Backport PR #10527: Document _repr_mimebundle_

Unfinished as display_* are broken with `_repr_mimebundle_`

IPython/core/formatters.py

@@ -1,1037 +1,1037 b''
 # -*- coding: utf-8 -*-
 """Display formatters.
 
 Inheritance diagram:
 
 .. inheritance-diagram:: IPython.core.formatters
    :parts: 3
 """
 
 # Copyright (c) IPython Development Team.
 # Distributed under the terms of the Modified BSD License.
 
 import abc
 import json
 import sys
 import traceback
 import warnings
 
 from decorator import decorator
 
 from traitlets.config.configurable import Configurable
 from IPython.core.getipython import get_ipython
 from IPython.utils.sentinel import Sentinel
 from IPython.utils.dir2 import get_real_method
 from IPython.lib import pretty
 from traitlets import (
     Bool, Dict, Integer, Unicode, CUnicode, ObjectName, List,
     ForwardDeclaredInstance,
     default, observe,
 )
 from IPython.utils.py3compat import (
     with_metaclass, string_types, unicode_type,
 )
 
 
 class DisplayFormatter(Configurable):
 
     active_types = List(Unicode(),
         help="""List of currently active mime-types to display.
         You can use this to set a white-list for formats to display.
         
         Most users will not need to change this value.
         """).tag(config=True)
 
     @default('active_types')
     def _active_types_default(self):
         return self.format_types
 
     @observe('active_types')
     def _active_types_changed(self, change):
         for key, formatter in self.formatters.items():
             if key in change['new']:
                 formatter.enabled = True
             else:
                 formatter.enabled = False
 
     ipython_display_formatter = ForwardDeclaredInstance('FormatterABC')
     @default('ipython_display_formatter')
     def _default_formatter(self):
         return IPythonDisplayFormatter(parent=self)
 
     mimebundle_formatter = ForwardDeclaredInstance('FormatterABC')
     @default('mimebundle_formatter')
     def _default_mime_formatter(self):
         return MimeBundleFormatter(parent=self)
 
     # A dict of formatter whose keys are format types (MIME types) and whose
     # values are subclasses of BaseFormatter.
     formatters = Dict()
     @default('formatters')
     def _formatters_default(self):
         """Activate the default formatters."""
         formatter_classes = [
             PlainTextFormatter,
             HTMLFormatter,
             MarkdownFormatter,
             SVGFormatter,
             PNGFormatter,
             PDFFormatter,
             JPEGFormatter,
             LatexFormatter,
             JSONFormatter,
             JavascriptFormatter
         ]
         d = {}
         for cls in formatter_classes:
             f = cls(parent=self)
             d[f.format_type] = f
         return d
 
     def format(self, obj, include=None, exclude=None):
         """Return a format data dict for an object.
 
         By default all format types will be computed.
 
         The following MIME types are usually implemented:
 
         * text/plain
         * text/html
         * text/markdown
         * text/latex
         * application/json
         * application/javascript
         * application/pdf
         * image/png
         * image/jpeg
         * image/svg+xml
 
         Parameters
         ----------
         obj : object
             The Python object whose format data will be computed.
         include : list, tuple or set; 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, tuple or set; optional
             A list of format type string (MIME types) to exclude in the format
             data dict. If this is set all format types will be computed,
             except for those included in this argument.
             Mimetypes present in exclude will take precedence over the ones in include
 
         Returns
         -------
         (format_dict, metadata_dict) : tuple of two dicts
         
             format_dict is a dictionary of key/value pairs, one of each format that was
             generated for the object. The keys are the format types, which
             will usually be MIME type strings and the values and JSON'able
             data structure containing the raw data for the representation in
             that format.
             
             metadata_dict is a dictionary of metadata about each mime-type output.
             Its keys will be a strict subset of the keys in format_dict.
 
         Notes
         -----
 
             If an object implement `_repr_mimebundle_` as well as various
             `_repr_*_`, the data returned by `_repr_mimebundle_` will take
             precedence and the corresponding `_repr_*_` for this mimetype will
             not be called.
 
         """
         format_dict = {}
         md_dict = {}
         
         if self.ipython_display_formatter(obj):
             # object handled itself, don't proceed
             return {}, {}
 
         format_dict, md_dict = self.mimebundle_formatter(obj, include=include, exclude=exclude)
 
         if format_dict or md_dict:
             if include:
                 format_dict = {k:v for k,v in format_dict.items() if k in include}
                 md_dict = {k:v for k,v in md_dict.items() if k in include}
             if exclude:
                 format_dict = {k:v for k,v in format_dict.items() if k not in exclude}
                 md_dict = {k:v for k,v in md_dict.items() if k not in exclude}
 
         for format_type, formatter in self.formatters.items():
             if format_type in format_dict:
                 # already got it from mimebundle, don't render again
                 continue
             if include and format_type not in include:
                 continue
             if exclude and format_type in exclude:
                 continue
             
             md = None
             try:
                 data = formatter(obj)
             except:
                 # FIXME: log the exception
                 raise
             
             # formatters can return raw data or (data, metadata)
             if isinstance(data, tuple) and len(data) == 2:
                 data, md = data
             
             if data is not None:
                 format_dict[format_type] = data
             if md is not None:
                 md_dict[format_type] = md
         return format_dict, md_dict
 
     @property
     def format_types(self):
         """Return the format types (MIME types) of the active formatters."""
         return list(self.formatters.keys())
 
 
 #-----------------------------------------------------------------------------
 # Formatters for specific format types (text, html, svg, etc.)
 #-----------------------------------------------------------------------------
 
 
 def _safe_repr(obj):
     """Try to return a repr of an object
 
     always returns a string, at least.
     """
     try:
         return repr(obj)
     except Exception as e:
         return "un-repr-able object (%r)" % e
 
 
 class FormatterWarning(UserWarning):
     """Warning class for errors in formatters"""
 
 @decorator
 def catch_format_error(method, self, *args, **kwargs):
     """show traceback on failed format call"""
     try:
         r = method(self, *args, **kwargs)
     except NotImplementedError:
         # don't warn on NotImplementedErrors
         return None
     except Exception:
         exc_info = sys.exc_info()
         ip = get_ipython()
         if ip is not None:
             ip.showtraceback(exc_info)
         else:
             traceback.print_exception(*exc_info)
         return None
     return self._check_return(r, args[0])
 
 
 class FormatterABC(with_metaclass(abc.ABCMeta, object)):
     """ Abstract base class for Formatters.
 
     A formatter is a callable class that is responsible for computing the
     raw format data for a particular format type (MIME type). For example,
     an HTML formatter would have a format type of `text/html` and would return
     the HTML representation of the object when called.
     """
 
     # The format type of the data returned, usually a MIME type.
     format_type = 'text/plain'
 
     # Is the formatter enabled...
     enabled = True
     
     @abc.abstractmethod
     def __call__(self, obj):
         """Return a JSON'able representation of the object.
 
         If the object cannot be formatted by this formatter,
         warn and return None.
         """
         return repr(obj)
 
 
 def _mod_name_key(typ):
     """Return a (__module__, __name__) tuple for a type.
     
     Used as key in Formatter.deferred_printers.
     """
     module = getattr(typ, '__module__', None)
     name = getattr(typ, '__name__', None)
     return (module, name)
 
 
 def _get_type(obj):
     """Return the type of an instance (old and new-style)"""
     return getattr(obj, '__class__', None) or type(obj)
 
 
 _raise_key_error = Sentinel('_raise_key_error', __name__, 
 """
 Special value to raise a KeyError
 
 Raise KeyError in `BaseFormatter.pop` if passed as the default value to `pop`
 """)
 
 
 class BaseFormatter(Configurable):
     """A base formatter class that is configurable.
 
