding or DEFAULT_ENCODING
     return u.encode(encoding, "replace")
 
 
 def cast_unicode(s, encoding=None):
     if isinstance(s, bytes):
         return decode(s, encoding)
     return s
 
 def cast_bytes(s, encoding=None):
     if not isinstance(s, bytes):
         return encode(s, encoding)
     return s
 
 def _modify_str_or_docstring(str_change_func):
     @functools.wraps(str_change_func)
     def wrapper(func_or_str):
         if isinstance(func_or_str, basestring):
             func = None
             doc = func_or_str
         else:
             func = func_or_str
             doc = func.__doc__
         
         doc = str_change_func(doc)
         
         if func:
             func.__doc__ = doc
             return func
         return doc
     return wrapper
 
 if sys.version_info[0] >= 3:
     PY3 = True
     
     input = input
     builtin_mod_name = "builtins"
     
     str_to_unicode = no_code
     unicode_to_str = no_code
     str_to_bytes = encode
     bytes_to_str = decode
     cast_bytes_py2 = no_code
     
+    string_types = (str,)
+    
     def isidentifier(s, dotted=False):
         if dotted:
             return all(isidentifier(a) for a in s.split("."))
         return s.isidentifier()
     
     open = orig_open
     
     MethodType = types.MethodType
     
     def execfile(fname, glob, loc=None):
         loc = loc if (loc is not None) else glob
         with open(fname, 'rb') as f:
             exec compile(f.read(), fname, 'exec') in glob, loc
     
     # Refactor print statements in doctests.
     _print_statement_re = re.compile(r"\bprint (?P<expr>.*)$", re.MULTILINE)
     def _print_statement_sub(match):
         expr = match.groups('expr')
         return "print(%s)" % expr
     
     @_modify_str_or_docstring
     def doctest_refactor_print(doc):
         """Refactor 'print x' statements in a doctest to print(x) style. 2to3
         unfortunately doesn't pick up on our doctests.
         
         Can accept a string or a function, so it can be used as a decorator."""
         return _print_statement_re.sub(_print_statement_sub, doc)
     
     # Abstract u'abc' syntax:
     @_modify_str_or_docstring
     def u_format(s):
         """"{u}'abc'" --> "'abc'" (Python 3)
         
         Accepts a string or a function, so it can be used as a decorator."""
         return s.format(u='')
 
 else:
     PY3 = False
     
     input = raw_input
     builtin_mod_name = "__builtin__"
     
     str_to_unicode = decode
     unicode_to_str = encode
     str_to_bytes = no_code
     bytes_to_str = no_code
     cast_bytes_py2 = cast_bytes
     
+    string_types = (str, unicode)
+    
     import re
     _name_re = re.compile(r"[a-zA-Z_][a-zA-Z0-9_]*$")
     def isidentifier(s, dotted=False):
         if dotted:
             return all(isidentifier(a) for a in s.split("."))
         return bool(_name_re.match(s))
     
     class open(object):
         """Wrapper providing key part of Python 3 open() interface."""
         def __init__(self, fname, mode="r", encoding="utf-8"):
             self.f = orig_open(fname, mode)
             self.enc = encoding
         
         def write(self, s):
             return self.f.write(s.encode(self.enc))
         
         def read(self, size=-1):
             return self.f.read(size).decode(self.enc)
         
         def close(self):
             return self.f.close()
         
         def __enter__(self):
             return self
         
         def __exit__(self, etype, value, traceback):
             self.f.close()
     
     def MethodType(func, instance):
         return types.MethodType(func, instance, type(instance))
     
     # don't override system execfile on 2.x:
     execfile = execfile
     
     def doctest_refactor_print(func_or_str):
         return func_or_str
 
 
     # Abstract u'abc' syntax:
     @_modify_str_or_docstring
     def u_format(s):
         """"{u}'abc'" --> "u'abc'" (Python 2)
         
         Accepts a string or a function, so it can be used as a decorator."""
         return s.format(u='u')
 
     if sys.platform == 'win32':
         def execfile(fname, glob=None, loc=None):
             loc = loc if (loc is not None) else glob
             # The rstrip() is necessary b/c trailing whitespace in files will
             # cause an IndentationError in Python 2.6 (this was fixed in 2.7,
             # but we still support 2.6).  See issue 1027.
             scripttext = __builtin__.open(fname).read().rstrip() + '\n'
             # compile converts unicode filename to str assuming
             # ascii. Let's do the conversion before calling compile
             if isinstance(fname, unicode):
                 filename = unicode_to_str(fname)
             else:
                 filename = fname
             exec compile(scripttext, filename, 'exec') in glob, loc
     else:
         def execfile(fname, *where):
             if isinstance(fname, unicode):
                 filename = fname.encode(sys.getfilesystemencoding())
             else:
                 filename = fname
             __builtin__.execfile(filename, *where)