     This formatter should usually be used as the base class of all formatters.
     It is a traited :class:`Configurable` class and includes an extensible
     API for users to determine how their objects are formatted. The following
     logic is used to find a function to format an given object.
 
     1. The object is introspected to see if it has a method with the name
        :attr:`print_method`. If is does, that object is passed to that method
        for formatting.
     2. If no print method is found, three internal dictionaries are consulted
        to find print method: :attr:`singleton_printers`, :attr:`type_printers`
        and :attr:`deferred_printers`.
 
     Users should use these dictionaries to register functions that will be
     used to compute the format data for their objects (if those objects don't
     have the special print methods). The easiest way of using these
     dictionaries is through the :meth:`for_type` and :meth:`for_type_by_name`
     methods.
 
     If no function/callable is found to compute the format data, ``None`` is
     returned and this format type is not used.
     """
 
     format_type = Unicode('text/plain')
     _return_type = string_types
 
     enabled = Bool(True).tag(config=True)
 
     print_method = ObjectName('__repr__')
 
     # The singleton printers.
     # Maps the IDs of the builtin singleton objects to the format functions.
     singleton_printers = Dict().tag(config=True)
 
     # The type-specific printers.
     # Map type objects to the format functions.
     type_printers = Dict().tag(config=True)
 
     # The deferred-import type-specific printers.
     # Map (modulename, classname) pairs to the format functions.
     deferred_printers = Dict().tag(config=True)
     
     @catch_format_error
     def __call__(self, obj):
         """Compute the format for an object."""
         if self.enabled:
             # lookup registered printer
             try:
                 printer = self.lookup(obj)
             except KeyError:
                 pass
             else:
                 return printer(obj)
             # Finally look for special method names
             method = get_real_method(obj, self.print_method)
             if method is not None:
                 return method()
             return None
         else:
             return None
     
     def __contains__(self, typ):
         """map in to lookup_by_type"""
         try:
             self.lookup_by_type(typ)
         except KeyError:
             return False
         else:
             return True
     
     def _check_return(self, r, obj):
         """Check that a return value is appropriate
         
         Return the value if so, None otherwise, warning if invalid.
         """
         if r is None or isinstance(r, self._return_type) or \
             (isinstance(r, tuple) and r and isinstance(r[0], self._return_type)):
             return r
         else:
             warnings.warn(
                 "%s formatter returned invalid type %s (expected %s) for object: %s" % \
                 (self.format_type, type(r), self._return_type, _safe_repr(obj)),
                 FormatterWarning
             )
     
     def lookup(self, obj):
         """Look up the formatter for a given instance.
         
         Parameters
         ----------
         obj  : object instance
 
         Returns
         -------
         f : callable
             The registered formatting callable for the type.
 
         Raises
         ------
         KeyError if the type has not been registered.
         """
         # look for singleton first
         obj_id = id(obj)
         if obj_id in self.singleton_printers:
             return self.singleton_printers[obj_id]
         # then lookup by type
         return self.lookup_by_type(_get_type(obj))
     
     def lookup_by_type(self, typ):
         """Look up the registered formatter for a type.
 
         Parameters
         ----------
         typ  : type or '__module__.__name__' string for a type
 
         Returns
         -------
         f : callable
             The registered formatting callable for the type.
 
         Raises
         ------
         KeyError if the type has not been registered.
         """
         if isinstance(typ, string_types):
             typ_key = tuple(typ.rsplit('.',1))
             if typ_key not in self.deferred_printers:
                 # We may have it cached in the type map. We will have to
                 # iterate over all of the types to check.
                 for cls in self.type_printers:
                     if _mod_name_key(cls) == typ_key:
                         return self.type_printers[cls]
             else:
                 return self.deferred_printers[typ_key]
         else:
             for cls in pretty._get_mro(typ):
                 if cls in self.type_printers or self._in_deferred_types(cls):
                     return self.type_printers[cls]
         
         # If we have reached here, the lookup failed.
         raise KeyError("No registered printer for {0!r}".format(typ))
 
     def for_type(self, typ, func=None):
         """Add a format function for a given type.
         
         Parameters
         -----------
         typ : type or '__module__.__name__' string for a type
             The class of the object that will be formatted using `func`.
         func : callable
             A callable for computing the format data.
             `func` will be called with the object to be formatted,
             and will return the raw data in this formatter's format.
             Subclasses may use a different call signature for the
             `func` argument.
             
             If `func` is None or not specified, there will be no change,
             only returning the current value.
         
         Returns
         -------
         oldfunc : callable
             The currently registered callable.
             If you are registering a new formatter,
             this will be the previous value (to enable restoring later).
         """
         # if string given, interpret as 'pkg.module.class_name'
         if isinstance(typ, string_types):
             type_module, type_name = typ.rsplit('.', 1)
             return self.for_type_by_name(type_module, type_name, func)
         
         try:
             oldfunc = self.lookup_by_type(typ)
         except KeyError:
             oldfunc = None
         
         if func is not None:
             self.type_printers[typ] = func
         
         return oldfunc
 
     def for_type_by_name(self, type_module, type_name, func=None):
         """Add a format function for a type specified by the full dotted
         module and name of the type, rather than the type of the object.
 
         Parameters
         ----------
         type_module : str
             The full dotted name of the module the type is defined in, like
             ``numpy``.
         type_name : str
             The name of the type (the class name), like ``dtype``
         func : callable
             A callable for computing the format data.
             `func` will be called with the object to be formatted,
             and will return the raw data in this formatter's format.
             Subclasses may use a different call signature for the
             `func` argument.
             
             If `func` is None or unspecified, there will be no change,
             only returning the current value.
         
         Returns
         -------
         oldfunc : callable
             The currently registered callable.
             If you are registering a new formatter,
             this will be the previous value (to enable restoring later).
         """
         key = (type_module, type_name)
         
         try:
             oldfunc = self.lookup_by_type("%s.%s" % key)
         except KeyError:
             oldfunc = None
         
         if func is not None:
             self.deferred_printers[key] = func
         return oldfunc
     
     def pop(self, typ, default=_raise_key_error):
         """Pop a formatter for the given type.
 
         Parameters
         ----------
         typ : type or '__module__.__name__' string for a type
         default : object
             value to be returned if no formatter is registered for typ.
 
         Returns
         -------
         obj : object
             The last registered object for the type.
 
         Raises
         ------
         KeyError if the type is not registered and default is not specified.
         """
         
         if isinstance(typ, string_types):
             typ_key = tuple(typ.rsplit('.',1))
             if typ_key not in self.deferred_printers:
                 # We may have it cached in the type map. We will have to
                 # iterate over all of the types to check.
                 for cls in self.type_printers:
                     if _mod_name_key(cls) == typ_key:
                         old = self.type_printers.pop(cls)
                         break
                 else:
                     old = default
             else:
                 old = self.deferred_printers.pop(typ_key)
         else:
             if typ in self.type_printers:
                 old = self.type_printers.pop(typ)
             else:
                 old = self.deferred_printers.pop(_mod_name_key(typ), default)
         if old is _raise_key_error:
             raise KeyError("No registered value for {0!r}".format(typ))
         return old
 
     def _in_deferred_types(self, cls):
         """
         Check if the given class is specified in the deferred type registry.
 
         Successful matches will be moved to the regular type registry for future use.
         """
         mod = getattr(cls, '__module__', None)
         name = getattr(cls, '__name__', None)
         key = (mod, name)
         if key in self.deferred_printers:
             # Move the printer over to the regular registry.
             printer = self.deferred_printers.pop(key)
             self.type_printers[cls] = printer
             return True
         return False
 
 
 class PlainTextFormatter(BaseFormatter):
     """The default pretty-printer.
 
     This uses :mod:`IPython.lib.pretty` to compute the format data of
     the object. If the object cannot be pretty printed, :func:`repr` is used.
     See the documentation of :mod:`IPython.lib.pretty` for details on
     how to write pretty printers.  Here is a simple example::
 
         def dtype_pprinter(obj, p, cycle):
             if cycle:
                 return p.text('dtype(...)')
             if hasattr(obj, 'fields'):
                 if obj.fields is None:
                     p.text(repr(obj))
                 else:
                     p.begin_group(7, 'dtype([')
                     for i, field in enumerate(obj.descr):
                         if i > 0:
                             p.text(',')
                             p.breakable()
                         p.pretty(field)
                     p.end_group(7, '])')
     """
 
     # The format type of data returned.
     format_type = Unicode('text/plain')
 
     # This subclass ignores this attribute as it always need to return
     # something.
     enabled = Bool(True).tag(config=False)
     
     max_seq_length = Integer(pretty.MAX_SEQ_LENGTH,
         help="""Truncate large collections (lists, dicts, tuples, sets) to this size.
         
         Set to 0 to disable truncation.
         """
     ).tag(config=True)
     
     # Look for a _repr_pretty_ methods to use for pretty printing.
     print_method = ObjectName('_repr_pretty_')
 
     # Whether to pretty-print or not.
     pprint = Bool(True).tag(config=True)
 
     # Whether to be verbose or not.
     verbose = Bool(False).tag(config=True)
 
     # The maximum width.
     max_width = Integer(79).tag(config=True)
 
     # The newline character.
     newline = Unicode('\n').tag(config=True)
 
     # format-string for pprinting floats
     float_format = Unicode('%r')
     # setter for float precision, either int or direct format-string
     float_precision = CUnicode('').tag(config=True)
 
     @observe('float_precision')
     def _float_precision_changed(self, change):
         """float_precision changed, set float_format accordingly.
 
         float_precision can be set by int or str.
         This will set float_format, after interpreting input.
         If numpy has been imported, numpy print precision will also be set.
 
         integer `n` sets format to '%.nf', otherwise, format set directly.
 
         An empty string returns to defaults (repr for float, 8 for numpy).
 
         This parameter can be set via the '%precision' magic.
         """
 
         new = change['new']
         if '%' in new:
             # got explicit format string
             fmt = new
             try:
                 fmt%3.14159
             except Exception:
                 raise ValueError("Precision must be int or format string, not %r"%new)
         elif new:
             # otherwise, should be an int
             try:
                 i = int(new)
                 assert i >= 0
             except ValueError:
                 raise ValueError("Precision must be int or format string, not %r"%new)
             except AssertionError:
                 raise ValueError("int precision must be non-negative, not %r"%i)
 
             fmt = '%%.%if'%i
             if 'numpy' in sys.modules:
                 # set numpy precision if it has been imported
                 import numpy
                 numpy.set_printoptions(precision=i)
         else:
             # default back to repr
             fmt = '%r'
             if 'numpy' in sys.modules:
                 import numpy
                 # numpy default is 8
                 numpy.set_printoptions(precision=8)
         self.float_format = fmt
 
     # Use the default pretty printers from IPython.lib.pretty.
     @default('singleton_printers')
     def _singleton_printers_default(self):
         return pretty._singleton_pprinters.copy()
 
     @default('type_printers')
     def _type_printers_default(self):
         d = pretty._type_pprinters.copy()
         d[float] = lambda obj,p,cycle: p.text(self.float_format%obj)
         return d
 
     @default('deferred_printers')
     def _deferred_printers_default(self):
         return pretty._deferred_type_pprinters.copy()
 
     #### FormatterABC interface ####
 
     @catch_format_error
     def __call__(self, obj):
         """Compute the pretty representation of the object."""
         if not self.pprint:
             return repr(obj)
         else:
             # handle str and unicode on Python 2
             # io.StringIO only accepts unicode,
             # cStringIO doesn't handle unicode on py2,
             # StringIO allows str, unicode but only ascii str
             stream = pretty.CUnicodeIO()
             printer = pretty.RepresentationPrinter(stream, self.verbose,
                 self.max_width, self.newline,
                 max_seq_length=self.max_seq_length,
                 singleton_pprinters=self.singleton_printers,
                 type_pprinters=self.type_printers,
                 deferred_pprinters=self.deferred_printers)
             printer.pretty(obj)
             printer.flush()
             return stream.getvalue()
 
 
 class HTMLFormatter(BaseFormatter):
     """An HTML formatter.
 
     To define the callables that compute the HTML representation of your
     objects, define a :meth:`_repr_html_` method or use the :meth:`for_type`
     or :meth:`for_type_by_name` methods to register functions that handle
     this.
 
     The return value of this formatter should be a valid HTML snippet that
     could be injected into an existing DOM. It should *not* include the
     ```<html>`` or ```<body>`` tags.
     """
     format_type = Unicode('text/html')
 
     print_method = ObjectName('_repr_html_')
 
 
 class MarkdownFormatter(BaseFormatter):
     """A Markdown formatter.
 
     To define the callables that compute the Markdown representation of your
     objects, define a :meth:`_repr_markdown_` method or use the :meth:`for_type`
     or :meth:`for_type_by_name` methods to register functions that handle
     this.
 
     The return value of this formatter should be a valid Markdown.
     """
     format_type = Unicode('text/markdown')
 
     print_method = ObjectName('_repr_markdown_')
 
 class SVGFormatter(BaseFormatter):
     """An SVG formatter.
 
     To define the callables that compute the SVG representation of your
     objects, define a :meth:`_repr_svg_` method or use the :meth:`for_type`
     or :meth:`for_type_by_name` methods to register functions that handle
     this.
 
     The return value of this formatter should be valid SVG enclosed in
     ```<svg>``` tags, that could be injected into an existing DOM. It should
     *not* include the ```<html>`` or ```<body>`` tags.
     """
     format_type = Unicode('image/svg+xml')
 
     print_method = ObjectName('_repr_svg_')
 
 
 class PNGFormatter(BaseFormatter):
     """A PNG formatter.
 
     To define the callables that compute the PNG representation of your
     objects, define a :meth:`_repr_png_` method or use the :meth:`for_type`
     or :meth:`for_type_by_name` methods to register functions that handle
     this.
 
     The return value of this formatter should be raw PNG data, *not*
     base64 encoded.
     """
     format_type = Unicode('image/png')
 
     print_method = ObjectName('_repr_png_')
     
     _return_type = (bytes, unicode_type)
 
 
 class JPEGFormatter(BaseFormatter):
     """A JPEG formatter.
 
     To define the callables that compute the JPEG representation of your
     objects, define a :meth:`_repr_jpeg_` method or use the :meth:`for_type`
     or :meth:`for_type_by_name` methods to register functions that handle
     this.
 
     The return value of this formatter should be raw JPEG data, *not*
     base64 encoded.
     """
     format_type = Unicode('image/jpeg')
 
     print_method = ObjectName('_repr_jpeg_')
 
     _return_type = (bytes, unicode_type)
 
 
 class LatexFormatter(BaseFormatter):
     """A LaTeX formatter.
 
     To define the callables that compute the LaTeX representation of your
     objects, define a :meth:`_repr_latex_` method or use the :meth:`for_type`
     or :meth:`for_type_by_name` methods to register functions that handle
     this.
 