examples/notebooks/Custom Display Logic.ipynb

@@ -1,8702 +1,8702 b''
 {
  "metadata": {
   "name": "Custom Display Logic"
  },
  "nbformat": 3,
  "nbformat_minor": 0,
  "worksheets": [
   {
    "cells": [
     {
      "cell_type": "heading",
      "level": 1,
      "metadata": {},
      "source": [
       "Defining Custom Display Logic for Your Own Objects"
      ]
     },
     {
      "cell_type": "heading",
      "level": 2,
      "metadata": {},
      "source": [
       "Overview"
      ]
     },
     {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
       "In Python, objects can declare their textual representation using the `__repr__` method.  IPython expands on this idea and allows objects to declare other, richer representations including:\n",
       "\n",
       "* HTML\n",
       "* JSON\n",
       "* PNG\n",
       "* JPEG\n",
       "* SVG\n",
       "* LaTeX\n",
       "\n",
       "This Notebook shows how you can add custom display logic to your own classes, so that they can be displayed using these rich representations. There are two ways of accomplishing this:\n",
       "\n",
       "1. Implementing special display methods such as `_repr_html_`.\n",
       "2. Registering a display function for a particular type.\n",
       "\n",
       "In this Notebook we show how both approaches work."
      ]
     },
     {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
       "Parts of this notebook need the inline matplotlib backend:"
      ]
     },
     {
      "cell_type": "code",
      "collapsed": false,
      "input": [
       "%pylab inline"
      ],
      "language": "python",
      "metadata": {},
      "outputs": [
       {
        "output_type": "stream",
        "stream": "stdout",
        "text": [
         "\n",
         "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].\n",
         "For more information, type 'help(pylab)'.\n"
        ]
       }
      ],
      "prompt_number": 1
     },
     {
      "cell_type": "heading",
      "level": 2,
      "metadata": {},
      "source": [
       "Implementing special display methods"
      ]
     },
     {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
       "The main idea of the first approach is that you have to implement special display methods, one for each representation you want to use. The names of the special methods are self explanatory:\n",
       "\n",
       "* _repr_html_\n",
       "* _repr_json_\n",
       "* _repr_jpeg_\n",
       "* _repr_png_\n",
       "* _repr_svg_\n",
       "* _repr_latex_\n",
       "\n",
       "As an illustration, we build a class that holds data generated by sampling a Gaussian distribution with given mean and variance. Each frontend can then decide which representation it will display be default. Further, we show how to display a particular representation."
      ]
     },
     {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
       "The next cell defines the Gaussian class:"
      ]
     },
     {
      "cell_type": "code",
      "collapsed": false,
      "input": [
       "from IPython.core.pylabtools import print_figure\n",
       "from IPython.display import Image, SVG, Math\n",
       "\n",
       "class Gaussian(object):\n",
       "    \"\"\"A simple object holding data sampled from a Gaussian distribution.\n",
       "    \"\"\"\n",
       "    def __init__(self, mean=0, std=1, size=1000):\n",
       "        self.data = np.random.normal(mean, std, size)\n",
       "        self.mean = mean\n",
       "        self.std = std\n",
       "        self.size = size\n",
       "        # For caching plots that may be expensive to compute\n",
       "        self._png_data = None\n",
       "        self._svg_data = None\n",
       "        \n",
       "    def _figure_data(self, format):\n",
       "        fig, ax = plt.subplots()\n",
       "        ax.plot(self.data, 'o')\n",
       "        ax.set_title(self._repr_latex_())\n",
       "        data = print_figure(fig, format)\n",
       "        # We MUST close the figure, otherwise IPython's display machinery\n",
       "        # will pick it up and send it as output, resulting in a double display\n",
       "        plt.close(fig)\n",
       "        return data\n",
       "    \n",
       "    # Here we define the special repr methods that provide the IPython display protocol\n",
       "    # Note that for the two figures, we cache the figure data once computed.\n",
       "    \n",
       "    def _repr_png_(self):\n",
       "        if self._png_data is None:\n",
       "            self._png_data = self._figure_data('png')\n",
       "        return self._png_data\n",
       "\n",
       "\n",
       "    def _repr_svg_(self):\n",
       "        if self._svg_data is None:\n",
-      "            self._svg_data = self._figure_data('svg')\n",
+      "            self._svg_data = self._figure_data('svg').decode('utf-8')\n",
       "        return self._svg_data\n",
       "    \n",
       "    def _repr_latex_(self):\n",
       "        return r'$\\mathcal{N}(\\mu=%.2g, \\sigma=%.2g),\\ N=%d$' % (self.mean,\n",
       "                                                                 self.std, self.size)\n",
       "    \n",
       "    # We expose as properties some of the above reprs, so that the user can see them\n",
       "    # directly (since otherwise the client dictates which one it shows by default)\n",
       "    @property\n",
       "    def png(self):\n",
       "        return Image(self._repr_png_(), embed=True)\n",
       "    \n",
       "    @property\n",
       "    def svg(self):\n",
       "        return SVG(self._repr_svg_())\n",
       "        \n",
       "    @property\n",
       "    def latex(self):\n",
-      "        return Math(self._repr_svg_())\n",
+      "        return Math(self._repr_latex_())\n",
       "    \n",
       "    # An example of using a property to display rich information, in this case\n",
       "    # the histogram of the distribution.  We've hardcoded the format to be png\n",
       "    # in this case, but in production code it would be trivial to make it an option\n",
       "    @property\n",
       "    def hist(self):\n",
       "        fig, ax = plt.subplots()\n",
       "        ax.hist(self.data, bins=100)\n",
       "        ax.set_title(self._repr_latex_())\n",
       "        data = print_figure(fig, 'png')\n",
       "        plt.close(fig)\n",
       "        return Image(data, embed=True)"