     The return value of this formatter should be a valid LaTeX equation,
     enclosed in either ```$```, ```$$``` or another LaTeX equation
     environment.
     """
     format_type = Unicode('text/latex')
 
     print_method = ObjectName('_repr_latex_')
 
 
 class JSONFormatter(BaseFormatter):
     """A JSON string formatter.
 
     To define the callables that compute the JSONable representation of
     your objects, define a :meth:`_repr_json_` method or use the :meth:`for_type`
     or :meth:`for_type_by_name` methods to register functions that handle
     this.
 
     The return value of this formatter should be a JSONable list or dict.
     JSON scalars (None, number, string) are not allowed, only dict or list containers.
     """
     format_type = Unicode('application/json')
     _return_type = (list, dict)
 
     print_method = ObjectName('_repr_json_')
     
     def _check_return(self, r, obj):
         """Check that a return value is appropriate
         
         Return the value if so, None otherwise, warning if invalid.
         """
         if r is None:
             return
         md = None
         if isinstance(r, tuple):
             # unpack data, metadata tuple for type checking on first element
             r, md = r
         
         # handle deprecated JSON-as-string form from IPython < 3
         if isinstance(r, string_types):
             warnings.warn("JSON expects JSONable list/dict containers, not JSON strings",
             FormatterWarning)
             r = json.loads(r)
         
         if md is not None:
             # put the tuple back together
             r = (r, md)
         return super(JSONFormatter, self)._check_return(r, obj)
 
 
 class JavascriptFormatter(BaseFormatter):
     """A Javascript formatter.
 
     To define the callables that compute the Javascript representation of
     your objects, define a :meth:`_repr_javascript_` method or use the
     :meth:`for_type` or :meth:`for_type_by_name` methods to register functions
     that handle this.
 
     The return value of this formatter should be valid Javascript code and
     should *not* be enclosed in ```<script>``` tags.
     """
     format_type = Unicode('application/javascript')
 
     print_method = ObjectName('_repr_javascript_')
 
 
 class PDFFormatter(BaseFormatter):
     """A PDF formatter.
 
     To define the callables that compute the PDF representation of your
     objects, define a :meth:`_repr_pdf_` method or use the :meth:`for_type`
     or :meth:`for_type_by_name` methods to register functions that handle
     this.
 
     The return value of this formatter should be raw PDF data, *not*
     base64 encoded.
     """
     format_type = Unicode('application/pdf')
 
     print_method = ObjectName('_repr_pdf_')
 
     _return_type = (bytes, unicode_type)
 
 class IPythonDisplayFormatter(BaseFormatter):
     """An escape-hatch Formatter for objects that know how to display themselves.
     
     To define the callables that compute the representation of your
     objects, define a :meth:`_ipython_display_` method or use the :meth:`for_type`
     or :meth:`for_type_by_name` methods to register functions that handle
     this. Unlike mime-type displays, this method should not return anything,
     instead calling any appropriate display methods itself.
     
     This display formatter has highest priority.
     If it fires, no other display formatter will be called.
 
     Prior to IPython 6.1, `_ipython_display_` was the only way to display custom mime-types
     without registering a new Formatter.
     
     IPython 6.1 introduces `_repr_mimebundle_` for displaying custom mime-types,
     so `_ipython_display_` should only be used for objects that require unusual
     display patterns, such as multiple display calls.
     """
     print_method = ObjectName('_ipython_display_')
     _return_type = (type(None), bool)
 
     @catch_format_error
     def __call__(self, obj):
         """Compute the format for an object."""
         if self.enabled:
             # lookup registered printer
             try:
                 printer = self.lookup(obj)
             except KeyError:
                 pass
             else:
                 printer(obj)
                 return True
             # Finally look for special method names
             method = get_real_method(obj, self.print_method)
             if method is not None:
                 method()
                 return True
 
 
 class MimeBundleFormatter(BaseFormatter):
     """A Formatter for arbitrary mime-types.
 
     Unlike other `_repr_<mimetype>_` methods,
     `_repr_mimebundle_` should return mime-bundle data,
     either the mime-keyed `data` dictionary or the tuple `(data, metadata)`.
     Any mime-type is valid.
 
     To define the callables that compute the mime-bundle representation of your
     objects, define a :meth:`_repr_mimebundle_` method or use the :meth:`for_type`
     or :meth:`for_type_by_name` methods to register functions that handle
     this.
 
     .. versionadded:: 6.1
     """
     print_method = ObjectName('_repr_mimebundle_')
     _return_type = dict
     
     def _check_return(self, r, obj):
         r = super(MimeBundleFormatter, self)._check_return(r, obj)
         # always return (data, metadata):
         if r is None:
             return {}, {}
         if not isinstance(r, tuple):
             return r, {}
         return r
 
     @catch_format_error
     def __call__(self, obj, include=None, exclude=None):
         """Compute the format for an object.
 
         Identical to parent's method but we pass extra parameters to the method.
 
         Unlike other _repr_*_ `_repr_mimebundle_` should allow extra kwargs, in
         particular `include` and `exclude`.
         """
         if self.enabled:
             # lookup registered printer
             try:
                 printer = self.lookup(obj)
             except KeyError:
                 pass
             else:
                 return printer(obj)
             # Finally look for special method names
             method = get_real_method(obj, self.print_method)
 
             if method is not None:
                 d = {}
                 d['include'] = include
-                d['exclude'] = include
+                d['exclude'] = exclude
                 return method(**d)
             return None
         else:
             return None
 
 
 FormatterABC.register(BaseFormatter)
 FormatterABC.register(PlainTextFormatter)
 FormatterABC.register(HTMLFormatter)
 FormatterABC.register(MarkdownFormatter)
 FormatterABC.register(SVGFormatter)
 FormatterABC.register(PNGFormatter)
 FormatterABC.register(PDFFormatter)
 FormatterABC.register(JPEGFormatter)
 FormatterABC.register(LatexFormatter)
 FormatterABC.register(JSONFormatter)
 FormatterABC.register(JavascriptFormatter)
 FormatterABC.register(IPythonDisplayFormatter)
 FormatterABC.register(MimeBundleFormatter)
 
 
 def format_display_data(obj, include=None, exclude=None):
     """Return a format data dict for an object.
 
     By default all format types will be computed.
 
     The following MIME types are currently implemented:
 
     * text/plain
     * text/html
     * text/markdown
     * text/latex
     * application/json
     * application/javascript
     * application/pdf
     * image/png
     * image/jpeg
     * image/svg+xml
 
     Parameters
     ----------
     obj : object
         The Python object whose format data will be computed.
 
     Returns
     -------
     format_dict : dict
         A dictionary of key/value pairs, one or each format that was
         generated for the object. The keys are the format types, which
         will usually be MIME type strings and the values and JSON'able
         data structure containing the raw data for the representation in
         that format.
     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.
     """
     from IPython.core.interactiveshell import InteractiveShell
 
     return InteractiveShell.instance().display_formatter.format(
         obj,
         include,
         exclude
     )

IPython/core/tests/test_formatters.py

@@ -1,503 +1,523 b''
 """Tests for the Formatters."""
 
 import warnings
 from math import pi
 
 try:
     import numpy
 except:
     numpy = None
 import nose.tools as nt
 
 from IPython import get_ipython
 from traitlets.config import Config
 from IPython.core.formatters import (
     PlainTextFormatter, HTMLFormatter, PDFFormatter, _mod_name_key,
     DisplayFormatter, JSONFormatter,
 )
 from IPython.utils.io import capture_output
 
 class A(object):
     def __repr__(self):
         return 'A()'
 
 class B(A):
     def __repr__(self):
         return 'B()'
 
 class C:
     pass
 
 class BadRepr(object):
     def __repr__(self):
         raise ValueError("bad repr")
 
 class BadPretty(object):
     _repr_pretty_ = None
 
 class GoodPretty(object):
     def _repr_pretty_(self, pp, cycle):
         pp.text('foo')
 
     def __repr__(self):
         return 'GoodPretty()'
 
 def foo_printer(obj, pp, cycle):
     pp.text('foo')
 
 def test_pretty():
     f = PlainTextFormatter()
     f.for_type(A, foo_printer)
     nt.assert_equal(f(A()), 'foo')
     nt.assert_equal(f(B()), 'foo')
     nt.assert_equal(f(GoodPretty()), 'foo')
     # Just don't raise an exception for the following:
     f(BadPretty())
 
     f.pprint = False
     nt.assert_equal(f(A()), 'A()')
     nt.assert_equal(f(B()), 'B()')
     nt.assert_equal(f(GoodPretty()), 'GoodPretty()')
 
 
 def test_deferred():
     f = PlainTextFormatter()
 
 def test_precision():
     """test various values for float_precision."""
     f = PlainTextFormatter()
     nt.assert_equal(f(pi), repr(pi))
     f.float_precision = 0
     if numpy:
         po = numpy.get_printoptions()
         nt.assert_equal(po['precision'], 0)
     nt.assert_equal(f(pi), '3')
     f.float_precision = 2
     if numpy:
         po = numpy.get_printoptions()
         nt.assert_equal(po['precision'], 2)
     nt.assert_equal(f(pi), '3.14')
     f.float_precision = '%g'
     if numpy:
         po = numpy.get_printoptions()
         nt.assert_equal(po['precision'], 2)
     nt.assert_equal(f(pi), '3.14159')
     f.float_precision = '%e'
     nt.assert_equal(f(pi), '3.141593e+00')
     f.float_precision = ''
     if numpy:
         po = numpy.get_printoptions()
         nt.assert_equal(po['precision'], 8)
     nt.assert_equal(f(pi), repr(pi))
 
 def test_bad_precision():
     """test various invalid values for float_precision."""
     f = PlainTextFormatter()
     def set_fp(p):
         f.float_precision=p
     nt.assert_raises(ValueError, set_fp, '%')
     nt.assert_raises(ValueError, set_fp, '%.3f%i')
     nt.assert_raises(ValueError, set_fp, 'foo')
     nt.assert_raises(ValueError, set_fp, -1)
 
 def test_for_type():
     f = PlainTextFormatter()
     
     # initial return, None
     nt.assert_is(f.for_type(C, foo_printer), None)
     # no func queries
     nt.assert_is(f.for_type(C), foo_printer)
     # shouldn't change anything
     nt.assert_is(f.for_type(C), foo_printer)
     # None should do the same
     nt.assert_is(f.for_type(C, None), foo_printer)
     nt.assert_is(f.for_type(C, None), foo_printer)
 
 def test_for_type_string():
     f = PlainTextFormatter()
     
-    mod = C.__module__
-    
     type_str = '%s.%s' % (C.__module__, 'C')
     
     # initial return, None
     nt.assert_is(f.for_type(type_str, foo_printer), None)
     # no func queries
     nt.assert_is(f.for_type(type_str), foo_printer)
     nt.assert_in(_mod_name_key(C), f.deferred_printers)
     nt.assert_is(f.for_type(C), foo_printer)
     nt.assert_not_in(_mod_name_key(C), f.deferred_printers)
     nt.assert_in(C, f.type_printers)
 
 def test_for_type_by_name():
     f = PlainTextFormatter()
     
     mod = C.__module__
     
     # initial return, None
     nt.assert_is(f.for_type_by_name(mod, 'C', foo_printer), None)
     # no func queries
     nt.assert_is(f.for_type_by_name(mod, 'C'), foo_printer)
     # shouldn't change anything
     nt.assert_is(f.for_type_by_name(mod, 'C'), foo_printer)
     # None should do the same
     nt.assert_is(f.for_type_by_name(mod, 'C', None), foo_printer)
     nt.assert_is(f.for_type_by_name(mod, 'C', None), foo_printer)
 
 def test_lookup():
     f = PlainTextFormatter()
     
     f.for_type(C, foo_printer)
     nt.assert_is(f.lookup(C()), foo_printer)
     with nt.assert_raises(KeyError):
         f.lookup(A())
 
 def test_lookup_string():
     f = PlainTextFormatter()
     type_str = '%s.%s' % (C.__module__, 'C')
     
     f.for_type(type_str, foo_printer)
     nt.assert_is(f.lookup(C()), foo_printer)
     # should move from deferred to imported dict
     nt.assert_not_in(_mod_name_key(C), f.deferred_printers)
     nt.assert_in(C, f.type_printers)
 
 def test_lookup_by_type():
     f = PlainTextFormatter()
     f.for_type(C, foo_printer)
     nt.assert_is(f.lookup_by_type(C), foo_printer)
-    type_str = '%s.%s' % (C.__module__, 'C')
     with nt.assert_raises(KeyError):
         f.lookup_by_type(A)
 
 def test_lookup_by_type_string():
     f = PlainTextFormatter()
     type_str = '%s.%s' % (C.__module__, 'C')
     f.for_type(type_str, foo_printer)
     
     # verify insertion
     nt.assert_in(_mod_name_key(C), f.deferred_printers)
     nt.assert_not_in(C, f.type_printers)
     
     nt.assert_is(f.lookup_by_type(type_str), foo_printer)
     # lookup by string doesn't cause import
     nt.assert_in(_mod_name_key(C), f.deferred_printers)
     nt.assert_not_in(C, f.type_printers)
     
     nt.assert_is(f.lookup_by_type(C), foo_printer)
     # should move from deferred to imported dict
     nt.assert_not_in(_mod_name_key(C), f.deferred_printers)
     nt.assert_in(C, f.type_printers)
 
 def test_in_formatter():
     f = PlainTextFormatter()
     f.for_type(C, foo_printer)
     type_str = '%s.%s' % (C.__module__, 'C')
     nt.assert_in(C, f)
     nt.assert_in(type_str, f)
 
 def test_string_in_formatter():
     f = PlainTextFormatter()
     type_str = '%s.%s' % (C.__module__, 'C')
     f.for_type(type_str, foo_printer)
     nt.assert_in(type_str, f)
     nt.assert_in(C, f)
 
 def test_pop():
     f = PlainTextFormatter()
     f.for_type(C, foo_printer)
     nt.assert_is(f.lookup_by_type(C), foo_printer)
     nt.assert_is(f.pop(C, None), foo_printer)
     f.for_type(C, foo_printer)
     nt.assert_is(f.pop(C), foo_printer)
     with nt.assert_raises(KeyError):
         f.lookup_by_type(C)
     with nt.assert_raises(KeyError):
         f.pop(C)
     with nt.assert_raises(KeyError):
         f.pop(A)
     nt.assert_is(f.pop(A, None), None)
 
 def test_pop_string():
     f = PlainTextFormatter()
     type_str = '%s.%s' % (C.__module__, 'C')
     
     with nt.assert_raises(KeyError):
         f.pop(type_str)
     
     f.for_type(type_str, foo_printer)
     f.pop(type_str)
     with nt.assert_raises(KeyError):
         f.lookup_by_type(C)
     with nt.assert_raises(KeyError):
         f.pop(type_str)
 
     f.for_type(C, foo_printer)
     nt.assert_is(f.pop(type_str, None), foo_printer)
     with nt.assert_raises(KeyError):
         f.lookup_by_type(C)
     with nt.assert_raises(KeyError):
         f.pop(type_str)
     nt.assert_is(f.pop(type_str, None), None)
     