      ],
      "language": "python",
      "metadata": {},
      "outputs": [],
      "prompt_number": 2
     },
     {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
       "Now, we create an instance of the Gaussian distribution, whose default representation will be its LaTeX form:"
      ]
     },
     {
      "cell_type": "code",
      "collapsed": false,
      "input": [
       "x = Gaussian()\n",
       "x"
      ],
      "language": "python",
      "metadata": {},
      "outputs": [
       {
        "latex": [
         "$\\mathcal{N}(\\mu=0, \\sigma=1),\\ N=1000$"
        ],
        "output_type": "pyout",
        "png": 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BsF1UdAtic/PL8PnmY8yY5BRzScQinGioY6uwkODQIfH9OxtPTpRR7hrSz1H+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\n5xa8T9QZM2bztaOpwUrE7mXi7biWaveNjfI+38Lhtmdb77FjqtnEVyh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        "text": [
         "<__main__.Gaussian at 0x10aadf750>"
        ]
       }
      ],
      "prompt_number": 3
     },
     {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
       "We can view the data in png or svg formats:"
      ]
     },
     {
      "cell_type": "code",
      "collapsed": false,
      "input": [
       "x.png"
      ],
      "language": "python",
      "metadata": {},
      "outputs": [
       {
        "output_type": "pyout",
        "png": 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BsF1UdAtic/PL8PnmY8yY5BRzScQinGioY6uwkODQIfH9OxtPTpRR7hrSz1H+\n/p0tLglBvE7+w4cPk5EjRxq/B6BszMW/kRFtSS47yBszPP3c5yu3SU02bdg6KeQRe11UnsnqnGQt\ncmyz/J2ewIqENibV4hj1xOO53xinHc3mqu5YHrZqDW9MxKZcdH1QL5C/zZXGSn7+fcKmrZnTXQzn\no2GF00LXE6kBonsnPVEnQe2zSJuITu6ZyCABJ21W+8nrnauEdkZH/iYGV6ib8/R9mUnfeAa2Pn9o\n1KhHCCFf4s1YuxUMsNdMGHQluTZuXOWIBEsHvhnrhUrlunr1ppBGWaV9lkgl9uLlI1eP45msL9se\nr8s+Zq4kVXNTrafHH/+d9tp5eVdgwwZdKNwyW3+77h6ROcvZ81xpOQ5A6Dr6TfSlSx/UnhNN+55+\nepvmaPa+/VD3dM6d+xZOn2YWpu5dMkrfSaBzYAg8nl3Izv4C5869BkojDKjafEHBR1i//iFDe3Q8\n8X4cPJiCWbNexrhxdVi2bJKGk/4kgNPYvTsVpaUVUWWVmixP2bKNvAfgLEigFMzt8fbbNXjssX0Y\nN25kTESGdlYNcAIffXQXzp7tA9VC9XqXY+nS+yzXE11HJteYx/MJAgHxLE76RjOI/QB+rG3v8ePH\nIz5T1Ih3pXCm0VeGfiYQ4I+WFay4eIHjkKVkhIaZNCZe5iy2EnuJ1ui5ZsLaa2eFRO5LFVu21AsJ\nKdZrJxOm4u6ZmYssGi6zSKgWzdvp8dyfEIpn+5KKkcaC7ns9QVdq6r025/D3b0qmSk9/QPk8cYR3\nzvvFatl6vXO1Yan6BCr5eelctLbT43lAc82VjkJdI1kYslVfEXqfFY7GvOlZrGGyuuMWKM/5RwL8\nX+Syy75KKisrSQLEcxg9pNEfA9AKqglNtHzb3Hwap069hGRtMIrQFdlobNQQatC7hX4XAlgEgGvw\nHs9flBWbQvQ/Ow0Fi4YGGQDWrHkN779fhvPnR8BshXA49fvRPYAloBuCVgsnmRWlTMXdb7jhNVx2\nGadyJcSDp5/epqV4DgQ4xTF7nlj4UHTvIytrf4iTRzf+7JKuGKWv1Zrt7h5jPEd8/6ZkqmCwAnzO\nfAxAjHCi2n119Z8QDJ4BtQLtqagjwWnx+Eh7ANbr0Gd4++196OjIhs7yDwS+guZmNZy3FOvWvR4x\nAi3SXpHMNcPPy8ur0p4nUoK36gtf4aqrLkdHhziGdH13Gei75/sxwJPw+baiqqoKP/xh4gqP9JCg\nHwTg56CpGegZAAAgAElEQVQvlBFovQqgDamp3Th7NhXy5gV98X/5y1n4fEvwxBNlmo0sGU5Cw7iZ\nxSbMSyEzSh/WNmxYHvr0YW6db4O9kLS0ncjIyEcgYG/qRcNHzo5rbDyB5ubTyM4uDFfO0XFa+3xL\n0NCgmqPPoLNzjvZZnJMrjQewCepE00UiJRJW4epHVlYNzp8vBCEEEycOwsaN54Xvq6DPRP4Z1qyZ\njzNnBsUcp8wX1Pk4fLgVQB8UFKTg3LkVaG7O1pwxyTb7+cSJXDQ02C0Qsstm4MAPsX79YkuQwpw5\nNZLLkiogr4MqIFXC53L+Av8uXTmGKlW7dh1wtIjr5545zPbNN6u038nX4W09d47NQ901nS0yuoUr\nkiIVjUzR55Oo8KO5+TS8XmDAgDIUFhaiqalJQ/o2CVlZ8kKV6HDsMOIxB6ZPn04GDx5MPB4PGTJk\nCPnFL35hOQaAYq7UECsHtbjBaG9expM9aS5MbuaHsa+uE72pZ4do3C4mIriCgjJbN4Cz/rE3dZMF\nkYxLdQdYOYOmhdpp5XCPpw/Etug28IqKyrTuJDu+oi1b6onHo8t4rSdpad+S2u/1ftc4lu0LTJv+\nJoS7+pzNsWj6JBbuGTN1N3uf6jXVDWvWX+bNet097d6PU5lirX5VT4Dl0v9paQssfVtZWWPkqVLb\nxTaj4xTPEuLS6P/93/89hrOaAHwFcoKSuMGoxhbrkwliSZiQC5OLoOeKdSvZNfUbYdGbetEXUaYw\nZd19/HGT9l7DhuWhf//YMge55pOi/T7ZNTj1iUwUNKwU4BrgEtDNrPNQ6w6fP69vv86q0b0bQKc9\nU5dEaelqVFffFtX4mzx5PIYMeRGHDskWIPBLpKT0hZqsZ4J9gWnR/aNq7qyqE6MuTkEsLhzd3Ium\neLwuSODgwbM4c4YdwbLM94G7SsX3rboUnXNS2cXeRyNTrG6nfaD1r5n7ZT+6uuRxc/Dgk9i5czXW\nry+NeA95c1elrY4dPc5Hr78lcxeI36vJBH488EANRowwpyeL0E1gPlH0/uCbbtpqMTf1Zl20pt7v\npbj/vXtXYMOGSEWUzaY196XLgiMrayHWrp0FID5ypTVrXsNf//pQKG/AfvImA3pfsC72eAPkyeAH\nkIJz585qrysWQu/sTMcXXzTi+PG+aG6+F6yvt2//MXJyitDScr32Gh0daWGhwa719NPbUF1dZzsm\nr7zyOhw6dCtkf2wWgsEaiO+6uTnbsjcl7itxF5HYJ4Do/klP34tg+Ks6UCXKD2ArgM8B6KNinLj3\ndALTWjzej4aGOnzrWy/j+us34YknaI6LjkisqIgWmqcQFys/gNVISdkLQv7/0PeqSzFyLodTOE3C\n+uKLk+D5JH4A9QB+LRxRpZxB3+3OnY0gxH6MAHplLxHoEUHPuU8Ak5AEykKDeGDof1Wzfwvt7Zts\n05MZZF88D9G6996hobYwzYZ/n5W1HyUlEyzX0vn3vN4mAPrMQnWB+fjjT9Hc/Kp0zebmZ7Bs2XSb\nhehFAHvBNn9bWuSMOe5LB0TBUVTE+yNaYSy2e+DAy/GDHxTiv/5LnLx0QiYrc0+ENSQwHUAzPJ75\nCASuEI4sEv7mikF3N9sLkgVASckQRdhUQKUhCAQqEAj8CFxblGuWtrZ+BsB5qCGb2JwTSey3KqgK\nDSAnv+kKpTD/f0ZGG5qaxHE4HsOHv4mZM0sFLVtnfeqLmcRqsbG0/o6OH0nPI46Zvn1Pa4MEZG4k\n6/5GU1ORwFap1pM2W+I6RMONZD62E8BxcMuoUDlTv//gpJAOYA42iRsJcwIZAEDyj/l85UYO6srK\nGuLzlYd8oKI/0nnFeUKYH01fb5L5xK666ltKwQ/OWqheT5egpfP56Xx9qakPaNuekjJP68ejoXD2\nfs9ILKDRJpuY9gZMYaeJYjm0K79oTc4iJDt7CklLm+zQL033TwoKZkv9Ih9TqTmvUjjf2gavd7nh\nWmwM6ZPozP7taEIrrd+bfM/sc+t+hem5HnHkozeNLb5/oG8vD1W2+tPt/Ofy88ceWh3N/pe+3gU9\nlrPVlhPgds1cFeVO9PNHft7EieceEfQqtmypJz5fOSkomE4KCmYTn2+xZXOEUhazjZc5Np1pfWlO\nik5bY5P114tmgOgnpW5j0JyNS4VrpbbtbJPJrgBJLDH0JmESaXJGS3Gs1mm1a6ue7liNBRf/tu8z\nPi7Efi/TnCf2hXmi6mOzzfkNrA/UjEq5aA0/p7h4gdJmuS8KCsoc9b11rMQWSGC9jqwYFRXNsn0P\n+g1ys7Kmv684BmhfZWU5y4yPJlfFmkuygADTSG7udIVKfRrRyQ7gPlJUVEZSU2dEHJPsnmLWNM8X\nSJx47nH2SpUMTIfJk8fje9/bhyefFGt5irDPsKV8JGYfK6CaSObrEeKc5dFsdqmbcEdhMtmvucYD\nJ3sAfft+hpycu9DZmYbMzFz07ZuPzZvPCOaxc1Y8c7s7hb+5C2P37l0oL/9Ccl1FW1P37bfLQuRs\n/PpiVmcwqLKRqu+Iuqzy8v6Ca65hdYetT8A4aDo700PjQg3jVamlRb+v6iqg6OhI04QIvgrgHCK5\nYtT+2bz5AzQ0WM85dGiRwosi3usttLT8KkwYF8kd0LfvZygooNnM588HQ3VYnQUSMFgZF0VXqh+p\nqS+AuzOssAYJ+JGe/jpOndoUeg4/3n7bugenbpQePfoRGhtPIhD4/wBQtlGWGc/aqXPNOM2/sfJJ\n8VDstjagrc2P9PRFIblUCJ0L9eqrszFixFAcOqTvS3Eey3ODzrGMjPeRl3e/MUY/JiRsyTAAQJwr\nMCsOIIa06bUGnmGrhmhZS7PJK7xZG4yGK8SqNTAzea6kPaWnTyEmi4Nm1Kl8KvMIMJmMGvWIsOJb\nNQm7koZ2mr0p8zI39w7DvWJxpanHVyr3jBS2Z/8e9OGQ31WyKesJcK/y/1QiFx6h5/l8i23DNPn9\nWNtXCT+RNUcGWYO0u49d30eqCWzXr/L5JktNngemurvMpWHOZmYWjbV8aHyZ8ZF4f/Rz01oQx8on\npZsbC0h6+l0kN/d+Y1/KBYnEObrQMDd0lgG0YyYWJO5KphsAmkm8MKKpL3cUE/bTCfAtkpV1t7aD\n5cFTQ4CF2g60xrWaB4GTqlcMVjNTNAG5oC8qut9I2JWTcyehgme5cK5uoptS7Z0JA725aO0rr3cu\nycu7T7mWKnSduNJMbTW1V/V3O3sm0TWi32N4RNNm+n4yM2U3YqT4au5iZH1ST6KJ7WYw5USIixh7\nLjt3mvpuTe4SXfW0ysoaMnbsPE2OwEoHipFuPNAawKaKavYLh3mOmRSvSLkTlZU1JD19odA+/Xjl\n+3usn3Xjhc8NUwUyPi7sXWT2exswjplo0UPhldbsRZ3rQ9zppmZ2ENx04lWlurqmhfi0WVjcSaSm\nNqGtLU+42mJw09w+rrWx8SQOHVokkFaJWYWiqUZhCuESMypptIpIVsWf9corq9Cv30khrIzD4xmI\ns2czATC3iOqyEHMB5IgQoBCZmQ+ho+Ny64Uhk57piJjy8p5Da+t/Suc0N7+MgoI5ypVUd4ITV5oK\nMZtUH1aamno0TMh29OiHaGxcEDbZAf17OHHieKgKWR+cP69zgeVo2kzfT0cHcNllqy2RS6ZQ1cmT\nxapoLKpGHmsMdhEtgwfnCJEl/Pn37duPqqoXpSgeUz0GPWFYleZu41FU9G8YMoRnYQeDGVi37u9o\nb/dCLsTBXX/f+94EIfrMru4uwPqzpGS1sbKa7JJyTmtiymI1FSRi19ixownBIMtuPwCZLoKPVxpl\n9xYOHmT1LVi+inWMNze/jKKib2HAgDIEg1lIT2/HTTcNDZEuiuHPdLwMH74yHP5sfZ4ki+KELRkG\nAGpmrF7D0W32pKTMMK72RUX3E4+nXFlpYyMfY/fXRynQtgwcWOa45qs5A5drGfYUuZU27WfX1NfO\nLSq6P6IVEu3mqz5yQ7y3vo9lV5o5K5BfP5L1xbUj1QWoj9SxsxTM4yKajWar6W3OsjbB6gbibZW1\n0FUkI4PV6tW7Q51GqeizU1mfMGvY+h70mctiO5m2+10yduxiYx+as2OtblZ7OWFP5czGvGwJ2MsE\nFixCrZvvEHM9aCvpHs+AFr0Qs0le3r0RNpsvCo3eClXD0SUKEHIOppXus8+6EAj8HDJRkzWBgpNR\n2d/fvirSeBQXb8P27VUAzOXtGPjGjzmhw6QtAsADD9QIbVY1GHbNPlA1DOBJ5OcvQXV1GR5+2Jwd\n62zzFWBaXSDQriTqjIfX+0sUFlJtmxKMWa/GyeoY9FwutDwiy6GwWgYvvFAmZKnSc9SSf3KpQ5GS\ndxEoTxHPl7j33qGoq9O3WS46Qq/j9/PEH9UKteZZbEVGxj5kZt6PoUOvQmFhrqPMWUCXjbspZEly\nK/P8eYDmWbwClk0ubkjK79Y8/uT5xs4JgicB6a1gpqFba+mODpcKbG09hqamfDQ0WDfrAViyYzs7\ngyGL+tuIVHHJbt7YjXnZErAPdmCyoKrqRTzxxFZ0d5dCXw+6TipGBPgRCPQDf18bwMbQ2bOHsHo1\n71O1zOJ//VeDkKSYePSQoJeZH3UmtzUr9C3QdHB9we3OzozQX+J5fAe8X7+jKCm5UknRNt+fQR/l\nUIe9e4+itLQCN99cqK32IybKcFdFZLIqnQB47LF9IcH3bQDNAB4C8NPwNb3eX6KtrTMUPSG7bzo7\ngxFdDibzV46M4ElbZ8/S+4iJLEuXPqhwclv7ODu7UBCm3H1VXFwlnbtx47HQs+p59oPBLO3nomlP\nx88ZqMlmOqG4a9cqfO97+nFBiEcQ8tbEHwBS26ur65CZ+XmYvIr2zT9Zjnn66W344otGAH3Qt+9l\n2upq3A2E0P3/HvpbdRs0WfqKuR769CHCp4xOoAzp6Sno149g5swJGmoPNh4KATwLYAx0EPvbLnKu\ntLQCe/ZYC8evWTMfTU3doQUZALzweo9jw4Y5APS0E7oIN7t7m8a8zACqzim9TNi8+QN0dy8Hp2CQ\nF02P52CIwVZkEB0B/r7kJL6Ghjrcd9+/ICXl8pALkikSf8L11+fiBz8olurqvvWW9hFjQg8Jes78\nyIQdIIddysUKxIEt8l4AjNWws7Mj9L+9f7C21o/Nm/eEw8tosQyrZsbAC5EMBtUIUwD8DC0tNLPN\nGhaoo0t9EcB8ALPAhfB7uO22rzjKKKVFyV8MXZNpBauRmfkpbrghF2vXPojq6jrU1alheX7s3/8s\nRo9ebksTIWuhnOKAkNyQdjEfDQ2nQIjorx+P9vbxKCy0+l1NC0t1dZ3R98zCDWXNsk7bH+npGpMM\nslVGF6+PQIWg+H70QlHeo+GMoQcOmISrvO+gKy+ZkTEP6emBMCWCrBRYQyjNJQbZ/btZDyhPrqd4\n6OhIw6OP3qq822OglgHVkJnmL2cf7wcwFTQkeSiiofgArFmkx4/r2/fRR004e/ZGiNw+zc2rsGbN\na9i9++fKQic/lxOIFCGNjScxZ04NCgt5uObMmVdo51RhYSf69h0gUVkAwP79beDKGqOPmI7s7FRc\nd10O9u07D/m9VgG4FVbeLtEiqwC3Ol8BMBgdHcPQ0BDE8eO7sWHDnPBzpKTIi2VcSJgTyABA9tEX\nFy8gY8fOIxkZLCuwkgDzSFraN4nHw1jfVH8Y9c1mZ98j+AaZj9rsE42lCEdlZU3I92/yceoiJNQE\nqDKtn9MUbaTzCTvJiLQyOjp/VtkPKZ/jJGnLCcy+Z942OeLE7MuPxC64ZUs9Ae7UtDuyP1a+NutT\n3XuuJzk5d4b6TH3nCzTvW3w/zqKGeFseIbwwherDjhwiad5v4j56uqfBfu4R2qkLd12gLfIRTQhn\nero+Wq6gYDohxFwAyBThZm4LC0+eR+hcnE08nnuEpC75neqyYM3lAGl7eHSO7h2z56hUPhc/0++x\niVE5iRTPPeyj94cKJwPUxOHcGF1dG9DV5QfVhFVmRqqlZ2WV4dQppjXPBl0R+Urr8aRg5Mj+YY29\ntLRCk+xkLk5eW+vHunX1CARUgjUROtZItRhwVeg45l+lmmx7+0AtYZWOMyU7+5y2/3btOoCJE6vQ\np08Qgwb1wyefsO+iKzQs85PI59AomwLLOUBkPhSVNIyQNqSn/78IBjdb7rNmzXx8/PEXwqfc1VVQ\n8CluuumqsDkdySqbPHk8cnNfQlubLiJEdG9R98nevW0oLa3QFCDPB2VJVIvR0Pd79uxY0HFbBfmd\nM02No71d5EGJHFkiWkZbt/4N3d1jQf3sr4G7GuqgcyNkZS1ESckYwUomGDJksDZChxGzDR68Cc3N\nnQAuBy1MDnDun1IwK5zta+hcllYOGz/a2/OQklIOQnik3PDhK/HZZ7khd6MKD2pr/Th+nLFs2pfz\nM80Z3pby0KeXg0XrBQIIlcBUoee0p3OgzNKejIxpOHHiMhw6dBZ0vIqlN9meCDuPJY+J756NzzaI\nkYQUTxraGD96VNBnZdWE3B7TwR9SFVCDQF0e1k0kq88XALaiX79OlJRcg5KSwdixoylsgllNSF63\nUZdVyLPiGHQmbL6lbdT0DQqfBWEV/hRiliRgpiYeMKBM23YxIzIrSzwm+spb9puyuo3thVi69DuW\no0V2xQMHWhAIfAWU+CkdNIytSnuXw4dbFRZOKpBTUw9h6NACLF16GwDGesgnRf/+q3SXwzXX5KOh\nQW13IaigZIVveOhsXR2QmTlHuUp66GeOch02TtmzBCGPXV3VpKPC/+a9H5+vHKLv/uabC7FtWzq6\nu4+H2svavhrA38AXFJ6Nedllf7cIYnl8cLDFum/fywB8CLmAhuiqoK7WX/5ySWicmpQC8ZneAjAb\nhLwKYAZSU7swbFgW1q+fh2XLNmgF/bBhuaHNdMayyZ+rsLDNoqhY58yLOHjwY6SkkND/beCKJAch\nwzW9YTcH1KzXY0hJ6YeGhhrw/soRzuF9l5OzD6mpQXR2LkQgIGZYi8EUDFwRaW09lxyG2ITZBgYA\nCIclcjN9tsaUUU0cHko3cGBZRHeGzoS0FnuwN5+tHDk698s0oW0LQqbbdwgNo1LN68jmuikBxFpH\nV80ULiPA3SQl5buOnk2FnOwj//AsQ3M4I4NMACWao5HD/Hg4p5pRSd0hmZmzNcla9uY8T/yi7U5J\nMZGgmcbcXGF8iskuav1gNTlKV+zDxMtj+lscY8w1UE5YiB5QRtLS7tT2h/5d6pOj5GxRcza1GCLp\nLPRWdfvQ95iaOoMUFZWFyAyXK+cv1rjwePtVTp8tW+qVtohzlL2D2cRpOKTJzaTLtJXliX04LXNz\nFRcvILm5dwhuaXpuSsrtxn5nbs1Eiuce0ehZWGJpaUVocy5X+NaUOKGP0rBSBs/FiRNZmDXrRbS0\nyEkQgcBAyFqZvdZLuaaZ2VUKupHFN5I9nl3o2zcDhPw7OjpmgHFgUIjUryza4R3b+wGmCBi5FFlu\nbgaOHQsgGGQbOKyMGUCIH2lptyMjA+jstJrLuugiZvrKSR38HM5pv1XYXF2iTXB76qk6BAK/B9VK\nToJbanZhfqxMIHMDjQfVaKw0tx0dVdAlhokuLJEXZcMGud1NTdcIG8K69z8plGTG3CIvg79LMdGt\nInw8f5ZN0nXkZxQ38phGeAKpqZPRr1+eMFZ15RCvB93UY9o8Qn3wGrq6FkN9Z17vXLS16es8sOQo\nUyTK9u3PhCJH5LZmZe1AR8cgNDQw91OH9fJQI7XSoY84AQ4dEjchucY+bBgtvGwtpGO1YPfunQeg\nH1parhSOE0NBWW3nXJhqTog1iK2FUyjkOcBDRvfty5OuRbEV2dkfIDt7OgYPHozCwlyUlAxRrCs/\nPJ4fIzf3W8jIyMGwYbmYMmUKXnqJlaY0b/onDAlbMgwQbyFvluhS/KNLc/f5ygUNTscCOJvIWpk9\npwjfnJpHgDss2oCsqdjRk+o0AP3zWClR1eQT9r+JS0XkxaEWhscz3cIIKsLKbSNbTk4xduw8oY9X\nErOGy5NHUlNvDyX8qH1WqTmPEOumVT3RJfPoEmusNABmTh+fbzHp12+O8V3KvDm0z3jykqhBU0ZH\nu41H++QdE3WGqk3Sz/Py7gy1KzYKXzn4gD3rI6SoqMxBv3PqhIKC6aFnNr1HnYZNwtq6Mz4l0Zpi\n70J9Z8wKul/zDvVUzHY0yfKccdbH0TDj2lFaJFI895iPXo45rkFubgbOnqWrYEZGG4Al+PzzE/j0\n0/ngWgyQnk43mRjEGFoar8s2j66E1SdeAVkrEwtSyJWTVq/ehObmOQB+D+BeWGO6Vc0rU/neWgSh\npGSSbQy/HEO+GsAJAEcRDL4h3ZcnzbwMYJhy31dBNXzuj6RFy084ZKvUW06sfXaFGijVgBg3LFo1\nTMOVKSy6u1lhD6alfw6gDKmp7ejuBqxat5oYVgcxJwOwbjpbGQHZO1fbRK/b1gacOSNWO7LmP2zY\nQEOCeQgpsHTpPymfccvH5ytHQ4O6l7MSw4bl2iTviGXzxPR5P1JS/gZC2HH8naWnTw+xiOqLrUSq\ntlRVtRjjxvmVZ7gPs2a9qLSd3e9ufP3rvtD4HoKXXvoYzc3MivODxuED1veoD9lsbT2GvXsDsFo/\nRzVHi9c8EzqWbdqplBZ+ANUAJiM9PQ9ZWQHccss14ZwGHZMuDU5IR3U1DfO1JkHeCrWPMzMXYenS\nb0tzZe9ese3mIIk333wC48bVoU4TVZzosp1xC3q/34+FCxciGAxi2bJlWLp0qeUYa8WnwTh3ju7k\nnzqVgc7OfujTJwhCgE8/LYNo2gWD38HOnVu196adL5qKKq+Nak7TZKPs7OloaiqQyp6lpn4cutYz\noAuEaB4C1hKH6vf0+mo5QnUSlZQMCQ+2PXv+gtbW3wvnvwVgsHJNsULQJlgnTPS796aEKUbpe+zY\nSXzyyVEEAlciEOCZrVY63D6Q6/2WgSa5PQM2cVNS1oGQLcrzWDep09LKMGgQM2UBvhCoG+rpyvfU\nndPYeDJ8hLxZJ0fyDBvmwYEDVk4ffbWj8Rg+fKUlyU2F7rMnnpiN8vJX0NzMx7LX24y1ax/Eu+/u\nw7ZtjD9JHKN6KuaMjN04f16fxMQ39Vgb5gNoRXp6d2izVYa6eN98c6HEpbN0KVvMdclr45GX93LY\nFevzLUFzc430PbAPKSnzQIg6jq2b+17vXDQ15aOlJVs4X3WVAXJCEsBdbADNWVkEquyI2AdgIICf\nIRgEWlv9+M1vXpc4q1ii4+bNeyw5EfocBysl8Q03UIFsrVzGYO8u1lWwYwv0W2/1ojj6G2+8kdTX\n15MjR46Qa6+9lpw8eVL6HoDBNGMmFjdXTIyOpthtel3RJDRt6EyXzDI9Nah4rUobU3Kx5ly+eTh2\nrNllIruu5hFghub6JgpY0U0jtktfuCIn527jO7On9BVpd+3NVB73PEtpI3MrTNVssplNYJ+vnPh8\n5aEcC5M7zxTnzXMUIlFL233vxIwX+9GOE8d0LT4fmFumnACLSXq6Pu6dupT0lLdy7Ll9LoWOT0p1\nE2ZlTSNXX/0dkpp6u7YtPt/i8POZ3A45OXdrczQY/bOVXdTOVabbuFbfXw0B7hLmwALC6ajF3Bar\nbKBu02hzHFjfPm4IEondHS2OkwSI5zDi0ujPhMq3jx9PV7pJkybhT3/6EyZPniwdJ2veDHUQXTQA\n0NGh05LNZsyyZZPw9tsiL0yO5iirls3Tv8U2TQJnjNSt3h8C+JZwD1GDSgdgrasKQIop//jjv6O1\n9RFQbVbVQEz8OJME9kx6T4/nx/B46MZOR8ff0d5uzZA9e/ZPyMujxwwdmivxtOgyWU+cyApxkzDu\nIN5fIsSN5CeeKEN5+Qo0N3sguxrGA1iJa67pj4EDRWZG9nx6qoO8vCuwfXsVfL4laGgw8RdNAnUP\n/E46V2RE1dec5fVeTRZNZmaX4yLRplhuQOZl0V2L1/yVv8vLm66Ne