 
 def test_error_method():
     f = HTMLFormatter()
     class BadHTML(object):
         def _repr_html_(self):
             raise ValueError("Bad HTML")
     bad = BadHTML()
     with capture_output() as captured:
         result = f(bad)
     nt.assert_is(result, None)
     nt.assert_in("Traceback", captured.stdout)
     nt.assert_in("Bad HTML", captured.stdout)
     nt.assert_in("_repr_html_", captured.stdout)
 
 def test_nowarn_notimplemented():
     f = HTMLFormatter()
     class HTMLNotImplemented(object):
         def _repr_html_(self):
             raise NotImplementedError
     h = HTMLNotImplemented()
     with capture_output() as captured:
         result = f(h)
     nt.assert_is(result, None)
     nt.assert_equal("", captured.stderr)
     nt.assert_equal("", captured.stdout)
 
 def test_warn_error_for_type():
     f = HTMLFormatter()
     f.for_type(int, lambda i: name_error)
     with capture_output() as captured:
         result = f(5)
     nt.assert_is(result, None)
     nt.assert_in("Traceback", captured.stdout)
     nt.assert_in("NameError", captured.stdout)
     nt.assert_in("name_error", captured.stdout)
 
 def test_error_pretty_method():
     f = PlainTextFormatter()
     class BadPretty(object):
         def _repr_pretty_(self):
             return "hello"
     bad = BadPretty()
     with capture_output() as captured:
         result = f(bad)
     nt.assert_is(result, None)
     nt.assert_in("Traceback", captured.stdout)
     nt.assert_in("_repr_pretty_", captured.stdout)
     nt.assert_in("given", captured.stdout)
     nt.assert_in("argument", captured.stdout)
 
 
 def test_bad_repr_traceback():
     f = PlainTextFormatter()
     bad = BadRepr()
     with capture_output() as captured:
         result = f(bad)
     # catches error, returns None
     nt.assert_is(result, None)
     nt.assert_in("Traceback", captured.stdout)
     nt.assert_in("__repr__", captured.stdout)
     nt.assert_in("ValueError", captured.stdout)
 
 
 class MakePDF(object):
     def _repr_pdf_(self):
         return 'PDF'
 
 def test_pdf_formatter():
     pdf = MakePDF()
     f = PDFFormatter()
     nt.assert_equal(f(pdf), 'PDF')
 
 def test_print_method_bound():
     f = HTMLFormatter()
     class MyHTML(object):
         def _repr_html_(self):
             return "hello"
     with capture_output() as captured:
         result = f(MyHTML)
     nt.assert_is(result, None)
     nt.assert_not_in("FormatterWarning", captured.stderr)
 
     with capture_output() as captured:
         result = f(MyHTML())
     nt.assert_equal(result, "hello")
     nt.assert_equal(captured.stderr, "")
 
 def test_print_method_weird():
 
     class TextMagicHat(object):
         def __getattr__(self, key):
             return key
 
     f = HTMLFormatter()
     
     text_hat = TextMagicHat()
     nt.assert_equal(text_hat._repr_html_, '_repr_html_')
     with capture_output() as captured:
         result = f(text_hat)
     
     nt.assert_is(result, None)
     nt.assert_not_in("FormatterWarning", captured.stderr)
 
     class CallableMagicHat(object):
         def __getattr__(self, key):
             return lambda : key
     
     call_hat = CallableMagicHat()
     with capture_output() as captured:
         result = f(call_hat)
     
     nt.assert_equal(result, None)
 
     class BadReprArgs(object):
         def _repr_html_(self, extra, args):
             return "html"
     
     bad = BadReprArgs()
     with capture_output() as captured:
         result = f(bad)
     
     nt.assert_is(result, None)
     nt.assert_not_in("FormatterWarning", captured.stderr)
 
 
 def test_format_config():
     """config objects don't pretend to support fancy reprs with lazy attrs"""
     f = HTMLFormatter()
     cfg = Config()
     with capture_output() as captured:
         result = f(cfg)
     nt.assert_is(result, None)
     nt.assert_equal(captured.stderr, "")
 
     with capture_output() as captured:
         result = f(Config)
     nt.assert_is(result, None)
     nt.assert_equal(captured.stderr, "")
 
 def test_pretty_max_seq_length():
     f = PlainTextFormatter(max_seq_length=1)
     lis = list(range(3))
     text = f(lis)
     nt.assert_equal(text, '[0, ...]')
     f.max_seq_length = 0
     text = f(lis)
     nt.assert_equal(text, '[0, 1, 2]')
     text = f(list(range(1024)))
     lines = text.splitlines()
     nt.assert_equal(len(lines), 1024)
 
 
 def test_ipython_display_formatter():
     """Objects with _ipython_display_ defined bypass other formatters"""
     f = get_ipython().display_formatter
     catcher = []
     class SelfDisplaying(object):
         def _ipython_display_(self):
             catcher.append(self)
 
     class NotSelfDisplaying(object):
         def __repr__(self):
             return "NotSelfDisplaying"
         
         def _ipython_display_(self):
             raise NotImplementedError
     
     save_enabled = f.ipython_display_formatter.enabled
     f.ipython_display_formatter.enabled = True
     
     yes = SelfDisplaying()
     no = NotSelfDisplaying()
     
     d, md = f.format(no)
     nt.assert_equal(d, {'text/plain': repr(no)})
     nt.assert_equal(md, {})
     nt.assert_equal(catcher, [])
     
     d, md = f.format(yes)
     nt.assert_equal(d, {})
     nt.assert_equal(md, {})
     nt.assert_equal(catcher, [yes])
 
     f.ipython_display_formatter.enabled = save_enabled
 
 
 def test_json_as_string_deprecated():
     class JSONString(object):
         def _repr_json_(self):
             return '{}'
     
     f = JSONFormatter()
     with warnings.catch_warnings(record=True) as w:
         d = f(JSONString())
     nt.assert_equal(d, {})
     nt.assert_equal(len(w), 1)
 
 
 def test_repr_mime():
     class HasReprMime(object):
         def _repr_mimebundle_(self, include=None, exclude=None):
             return {
                 'application/json+test.v2': {
                     'x': 'y'
                 },
                 'plain/text' : '<HasReprMime>',
                 'image/png' : 'i-overwrite'
             }
 
         def _repr_png_(self):
             return 'should-be-overwritten'
         def _repr_html_(self):
             return '<b>hi!</b>'
     
     f = get_ipython().display_formatter
     html_f = f.formatters['text/html']
     save_enabled = html_f.enabled
     html_f.enabled = True
     obj = HasReprMime()
     d, md = f.format(obj)
     html_f.enabled = save_enabled
     
     nt.assert_equal(sorted(d), ['application/json+test.v2',
                                 'image/png',
                                 'plain/text',
                                 'text/html',
                                 'text/plain'])
     nt.assert_equal(md, {})
 
     d, md = f.format(obj, include={'image/png'})
     nt.assert_equal(list(d.keys()), ['image/png'],
                     'Include should filter out even things from repr_mimebundle')
     nt.assert_equal(d['image/png'], 'i-overwrite', '_repr_mimebundle_ take precedence')
 
 
+
+def test_pass_correct_include_exclude():
+    class Tester(object):
+
+        def __init__(self, include=None, exclude=None):
+            self.include = include
+            self.exclude = exclude
+
+        def _repr_mimebundle_(self, include, exclude, **kwargs):
+            if include and (include != self.include):
+                raise ValueError('include got modified: display() may be broken.')
+            if exclude and (exclude != self.exclude):
+                raise ValueError('exclude got modified: display() may be broken.')
+
+            return None
+
+    include = {'a', 'b', 'c'}
+    exclude = {'c', 'e' , 'f'}
+
+    f = get_ipython().display_formatter
+    f.format(Tester(include=include, exclude=exclude), include=include, exclude=exclude)
+    f.format(Tester(exclude=exclude), exclude=exclude)
+    f.format(Tester(include=include), include=include)
+
+
 def test_repr_mime_meta():
     class HasReprMimeMeta(object):
         def _repr_mimebundle_(self, include=None, exclude=None):
             data = {
                 'image/png': 'base64-image-data',
             }
             metadata = {
                 'image/png': {
                     'width': 5,
                     'height': 10,
                 }
             }
             return (data, metadata)
     
     f = get_ipython().display_formatter
     obj = HasReprMimeMeta()
     d, md = f.format(obj)
     nt.assert_equal(sorted(d), ['image/png', 'text/plain'])
     nt.assert_equal(md, {
         'image/png': {
             'width': 5,
             'height': 10,
         }
     })
-    
-    