6eZweJ4PAHgNNLTUwHkhJhc\nn0GkXApu6XANORhkm8KsmMgSfPLJWwAWgFtn9HuPpxrnz1+J0tKKUPaoyo1E4fFkY/fun1v4cETa\nDAAYPXp56C95ruXm7sOGDcsAqLQI7DiVFmUxgE/Aw2grQC1jNbdFBYuh131nznFQN7ZlOgnezoKC\nGSgs7Csw41KoLjWT6yiRiEvQv/vuu7juuuvC/99www3YuXOnRdDTiaXeKlIEBIWp6Dbzr3FeGNUM\nNp/PuWjUNuSB+3BlitGsrLIQ6ZaYSCRGi3CwZKAzZwYp6e9DIMdjiz6/oHBNQPQPL1kyXuLAWLr0\n/5H80VOnViMQ+G3oPBaZcxXa2gYDSEdLSxAzZ/4cGzeahdDEiVVKn0ROg2dRLrNmvYyWFp5gA3QB\nuB15eduwbNmtFtM0JeUEuL/Zem3Z5WDlL/rww8uERDEO0RymNBZeiGOhqWkFamv9tuayU5jyH5hQ\ntdvfcMY1xNs1c6YaGcIrHjU0UIppn28JDh48i5Dupe0XusCYhB8blyJJIMAWltTUIAKB34YqStFF\nraAAaGnR70MA9pw0ANDUJEba8IUvM3N6+DwrLQI7RpQTftD8Arb4s+gsceHT9bnzsW73PPr3SRXM\npUtvw+rVr+LIEXOyn53SkCj0yGbswIHHkJ7+LoJBAJgY+nEW/rR06e149919WLdur7Qqso5QN5Na\nW08AoKyKMrOd2JGMY36gcO86UI3ADzHbNjc3BV//+gg0NRXi/ff7wboho+/Cw4db0dLCLBZxErHj\nT0IW6oxpkWnuVv+wDjTDcaOSIZsCmhXIF6DTp1dZsnJF8MHKfpsXTfX+dEPJqqFmZm6VNKHGxhOh\nzOjHba9tnTgyf1FpaYVW0IvsgzTrUxbEzc3PhDfBWJt0YYdOYFeaLpK2b1po1JA+sV1sjO/adcAS\nRtzc/DLGjFmNgQMLlI09mZCP8kmZhF+68hvgwrcC3d1WZcbnmw+vt1m7D+EEXm8+Tp2yLhSXX94v\n/DWBR2cAACAASURBVB8NeVYhywnKniruYbAwaWY5+qEjMuPMts7Gugmm91lSMsSY7KcqntRq2R76\nAQ4ezHB0b8eIx+9z+vRpcuONN4b//973vke2bNkiHQOAbNlST4qKppKUlLmSH0vlsNbxdldW1pDU\n1HuNfi4n3OH6RKsakpZ2C0lJmRf6396vK4dXRQ7ZlP2XlcJ5LOFK9LVTP2Ja2l0kK2sSyc29nxQU\nUH+/jl9EhJXzptLgj6Shfab+0vPS6CsvqYhUiUn/HsxhnTzUle85eL3fdVz5iRCdH572cb9+cxwV\nM48E/ZiiSWiRqh2xZ3C6FyAi0v6CtZC26PeeSzyemRF8yTp/s32R+Fieg/ehXIEJqA9fh3NiyQXB\nPZ77peQ9OdFRnFuLhf95+HFKygPE51uscCg5G+sm6PrBedlD/TuNUzxLiEuj79ePrrx+vx9XXXUV\ntm7disrKSstxDz/8Fg4d+g+oLIxTpsgc1oR4LAxy69bVo7tbH3HQ2HjCEXe4VfuirH5dXdtCf+v4\ndSiYlkjdAa+guVl26WRnT0Fn50J0dfHolPT0hSgoIIK/lWklLJGK+ZjZvamPv6vLj/Z27mtvafHj\n/fetkQKA7NeTaQSCMFXbCQTO2ZqItIj0TxEInENqqsinPi/sjrAr9B5JQ3Ya1knRD7JLbEX4Lyf3\nsxbvpv165gylPohUUBuwDy+1anG82LVTn28sae6R9hcA2Gr+eXn3hhKkANGizMl5H93djBpbDEE2\nRZjJexoiHTObv5FcWLyak0kTZomBLwJ4HayuQCAwEuvWUX9OVdXiUJ8wrTwFVJOnCWZ0DI2DOJYI\noeHH1tBSoKTkHyQaFRMDrArd+7T67ilkax8wuY4SinhXiu3bt5PrrruODB8+nKxfv97yPQBhxeQa\nmsjSZmKZ5CyK+pVRrssoRxOwxJVJk1ZpWPF0CQ3OUpkzM0tJevrdJDf328TnWxy6tlUrkVdtNenn\nEUNb7CJu9Joh1/BEWoa7tH2elXWX9nqRCisz7coaRTHXtoqQikiMnPbHmYuP62CuYGS+r76Orr5P\n2PH6YtexJS85gVPryTm1hrV4d3HxAjJwYFmo+DWLENMX/Da3Sa3LHLkPrZpwpdCf5kgr2RpVrQ99\nAW/GmMnaMHbsPJKTc6dg4cvtdRJh5ZSBNjd3uvKZXvYkQDyHkbgrmW4AaB8kM3OREm6mPviqULiZ\nmTaVh+7ZZ6JZi/iKk8DsTpBL2OkHrH5CUY6O4uIFZMCAaSQn5ztEL4jVtqjX0k9WMdzU5Jai4WVq\nacZvaa+Xk2PvGtOXOouOFpmQeIRU9Pdi9ystrRAyXs39aG1bdMJabnP05QSjgZodLi62TDGJRFHs\nxN1SXLyAqG48YDbJyblPOsdELxyppKUJ1oLZlRHfh5ma2cTRMzt8Hi9B6dTVEils1W6he9zA31RP\nMjLukt7Jl1DQOyET002SVYSTFnEhnJp6X3hAWwWiOc29qKiM5OTcSShvOfve7H90UvvVPoaW/nAf\nus56cKrR82cRa2mahKfMvW0XG19PUlNnaD5X+0AVvs4Foaopi7HUzvZUIk9yO23LiSVhPUZ9Xt4n\nOsi5GdwfnJs7PWrftZN9J3acOS5eV/c1usXGJKgHDiyT2qDPf6kn6ekPaM8vLl7g8H2J49bZ+7BS\niugXIeaHp89oGuP0J9KeSySyRXVRlRdQ9vM4KS5eID1LIgV9j0TdZGYeRYeGE4n5LK2VdUSK2b2g\nvjlKmwrsRVnZNaiqWozaWn/IT5oinK9msLI0dz/OnXsB3d03goZPzgONZTf7Hzs6dJEIDJQbvrCw\nn1JPVUdStSR0jFoTlUbbpKbOQ3f3yzDH0Eeupan6q59+ehsOHVL71JomT6mjr3HQB2Js+qsANAHf\nsNIi6yJQhg9fhbVrb7Wt8iX7v/XDtLHxBHy+cuzb14rz5/kz7N37CjZsgI0/3RpVYd3Hia7Kkimk\nMzd3BUpKBmtT7xlUDv/jx/uG4uIpTPsJy5ZtwKFDrwqfiHQZMiFfVtb+cBlBpygsLNTW1R08mGe9\n0thvdQ7RuRcMfkVzVVqT4oMPuM9cfT7r+6qGk/dhpRRJg8dzGB7PQrS18T00r3c5pkwpDhH7RaIl\nB0x7XnLYqv57ne++uroOH3wwCWo48pAhegaARKBHBP311+eGOEQYrHVY+YsVmyQW7yChz27ARx/R\nxBfWgWvWvCYU1mUbn6Jwo8kh3d1fAd+U2QST8GMbQi+8wAJ4dVzilFmPbrjyeqqNjX/XJL1QFsGm\npqPCd3wz8vrrF4YZBtXw0JKS0XjhBftamqbBxCHSKABsgBUUfIQhQwrx/vvW8DLG4cGvMwl0cVSv\nKcNJ0Xe7giiA+F7nh8rP6Y7SFbGhYOXp7BLE7Ddv2fM6D7kzh3Teq5SZlAWbdSG0FjDR9VdV1Ys4\nfFhtM3snKu+LtZi6E6SnB7SfZ2Twz2UOGEZx8jFoHQKTYmEdy2vWzLcUzN65k4XkDkR7ez/Q8ceT\n7dT3oaO+CASAkSPnKyHb92H16k2hIiUiXYH+nfftm6tNZGNj3W6DXAfTJnQ0eRzRokcE/RNPlAnF\no9XiD368/XYNBg3KwIABZejs7BKKE0Qu3iHu+j///Gq8884RnD27CkCGcm6V0CI/eAUhq/CbOfMb\n2LjxmEDjKyZQAfIi8iqANrS3Z+LIkcMYMeIK7aAYMmQQPB7dIkC/U+uwiti+/YTjWppiERBuaYgD\nkS8wN920GgcOfGLpA1rw4bSGGnoTeMKYfWES1o4//alR+0xO6oA2NXWHaoyq/W8qYsNg5fqJFOVi\n1SI5L9Jnn7Wivb0Thw9nY/r0T3DNNZtw993FEkfMsmWThEQvMSN3v1awWbNVGZwVkHnhhXoQIlpi\nrPar82tERifUfgdWAuCCnnPA7AONjBEzTU2KhXofP/7613Sp2tnBg6uwfn2poP2+BVoMhl4rNXUv\nZs78poZ4zIq8vCukzPjaWn+oHixAx/ErynOuhsdzGCNH9sPatbR4C5dfFKJgjjYBz2mUWiLRI4Le\nHPbF0q43hRNgvN55yM1lKd1qdhtFR8dPjZXhJ06sQn39raBp0mrVJ35P2WUjC78dO5qUyUcTqDIy\npuC660aEtHYrN3xrK3D48CwhJZ2CWQgvvdQElT3T4zmCEyf62VaVcaoxWLVDamnk5p7DqVPMPSS3\n6Y9/3C20id1/JfLz88L9CtB3t3PnWZw5w4SZdXEoKtJpqaLGZN92K13EDZC1W0rYlZHRjbQ0llCi\nN6sBj+FzM2h4Kc9gnDLla3jppd04ezYH9D0/GcpG9WPv3n+TQmpZKTurYlKlvZfZ7Hf2roPBLFjZ\nOJlikqKeHr5GJEZSEX37DgHV1q0ZzwxcyKWAs4qqz0Ct8fPnz+DIER1tQp2UDQ/wxdBKn0Lb2t1t\ntVAiUV8wyO4m9uyvAZiBjIwuXHllKvr1G4C8vMvCIZaskLxOMMciuGMNr40VPUZTLAti9qlViDc3\nvwyfbz7GjFmNxsaT2L+/NURfK0PUTqz0BlWhb0ROFbZyM4ZLP6gpmAKq3feBx3MGJSWTsH37CeE8\nvgj84z9WYfv2KpSWVqCujrJwqmb26dOvweebj8LC+Th8uBW0RFwuNm8+I5RK47HzgYDMj6N7+U41\nBqt2OD7k2ngd3d2cCjk1tQnB4GC88MJBBAI3IdJkZu+OPrfeOgCAIUNWa9oR2QVipRVmdBFqPv8g\nAD/H+fPA+fNsARGL2PAJHgy2WhZPk5Dj958dPr+jYz9On96J5uarQmeL77lOEvIAzxSVXROili3D\nbPaLwrsOdA+nCR9+ODjMMTN58niF/6YGVMjXgVIBNIGOMZnuu3///Ij8PCJkxkYmOOskwcnOozQY\numdgi54fbW3nobPO7Pbw9PQp/HsRkagv5LwaMcOdjuPMzEX4wQ9GY+PGYwLXErcu7KzunhbcUSNh\n27oGqLeQd6gj76RHqgxvjTyoITQTTrfjXk94yb96Asy07H57vcsd3ZNGGujbr4tVliMToo+zdhIS\nd/XV8zXXVSN31DDT6KJneHEWc1EHfXgkDXPUtV0eE2Kkky42XYxqYdFYKsshizKJHALH452tUSo0\nGqlS857N45aH/NrnZ9i1Kz//vlBBE/MzVVbWCBE2C5R76TNO8/LMhXB0kT5y6KE8RyJHNqnFecxh\nzHbzzZr5bT9GI81dua1yH/l85Y5zPaKB0ygqFYkUz4m7kukGSmOjTWSJFHutp2mtCQ2yewjwXelc\nPmjs6XIjxXvT+7IJxZOSzBMq0gJnrY8ZDbZsqSepqbqEKPFeusQxfY6CXUifz1dOcnImS4ljouCK\nNn5aX3GpngB3C22r1LS1nqSk3Eeuvvo7JCNDnwzmJASOhrvp2myq6uUk3NZ5FS91Eedj2n5+VFbW\nkIEDywgPF7YLEzSH0eqTqFaGEol0ytIqUlAw20ChwY+VlRtdm3TUDdb5Zg2ZlJMZxTkTiaLa2laZ\nYlxfu9YcVutkXkZKGjMhkYK+R1w3ato883c1Np50TOEp1m5kVAmrV7+KDz4QfX514OYiN59TU6ei\nuPjqUD1HxgRoJg3Ky7sCa9feautze+KJMsyc+RxOn/4cYsWjlJQH0N6uo0sWmTnNUTzMreUkRV9E\ndXUdursLYd08E10HbfJJYJtcnHkyK2s/HnvMHIZnZ6JGqkVr2pzSV1waD/oOWdsOQN5zoccQMh7X\nXbcaQ4emaTas/eHasnLVH+7i2bXrAILBAIDRmpZNQkZGDc6fz1WeZxLS0mTaC/H5qJtNHF/2dA+R\nmURlMJdFVdViVFUtxujRy0MbnHZsjHXo7i5SPqP98NFHzQgGra6oNWvm48iRgHI8C6R4EXV19fif\n//kYOTnPYcWKb2L9+lKsWcNdlsFgq+CScUbdoJtvuipY1rqs4j6J/j4MYlQX3QTmFONZWWURzzdB\n5xqMJeosKUjYkmEAANvVzC7LT6f5WLMXVU3ZmZUgJ0o40zxV6M1Ee0uBaZCyhuKszSYyskmTVoWy\nP3Umu6gNscQP0QqZR1JT74iJlEpFrLVozWRc6t9OktvYsWravq7YDP3xeKbbvjOdBVNZWWN0pemt\nGr0mbN+P+oxx9RrW43WZ6LOJuW/1FgClvNC51UQ3F21TSsoMcvnldysZ6GICV2KzhZ0ThtEiJs6z\nh+u11kN0lBtc1uktBNl6NxEXJlI899hmLIO6monhkZE2injsK4O6qeJs42by5PF45RWESr3Jmmd+\n/kycONEPEydWWaIS1BU7GNRFdphrS65dO0u6FtNQ9u49qg27ZG029c277+4TtJoKcA1dDnl87LEx\n2LlzNd55pxVnz7JEMX5Mevp8PPqoPoHJbgNT/dwJaZkY/tncfBqFhYUYPDgnHDet5hKIf+/Zcwat\nrYAuquLRR2eFNGlm0cl1dGXSK1nDCgSGwxQuKr4zp2DjyxxSbG+x8c13cePSfI2bby4MlSYUCckA\nkUCQkFw0NIiRUgdAY90Bvba9KWR9irHw7P3Wgwc00DYR4sdnn9WAFyoJXTkYRHr6PcjLy0dBQSfy\n82UK8WjGnAi7UMopUwbhhRfKEAxmoavrBDo7i9DQ8ELoCD+2bWNEgVWaK9CcF5bX4jT00aS5Dxig\nWggvAmgQrHc//vAHawRXwpGwJcMAKBq9yd8VaRNky5b6kOalas+i9iiWEIusHTOiMkYLXFRUZtFI\nGDmajuRKv0lk3ugxIdKzm76XtUZx84/eNytrmkTnSvvQvCGnIlqyKucb57Fz1/DNQSttraxJ67VU\nfVp+PcnIKJf6TqXCjWVDzcy/Yu5z9VyZYEx/DZlYbwGhltsjkiVlfZeV0vNb9z5mKN9XEG4Rfkcz\n1tUSf7G/Yyc+becavd3+ij11AZMRAwZwgkRT+52RyNUTum9oao/chkSK58RdyXQDWAW9Tujqiae4\niZObewexbphZ67ampf3fCu+9M6Y9K9ucqWasfH/VzOO1LvX314EKsOXSc3g83yFFRTQigfeNvPGb\nna1urumjW0QhZWXOoz/q4mu3qWr6vKjofluz1wl3UCRwoaZnMrQSYsl9pt8orycezwNEXJjz8+8L\nm/tFRVNDUTDWMeNkAXCyQRgJdoLEaa1l0U2qdy1VkIKC2TZuzXqSlnY/4aR8al87E6J2cBr1YtpQ\ntRKGVUrHAKKcMTPWRquQ2LW7srKGDBgwjaSl3U2AbxvaR6R20jkPx+MjEnrcdSNuWtkn1qgblNNB\na0OKpul4AM+hqGg6mpoK0NHxU3R10XMZJQHlU+eml93miGwOqjH+IocOdxtcdtkpXH+9uFGchUDg\nLM6fL0NhIb8/YN2Uls3BM5Dj6/04dIi5YSpgTcQBOjruU/pMrsRk7eMXAeyGDq2tx8LtY3wrMg8I\nB03WUeFHU9Nl6OiYARO/yvHjjMvAzB2kc5mJoNmnOj4hWjO2Tx8S+qQQwDQA10jHdndPtyS00dj3\nX0ttOX26OxRLzWLhZ4K+h5MATuPgwUJMn/5j5OZep+WlAaDkdvBrs/Gzb99+baKcznVhSgb69NPP\n0NEx0tKXIsWIWDdAdKHJ2Z7jMXz4m1i/fh6efnpbKOlQdmVlZLwAQgIA7gCthsYqtOnqHceWnWvH\nG6P2T2bm58jMvAWdnUUg5GV0dAAdHVXKmUHIc0eUM9yVVVDwKW666SosXXq7ICMqQIMBWGW4IA4e\nLMXzz2+1vDO7KlM0y34TgIWgla7U9jHIdRNo3k9i0ENRN3p/l31ijTqZ+0CXjZmT04URI0bg0CHR\nH0sThZqaatC///VhvpbJk8fbDiQ5+kOXsWgVtidPLsKLL94WKnfYjPb2slDbB+Pcuf2YOnUCALWU\noeyjra6uCyVTiTwnauFylujF0d29XCFUs+P/eBGUIO5RqBPY652LpqZ87NnD7s3aoc9qpck6IvwA\natDRIRZx9qO9PYjq6j9hx44m3HxzIT7+mBV3YX3JBFYjgL6Ooo7MCTQqydxAAJdBXRDOnv0Vrr2W\nJuSxMUnLRIpHiX1fByAfPDqJ1msFgLa2CrS1/Uh6loMHU7BsWTVSUq7VlK78tnCdOpw6dT0eeKAG\njz22D1VViwGY92NmzrxCmwzU2TkL8txxth9gF+lC54t1rmVmBtDa6gNVuF4EUAugHLzQvboHYEWk\n6JVIWeDW5LoayImRugQ0ce6ocoYvcKxPHn+c1Z49CXW+A/Pwzjt/tygkpv6UZdxp0DGpFrtnJUSt\nCkzCkDDbwAC7W9gl1sil+AjhMeCyKV5UVKYU3xCTaSK5Z/g5tHSf6IePlADCf3y+8pC/Xu9SMPmu\nWYIGd82I/aE+kzkG2i6RiveN6s+nboqMjLs07RPvbWfaisdUKteXzeqUlLuFz9XkpOiStqx7I2oi\nGOPeV9tEx01BgRwFZE9RXCn0ne44ax+lpJj5xu3cTvq28L4wR3mJ71S/H0Aj2uaRgoKycJlK5/TH\n9L3TCBLdvCi3FOxw4sI0JWnZxdRbk+t0MkQXVaWXM7qIKT6+7FzFslxxJuMeCV1jLhHdhCkppcTn\nW6xxX8N43WjR464bEXZFoAkhSqHjMgCzAFwFcdU7d25FqICwap7pGQBlE0vWflpaKNdOURElsjp3\nbi4I+UW4benpNaEC5zIOH25Fe/v1MLkUjhyZo3l6kciJac5qPLkfwO9BIxmWaK4RmRCN97HobmER\nMX50dzfg0CGVHlIsfQgw6oSMjCZkZ4/Ajh1N4SgZzl0kav8i6RuLyqiCnLIvWidaekqtmT958ng8\n9tg+rFsnWjKbQtfkz0dIHaz8RvTdtLTIlBNWs1t9D4Whv3VWnvWdE6KLyR+P7Oxf4MwZs9spksXJ\nSdPYM1GKhJSUeSDkZdD+rdKc7cf773+B8+dHgPEytbQA5eUrJDpnBjvt1Mp0Oh5ZWf8Wjuzixz+o\nvYbsOrJaLuvXl9ryysj9Q90paj8DwMCB01FcfB0yM7tw4kR/hT0XAAhSUwkIIdKncmnOQuUc67uL\nFBMvy7gc8DnAKYnHjr0Su3fXhChGtJeJHwlbMgywu4Xd6q3LhjNFjHCNWqeR8R+2OWUfDcE2WK0r\nr+n+1PowF0fQ30e38atqwvcIf9vTDkTuYzvtRG2Leq96kpa2QKvJyNaUGpdt2pyrVO7nPJNWFw1h\niqQBphK7ykGmYt0+X7myOW7S6E2x/XZRUpVEl00tF6HXt9VakEMcs7Qv9Bvl5tyOaFL75agpfWSX\nU8RaLtKq0UfO7DbnaVi1cnk8q32pjlu9hajvM3Fu8XevFr2XrSBE3a8mXFCN3qQ5ALAUEMjK2o9B\ngwaFWS5F5OVdgUGDUoTv7P18eoI1hrqQplgB2fcHBAJ+rU+c8lUzX6AVw4bloX9/eaNGJnLiq3x2\n9gfIzp6OnJx0fPJJarhNvOCxSCXcFjG+lxdz+AiHDolEV+oeANPSdPfaj64uPdUu3/zU+WfF4SXe\nQy00Y82kFSmPAaoBrl79Kvbvz5CYDvPzVyEzs1ugtmYYj5ycdbj22hPYu/eM1hKzK9Yt5jkcPdqF\nxsYFCARmQtVmPZ5nhGLb/Fl142TmzAl46qktCATOQ66V8DL27DmD2lp/RAI7zhSpkteNR2Hhajz1\n1BILpS4da8OsHYDoqIv5fN0qzNclMWV4Wi0XanWdOrXJdp9G7h9nmd1m9lx2H66Vcw2cnS++b2cW\nogjx3o2NJ3DgQCoCAX3Re4oz4PMugYh1hfj1r39NbrjhBpKamkp2795tPC6WWziLG7fT6J1l4env\nU0msqzf/0fnE+aptLt9m5jOxalj8emW2bYmWf4Nxo/TrN4dkZKhaMNXS0tJ01od6fx4Cpssv4P5Z\nnQZcQXJy7hastUrpO2Y9iWXVeH/oxwUNvbWWZvP5yoUwUasWHa02K8a1jxr1SDh0TmeVmjJneYlH\ns2bJ+IR0/vQtW+o1+1fyeNCPtcSTdcWDeMpFiuUoaeayfWlKEZFCXa1eBm4tcUsvOaGj1u97gUY/\natQo/O53v8PChQsTt+qEYPJTer35yM+3ajuEeAS/GudVFzludNltOu0pK2t/iNpXbxX06dMNQggA\nhH+Lmk5jI8Fnn03H4MGDLfdVNUZV8/J65+LEiSzMmvViSOsoByLwi0cDxo1SW+vHnDk1Spk46rfP\nzy/TlI8zh4A1NNB9DZ9PzHh8EIBa+YveY/jwNzFzZik2b96DI0dm4MyZL0I01HrKY0CMHKrSPtfV\nV1+JY8f24/TpMtC9iHbk55/HlCnfDHHvTAAvikGRnr4IJSU6X7oeYgY3C30kJIhx40Zi3LiRjrnI\nr7yyKFTi0ezvXbr0Npw5MwgtLdT6UjXGcePqtL5c1WJlqK31a7PAvd7lWLpUDdHtGTgtF9nRkRZT\nOUoT6H6eFWLfAaqXYYm0tyBTMstttUOk0FHT94lAzFe+7rrrEtkOCaYQqyFDBmHp0tu09VGt4WDH\nkJVF0L9/PxBCr6eLT1Y3fjjpmZU32xqGKJuX0Qw6HVlbU1M+GhqeARdos0FjaVMBPASAuyxiLT0W\niXhs5kz2/OJzNwFgsef6GgJjxqyWqviwZxRdIK2tx3D6dCt+8pMWdHRsAF001Oo+VgHEJ4B58c3M\nHAox/T4zcwU2b/5AKBf3M+mcYPBnUZfWs9tAtNsQl9vKnsE86SMRYVHedTkXwE5oT548Hhs20IWX\nVt6ihVXWri27YBzq6vjft29/SMGw0lskihisttaP48c7EGm82c1lJwutCZFCR03fJwIX1Edvgp2f\nUvcSeF1THk0CvIWzZ38e9vft3TsPQD9LcotuklKmvK1obPxc0s5PnMgKCWII14idiU58ltLSCmEB\nUf2EW0GjXmiFK5OF4gTWSUMXxoEDP8TMmeOxY0cTMjM/x4ABYsLXgwBYlanGUDKHDJM2o3IZHTp0\nOeRcgch7D3wC6IuYEOKR3isANDc/g87OOaH/9MlujY167c6ERAgcuSKTFXJBdhlyH4u+3C4AX9je\nVzdvamv9EZL4kgs1gau8XF805Px551FZJnArlnH0RLfXJSLa0oHs/idPNgsMttbzdNdNGOz8Ot/8\n5jfJyJEjLT+bN28OHzNx4sSIPvrKykry7W8/SIYP/wYZM2aOI64Q1c/onP3Q5O+L30eZiFR2Z9dO\nDNMf5ROXY6dNfNt2nOQiYi3MwM8Tn9NZf1ojFypIZubsMA++/r3Uk/R0lqpvis5YGFWfJur9Mx88\nZYe0vuNYuY+cjmU2Lqz3N8eEx8L1E+25pn2raOsb6O5Px49+7I8a9YjjZxGvGZt8so5fhj/+8Y8h\nOTmeXH31hIT66OO+khNBH4moKJ5BxCB2vH6zKv5JmozqM+Zrc+6RWOiDZQIwfl2PR0+O5XQyRUpo\nMcHKQRPd4ms3sfR9t1L5HZ+wsN6HFbeZQ9LT7wqHGJqSgEwU07pnitTH8Sw4+o1tvlE9YMA0y7u0\n26CMNF+dkpTZPZdeCXGm+MicTfoxMHBgmfHdJQKxyo1eJ+j//Oc/m28A2D6oNXZUX6pMB9OL0d8v\nkXHE0Q+4nr427QNnRGw861E/yXSCy6k2I7dHFMLq37E/s71FRzM3aUx9fAu9XXRVevpCMmPGYxou\n9LmaDFFnLI7OFzbzoqy+O36uWvKQC3xWbUk/n6LLDo1GyEWSE9GOOf6+2AKywNJ24HFSXLwgqcpo\nrAtzrxD0//mf/0mGDBlCMjMzyeWXX05uv/12/Q0A2wc10wMstr2/3YvRfRcLq6TpvtEOuAtxbdrn\neuF99dXfCYcKsqQjvUYvLgp6IcDaHWkSmMzXoqKyqMLjnPSdbNGJdVTjW+jZfbhLiEh9w1kddQqG\nHN5pR1vtpA2RlALT/KALumjhiNQieq1d7s/orDC9da0vm5kcZUdss64wT72SjKZfZGJVRuV2RLcw\n9wpB7/gGgKLNyYPdFBNcUDDb9rpO+Ot18e7JEtK9DbR/zKaqzhzn1YDoD89NsI/5dmqa91T/USmt\nAgAAGMVJREFU64uNJ67CkcxJEqlSU6X23pmZi+J6/kh9aZ+LwgTeXMIze51SdJuVNrV9+twHe4sg\nWt+3nYJhzdo2j4FkKKPWvohuYf7SCXqTv9jrXW4sqFBQMN32usncGL0YsGVLPcnIuNvS58xUNaWg\nDxxYFp5k3J3jJC3fXlvp6Wfnk6ZSej6mzRUUTI95L0jW6CPtOSSGfiBaOOOvFxOpKm2ew0SXYX4W\nPi5iJ7CzgxMFQ1/acgHJyLgrnPBm7+4lIaqU2JRRtb3RL8yJE889El45efJ4DB68Cc3Navz1M8jN\nvRNqyBywEsOG5dpeM1JMqh2clCr7smPy5PEYOXITGhpYevgJUJrUQjQ3n0ZqarbmrPEoLt6G7dur\nANCQT7notAxreBsn2vrDH5owevRyDB6cc0H6t2/fz1BQMAOtrecE+oP/0965x0ZV7Xv829p4KIKl\nFrEgQmtb+0LaorQ8QhmVtnI5FQPhIh4bTevjcrX4wGMUSlr02gQIB6sRz41XNDFBxD+MppVHlUwH\nI7RF0QOlVBHRIpZTikKhLfJY949hZs+e/Zj9WHtmz8zvk/AH09mz11p7r9/6rd/6PYSgrMLCVYol\nEQMVP790yZOP/Z9QTvPgJjn5BE6fvuiTJkFcmFwuHz0P1GJRrr329NUkXzdCKHvp6+7p/7zd7UtM\nXIJx467H0aPqqbEB39iHE3AXXvcEsw3ItkuPqyQg5+rqwo8/xqCi4h1MnboTy5aV+rkrup99WtoK\nNDT8TTZ40p0Geiw87rfJySdQXf0IKio2KrRCkvtCkUBxNlYGSwFB9KMXZ94TmDjxFvT19aCnR/Br\nTU7uwcsvP6L6e0Z8WQHloBdAvn5nOPPKK4uv9lWcR72vDxgYCFztPpDPd3//r/j5Z4//tifT5v0A\nduDSpf/FgQMuHDiwEy7XO8jO/hCvvGI+QCeQYBae7/952+XOBS8VTHrfBbFw2Qh3MZx+n/7vBHAK\nwGKMGBGLmTPTUV39CFat+vCqYNWeI8UsgeaHOyo7BkKsxvsQgvLkFoliFBY2Y/v2V1BXt9FbkzUu\nblBUXMaDsND0AmAQspXK1zjQG+UtFozyOfgDZcKUkgBx1lt3HpqUlBH4/Xf9yqgerAyWAsBxb6CA\n5xa8T9QZM2bztaOpwUrE7mXi7biWaveNjfI+38Lhtmdb77FjqtnEVyh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        "prompt_number": 4,
        "text": [
         "<IPython.core.display.Image at 0x10aad6b90>"
        ]
       }
      ],
      "prompt_number": 4
     },
     {
      "cell_type": "code",
      "collapsed": false,
      "input": [
       "x.svg"
      ],
      "language": "python",
      "metadata": {},
      "outputs": [
       {
        "output_type": "pyout",
        "prompt_number": 5,
        "svg": [
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         "    </g>\n",
         "   </g>\n",
         "  </g>\n",
         " </g>\n",
         " <defs>\n",
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         "   <rect height=\"223.2\" width=\"334.8\" x=\"24.321875\" y=\"21.56\"/>\n",
         "  </clipPath>\n",
         " </defs>\n",
         "</svg>"
        ],
        "text": [
         "<IPython.core.display.SVG at 0x10aad6a10>"
        ]
       }
      ],
      "prompt_number": 5
     },
     {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
       "Since IPython only displays by default as an ``Out[]`` cell the result of the last computation, we can use the\n",
       "``display()`` function to show  more than one representation in a single cell:"
      ]
     },
     {
      "cell_type": "code",
      "collapsed": false,
      "input": [
       "display(x.png)\n",
       "display(x.svg)"
      ],
      "language": "python",
      "metadata": {},
      "outputs": [
       {
        "output_type": "display_data",
        "png": 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BsF1UdAtic/PL8PnmY8yY5BRzScQinGioY6uwkODQIfH9OxtPTpRR7hrSz1H+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\n5xa8T9QZM2bztaOpwUrE7mXi7biWaveNjfI+38Lhtmdb77FjqtnEVyh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        "text": [
         "<IPython.core.display.SVG at 0x10aaf8d90>"
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       }
      ],
      "prompt_number": 6
     },
     {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
       "Now let's create a new Gaussian with different parameters"
      ]
     },
     {
      "cell_type": "code",
      "collapsed": false,
      "input": [
       "x2 = Gaussian(0.5, 0.2, 2000)\n",
       "x2"
      ],
      "language": "python",
      "metadata": {},
      "outputs": [
       {
        "latex": [
         "$\\mathcal{N}(\\mu=0.5, \\sigma=0.2),\\ N=2000$"
        ],
        "output_type": "pyout",
        "png": 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/zIQJE4LPdO/enbq6OhobG/nmm29ITk7G4/G0afOyojXcbWsDiloS6UpKfGzd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ignFMIPfvBeBHzAn5kYQ2trV9koGW5lO68lvv9lpD3iXZ+H10sIPiE5OQ0QAXZy30j/eHl5FWpr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\nD+bM0OnTs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         "Q17.4844 10.9844 19 7.6875\n",
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         "Q10.8906 -19.3906 10.3906 -18.9375\n",
         "Q9.90625 -18.5 9.90625 -18.0156\" id=\"Cmmi10-3b\"/>\n",
         "     <path d=\"\n",
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         "    </defs>\n",
         "    <g transform=\"translate(128.521875 19.56)scale(0.12 -0.12)\">\n",
         "     <use transform=\"translate(0.0 25.125)\" xlink:href=\"#Cmsy10-4e\"/>\n",
         "     <use transform=\"translate(81.982421875 25.125)\" xlink:href=\"#Cmr10-28\"/>\n",
         "     <use transform=\"translate(120.80078125 25.125)\" xlink:href=\"#Cmmi10-b9\"/>\n",
         "     <use transform=\"translate(198.564453125 25.125)\" xlink:href=\"#Cmr10-3d\"/>\n",
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         "     <use transform=\"translate(361.166015625 25.125)\" xlink:href=\"#Cmr10-35\"/>\n",
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         "     <use transform=\"translate(440.833984375 25.125)\" xlink:href=\"#Cmmi10-be\"/>\n",
         "     <use transform=\"translate(515.47265625 25.125)\" xlink:href=\"#Cmr10-3d\"/>\n",
         "     <use transform=\"translate(599.53125 25.125)\" xlink:href=\"#Cmr10-30\"/>\n",
         "     <use transform=\"translate(649.53125 25.125)\" xlink:href=\"#Cmmi10-3a\"/>\n",
         "     <use transform=\"translate(678.07421875 25.125)\" xlink:href=\"#Cmr10-32\"/>\n",
         "     <use transform=\"translate(728.07421875 25.125)\" xlink:href=\"#Cmr10-29\"/>\n",
         "     <use transform=\"translate(766.892578125 25.125)\" xlink:href=\"#Cmmi10-3b\"/>\n",
         "     <use transform=\"translate(822.8984375 25.125)\" xlink:href=\"#Cmmi10-4e\"/>\n",
         "     <use transform=\"translate(920.779296875 25.125)\" xlink:href=\"#Cmr10-3d\"/>\n",
         "     <use transform=\"translate(1004.83789062 25.125)\" xlink:href=\"#Cmr10-32\"/>\n",
         "     <use transform=\"translate(1054.83789062 25.125)\" xlink:href=\"#Cmr10-30\"/>\n",
         "     <use transform=\"translate(1104.83789062 25.125)\" xlink:href=\"#Cmr10-30\"/>\n",
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         "    </g>\n",
         "   </g>\n",
         "  </g>\n",
         " </g>\n",
         " <defs>\n",
         "  <clipPath id=\"p6040b2b708\">\n",
         "   <rect height=\"223.2\" width=\"334.8\" x=\"33.421875\" y=\"21.56\"/>\n",
         "  </clipPath>\n",
         " </defs>\n",
         "</svg>\n"
        ],
        "text": [
         "<__main__.Gaussian at 0x10aaf8fd0>"
        ]
       }
      ],
      "prompt_number": 7
     },
     {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
       "We can easily compare them by displaying their histograms"
      ]
     },
     {
      "cell_type": "code",
      "collapsed": false,
      "input": [
       "display(x.hist)\n",
       "display(x2.hist)"
      ],
      "language": "python",
      "metadata": {},
      "outputs": [
       {
        "output_type": "display_data",
        "png": 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Ll2v8+PFWlxVQMJkZtZl0AADRw0w6AGBDhDcA2BDhDQA2RHgDgA0R3gBgQ4Q3\nANjQ/wPVCqfsJT8WpAAAAABJRU5ErkJggg==\n",
        "text": [
         "<IPython.core.display.Image at 0x10aaf3b50>"
        ]
       },
       {
        "output_type": "display_data",
        "png": 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dRiGEuHDhgpg+fbqYO3euKCsrC3tGIXznbGlpEePGjRO7du0SQogu30c4+MpZ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\n",
        "text": [
         "<IPython.core.display.Image at 0x10aa6a450>"
        ]
       }
      ],
      "prompt_number": 8
     },
     {
      "cell_type": "heading",
      "level": 2,
      "metadata": {},
      "source": [
       "Adding IPython display support to existing objects"
      ]
     },
     {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
       "When you are directly writing your own classes, you can adapt them for display in IPython by following the above example.  But in practice, we often need to work with existing code we can't modify.  We now illustrate how to add these kinds of extended display capabilities to existing objects. We will use the NumPy polynomials and change their default representation to be a formatted LaTeX expression."
      ]
     },
     {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
       "First, consider how a numpy polynomial object renders by default:"
      ]
     },
     {
      "cell_type": "code",
      "collapsed": false,
      "input": [
       "p = np.polynomial.Polynomial([1,2,3], [-10, 10])\n",
       "p"
      ],
      "language": "python",
      "metadata": {},
      "outputs": [
       {
        "output_type": "pyout",
        "prompt_number": 9,
        "text": [
         "Polynomial([ 1.,  2.,  3.], [-10.,  10.], [-1.,  1.])"
        ]
       }
      ],
      "prompt_number": 9
     },
     {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
       "Next, we define a function that pretty-prints a polynomial as a LaTeX string:"
      ]
     },
     {
      "cell_type": "code",
      "collapsed": false,
      "input": [
       "def poly2latex(p):\n",
       "    terms = ['%.2g' % p.coef[0]]\n",
       "    if len(p) > 1:\n",
       "        term = 'x'\n",
       "        c = p.coef[1]\n",
       "        if c!=1:\n",
       "            term = ('%.2g ' % c) + term\n",
       "        terms.append(term)\n",
       "    if len(p) > 2:\n",
       "        for i in range(2, len(p)):\n",
       "            term = 'x^%d' % i\n",
       "            c = p.coef[i]\n",
       "            if c!=1:\n",
       "                term = ('%.2g ' % c) + term\n",
       "            terms.append(term)\n",
       "    px = '$P(x)=%s$' % '+'.join(terms)\n",
       "    dom = r', domain: $[%.2g,\\ %.2g]$' % tuple(p.domain)\n",
       "    return px+dom"
      ],
      "language": "python",
      "metadata": {},
      "outputs": [],
      "prompt_number": 10
     },
     {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
       "This produces, on our polynomial ``p``, the following:"
      ]
     },
     {
      "cell_type": "code",
      "collapsed": false,
      "input": [
       "poly2latex(p)"
      ],
      "language": "python",
      "metadata": {},
      "outputs": [
       {
        "output_type": "pyout",
        "prompt_number": 11,
        "text": [
         "'$P(x)=1+2 x+3 x^2$, domain: $[-10,\\\\ 10]$'"
        ]
       }
      ],
      "prompt_number": 11
     },
     {
      "cell_type": "code",
      "collapsed": false,
      "input": [
       "from IPython.display import Latex\n",
       "Latex(poly2latex(p))"
      ],
      "language": "python",
      "metadata": {},
      "outputs": [
       {
        "latex": [
         "$P(x)=1+2 x+3 x^2$, domain: $[-10,\\ 10]$"
        ],
        "output_type": "pyout",
        "prompt_number": 12,
        "text": [
         "<IPython.core.display.Latex at 0x108f90350>"
        ]
       }
      ],
      "prompt_number": 12
     },
     {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
       "But we can configure IPython to do this automatically for us as follows.  We hook into the\n",
       "IPython display system and instruct it to use ``poly2latex`` for the latex mimetype, when\n",
       "encountering objects of the ``Polynomial`` type defined in the\n",
       "``numpy.polynomial.polynomial`` module:"
      ]
     },
     {
      "cell_type": "code",
      "collapsed": false,
      "input": [
       "ip = get_ipython()\n",
       "latex_formatter = ip.display_formatter.formatters['text/latex']\n",
       "latex_formatter.for_type_by_name('numpy.polynomial.polynomial',\n",
       "                                 'Polynomial', poly2latex)"
      ],
      "language": "python",
      "metadata": {},
      "outputs": [],
      "prompt_number": 13
     },
     {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
       "For more examples on how to use the above system, and how to bundle similar print functions\n",
       "into a convenient IPython extension, see the ``IPython/extensions/sympyprinting.py`` file.  \n",
       "The machinery that defines the display system is in the ``display.py`` and ``displaypub.py`` \n",
       "files in ``IPython/core``.\n",
       "\n",
       "Once our special printer has been loaded, all polynomials will be represented by their \n",
       "mathematical form instead:"
      ]
     },
     {
      "cell_type": "code",
      "collapsed": false,
      "input": [
       "p"
      ],
      "language": "python",
      "metadata": {},
      "outputs": [
       {
        "latex": [
         "$P(x)=1+2 x+3 x^2$, domain: $[-10,\\ 10]$"
        ],
        "output_type": "pyout",
        "prompt_number": 14,
        "text": [
         "Polynomial([ 1.,  2.,  3.], [-10.,  10.], [-1.,  1.])"
        ]
       }
      ],
      "prompt_number": 14
     },
     {
      "cell_type": "code",
      "collapsed": false,
      "input": [
       "p2 = np.polynomial.Polynomial([-20, 71, -15, 1])\n",
       "p2"
      ],
      "language": "python",
      "metadata": {},
      "outputs": [
       {
        "latex": [
         "$P(x)=-20+71 x+-15 x^2+x^3$, domain: $[-1,\\ 1]$"
        ],
        "output_type": "pyout",
        "prompt_number": 15,
        "text": [
         "Polynomial([-20.,  71., -15.,   1.], [-1.,  1.], [-1.,  1.])"
        ]
       }
      ],
      "prompt_number": 15
     }
    ],
    "metadata": {}
   }
  ]
 }

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