examples/IPython Kernel/Custom Display Logic.ipynb

@@ -1,1556 +1,976 b''
 {
  "cells": [
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "# Custom Display Logic"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "## Overview"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "As described in the [Rich Output](Rich Output.ipynb) tutorial, the IPython display system can display rich representations of objects in the following formats:\n",
     "\n",
     "* JavaScript\n",
     "* HTML\n",
     "* PNG\n",
     "* JPEG\n",
     "* SVG\n",
     "* LaTeX\n",
     "* PDF\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_` when you define your class.\n",
     "2. Registering a display function for a particular existing class.\n",
     "\n",
     "This Notebook describes and illustrates both approaches."
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Import the IPython display functions."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 1,
    "metadata": {
-    "collapsed": false
+    "collapsed": true
    },
    "outputs": [],
    "source": [
     "from IPython.display import (\n",
     "    display, display_html, display_png, display_svg\n",
     ")"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Parts of this notebook need the matplotlib inline backend:"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 2,
    "metadata": {
-    "collapsed": false
+    "collapsed": true
    },
    "outputs": [],
    "source": [
-    "%matplotlib inline\n",
     "import numpy as np\n",
-    "import matplotlib.pyplot as plt"
+    "import matplotlib.pyplot as plt\n",
+    "plt.ion()"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "## Special display methods"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "The main idea of the first approach is that you have to implement special display methods when you define your class, one for each representation you want to use. Here is a list of the names of the special methods and the values they must return:\n",
     "\n",
     "* `_repr_html_`: return raw HTML as a string\n",
     "* `_repr_json_`: return a JSONable dict\n",
     "* `_repr_jpeg_`: return raw JPEG data\n",
     "* `_repr_png_`: return raw PNG data\n",
     "* `_repr_svg_`: return raw SVG data as a string\n",
-    "* `_repr_latex_`: return LaTeX commands in a string surrounded by \"$\"."
+    "* `_repr_latex_`: return LaTeX commands in a string surrounded by \"$\".\n",
+    "* `_repr_mimebundle_`: return a full mimebundle containing the mapping from all mimetypes to data "
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "As an illustration, we build a class that holds data generated by sampling a Gaussian distribution with given mean and standard deviation. Here is the definition of the `Gaussian` class, which has a custom PNG and LaTeX representation."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 3,
    "metadata": {
-    "collapsed": false
+    "collapsed": true
    },
    "outputs": [],
    "source": [
     "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=0.0, 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",
     "        \n",
     "    def _figure_data(self, format):\n",
     "        fig, ax = plt.subplots()\n",
     "        ax.hist(self.data, bins=50)\n",
     "        ax.set_title(self._repr_latex_())\n",
     "        ax.set_xlim(-10.0,10.0)\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",
     "    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",
     "    def _repr_latex_(self):\n",
     "        return r'$\\mathcal{N}(\\mu=%.2g, \\sigma=%.2g),\\ N=%d$' % (self.mean,\n",
     "                                                                 self.std, self.size)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Create an instance of the Gaussian distribution and return it to display the default representation:"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 4,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
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-       "Gc2r+v7W2t51qwoAYM51TSyvtb4iySdaay9O8sokP7muVQEAzLne1XkvS/JbSdJaO5jkz2qtz1m3\n",
-       "qgAA5lzvcN55SR6ZaH9kfOyvTroiYK699LnnPvZZ55z90SR53qc9/WkPHzoy65IAZqIMw7Dmi2qt\n",
-       "NyV5U2vtveP2Lya5qbX2/snz7rrrrrW/OADAjFx22WVltef23om6K8k3J3lvrXVbkouXB6i1FgIA\n",
-       "sJF0zYlqrf1BktRa35HkLUl+cD2LAgCYd13DeQAAZzp75wEAdBCiAAA6CFEAAB2mtnderfUlSX43\n",
-       "yZe21j48Pva9Sb4po/D2htbam6f1/mxMtdarM1qo8OHxoe9trb1ndhUxb2w5xVrUWh9NsvR/yFtb\n",
-       "azfPsh7my/gJA29K8vbW2s211ouT3JLkWJL7k1zTWnvKyeNTCVG11s9O8m1J7k5Sxsd2JHlBa+1F\n",
-       "tdbNSe6utb6ttfb306iBDWtI8uOttd+ddSHMn8ktp2qtn5rkzUkuPcFlnNn2ttYun3URzK2bMnrK\n",
-       "wDPH7d1JrmitLdZar01yZZLbnuriqQzntdY+0Fr7tiSPZ/RHMUlemuS3x/1Hk/zXJDun8f5seD9Q\n",
-       "a31XrXX3rAth7thyirX64lrrPbXWu2qtz551McyX1to1Sd6XJLXWrUkea60tjrtvS7JrpetP6k5U\n",
-       "rfXzk/zsssMfaq1dfZzTz0vy3on20lYxnIGe6rOT5Dtba78xPufnaq0vX3ouGcSWU6zdc1trj9da\n",
-       "vzrJG5JcNeuCmFvnJnl0ov1ITpBTTipEtdb+PMlqb5M+mmT7RPvTk/zFybw/G9cqPzu/l+TLkwhR\n",
-       "LFn6f+Svx+3teXKogidprT0+/vquWuv2E53PGe1AnhyatufJoeqTnIrVeUtbv9yd5NVJUmv9lCSv\n",
-       "TGJCKE9Sa31trfUzxs2vS3LvLOth7ixtObU0IfS4W05BktRad9Zarxh///z8Q/iGT9JaO5xka631\n",
-       "gvGhq5LcudI1pyJEDUnSWnsgyR/VWv9XknuS/FRrzfbvLPd/kry51vr2JI+21vbMuB7miC2nWKP7\n",
-       "klxVa92T5Pokr5ttOcyxpfnb1ya5ffw36Hmttd9e6SLbvgAAdPCwTQCADkIUAEAHIQoAoIMQBQDQ\n",
-       "QYgCAOggRAEAdBCiAAA6CFEAAB2EKACADv8fn0xUCxJB1sMAAAAASUVORK5CYII=\n"
-      ],
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXsAAAEKCAYAAADzQPVvAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n1ADDXpIa8P8BEb7Ae9JKdQAAAAAASUVORK5CYII=\n",
       "text/latex": [
        "$\\mathcal{N}(\\mu=2, \\sigma=1),\\ N=1000$"
       ],
       "text/plain": [
-       "<__main__.Gaussian at 0x10665a4e0>"
+       "<__main__.Gaussian at 0x116fe76d8>"
       ]
      },
      "execution_count": 4,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "x = Gaussian(2.0, 1.0)\n",
     "x"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "You can also pass the object to the `display` function to display the default representation:"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 5,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": [
-       "iVBORw0KGgoAAAANSUhEUgAAAlEAAAGLCAYAAADnMccKAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
-       "AAALEgAACxIB0t1+/AAAGsJJREFUeJzt3X2QndddH/DvsUQs5cXIRoCNA9mGGIR5Dy9KiBMnMmnq\n",
-       "BAbamjOdYIOBafEMGd4MocEGUrAbG1Sgw7sLwWAI5bhT6tC0abCN4rQlSjEhmVAbG1yRRHgTYgsp\n",
-       "xEKOlKd/3LvmeiOvdo/26t6VPp9/ds9znufe32rvaL/znHOeU4ZhCAAAa3PWrAsAANiIhCgAgA5C\n",
-       "FABAByEKAKCDEAUA0EGIAgDoIEQBAHQQogAAOghRsIGVUraMv5ZSyq5Z1zMPSinnllK+atZ1AKc/\n",
-       "IQo2oFLKV5ZS3pPkQClla5IfTPIXp+i9P7eUclMp5d+XUv6glPIVp+J9n6KWraWUXy6lvHjp2DAM\n",
-       "B5K8opTyvFnVtRrHq32i77NLKb9SSvmuUsqvllIWTrYPWH9CFMypUsofl1JecZzjm5Jcn+Tnkrwo\n",
-       "yRcleWwYhvefgprOSnJtktcNw/A9SX4zydtKKdun/d7HqeU7k7w+yRVJyrLun0zyE6e6ptU6Qe1J\n",
-       "cluS24Zh+IUkv5rkd9ahD1hnQhTMoXEo+fKM/sgu97IkvzgMw68Ow/AnSb4/ya+fotIuSvI1ST5r\n",
-       "3P6dJM9I8o2n6P2fMAzDrwzD8ENJPnqcvseT3F9KedFaX7eUcnYp5UdKKftLKfeVUspE36tLKfeX\n",
-       "Un6/lPJPp1F7KeXzknzpMAz/c3zuO5N8finlczr7ntNbJ7AyIQrm08VJfiPJPy+lPG1Z38uS/GGS\n",
-       "lFLOS/IpwzB87BTV9XdJnp3kgiQZhuHo+Ni5p+j91+ItSV691ouGYTiS0Z2s25JcmImAOAzDm5L8\n",
-       "xjAMXz8Mw++tV6HLfEmSDyw79sGM7jr29H3NFGoEIkTBvPqKJD+S5ONJXrms7+xhGD4+/v5lSd59\n",
-       "qooahmH/MAzbh2H442Q0ByfJeUn+6FTVsAbvSfLCzmtfnOSOjIbEfnBZ3ydOpqhV+Iwkh5cdeyzJ\n",
-       "+Uk+vaPvM6dQI5Bk86wLAI7r3GEY9pdS3pTkqiT/JUlKKV+Q5P9OnPeFSf58+cWllG9J8vnDMFw3\n",
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+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXsAAAEKCAYAAADzQPVvAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n1ADDXpIa8P8BEb7Ae9JKdQAAAAAASUVORK5CYII=\n",
       "text/latex": [
        "$\\mathcal{N}(\\mu=2, \\sigma=1),\\ N=1000$"
       ],
       "text/plain": [
-       "<__main__.Gaussian at 0x10665a4e0>"
+       "<__main__.Gaussian at 0x116fe76d8>"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "display(x)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Use `display_png` to view the PNG representation:"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 6,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": [
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-       "AAALEgAACxIB0t1+/AAAGsJJREFUeJzt3X2QndddH/DvsUQs5cXIRoCNA9mGGIR5Dy9KiBMnMmnq\n",
-       "BAbamjOdYIOBafEMGd4MocEGUrAbG1Sgw7sLwWAI5bhT6tC0abCN4rQlSjEhmVAbG1yRRHgTYgsp\n",
-       "xEKOlKd/3LvmeiOvdo/26t6VPp9/ds9znufe32rvaL/znHOeU4ZhCAAAa3PWrAsAANiIhCgAgA5C\n",
-       "FABAByEKAKCDEAUA0EGIAgDoIEQBAHQQogAAOghRsIGVUraMv5ZSyq5Z1zMPSinnllK+atZ1AKc/\n",
-       "IQo2oFLKV5ZS3pPkQClla5IfTPIXp+i9P7eUclMp5d+XUv6glPIVp+J9n6KWraWUXy6lvHjp2DAM\n",
-       "B5K8opTyvFnVtRrHq32i77NLKb9SSvmuUsqvllIWTrYPWH9CFMypUsofl1JecZzjm5Jcn+Tnkrwo\n",
-       "yRcleWwYhvefgprOSnJtktcNw/A9SX4zydtKKdun/d7HqeU7k7w+yRVJyrLun0zyE6e6ptU6Qe1J\n",
-       "cluS24Zh+IUkv5rkd9ahD1hnQhTMoXEo+fKM/sgu97IkvzgMw68Ow/AnSb4/ya+fotIuSvI1ST5r\n",
-       "3P6dJM9I8o2n6P2fMAzDrwzD8ENJPnqcvseT3F9KedFaX7eUcnYp5UdKKftLKfeVUspE36tLKfeX\n",
-       "Un6/lPJPp1F7KeXzknzpMAz/c3zuO5N8finlczr7ntNbJ7AyIQrm08VJfiPJPy+lPG1Z38uS/GGS\n",
-       "lFLOS/IpwzB87BTV9XdJnp3kgiQZhuHo+Ni5p+j91+ItSV691ouGYTiS0Z2s25JcmImAOAzDm5L8\n",
-       "xjAMXz8Mw++tV6HLfEmSDyw79sGM7jr29H3NFGoEIkTBvPqKJD+S5ONJXrms7+xhGD4+/v5lSd59\n",
-       "qooahmH/MAzbh2H442Q0ByfJeUn+6FTVsAbvSfLCzmtfnOSOjIbEfnBZ3ydOpqhV+Iwkh5cdeyzJ\n",
-       "+Uk+vaPvM6dQI5Bk86wLAI7r3GEY9pdS3pTkqiT/JUlKKV+Q5P9OnPeFSf58+cWllG9J8vnDMFw3\n",
-       "bv/LJOcPw/ATE+dsS/LTOf6cnEk/MwzDe5+i77uSvGVpCOl4SinfkeS7M7p7tX1c7+NJXj4Mw4fX\n",
-       "sZYnGYbh4+PJ25uGYTi2mmsmfFWSmzK6k/OXpZQXD8PwjlLKjiz7955C7edm9O8z6fEkz0qytbMP\n",
-       "mAIhCubM+LEFS38MfzPJO0spnzkMw4eS/OMkbeL07UnedZyX+Wfja5d8U5KfnzxhGIa/TfLtJ1Hn\n",
-       "FyV5RZLLVjjnRzO6Q/L8jELGHyV5zTAMe9ezlhUsDTV+ZI3XbRqGYUjygVLK7yR5bZJ3ZHTn77cn\n",
-       "T5xC7Z80TyrJ05M8muMHtdX0AVNgOA/mz2VJ7kmSYRjeneT+JNeM+549DMPDE+c+LcnRyYvHq/cu\n",
-       "SXLXuL0lyQsynke1Hkopz8roTs0rh2E47h/p8V2zK5N8zzAMx8bzp/YlOZUTnR/PGv+fK6V8ZpLF\n",
-       "iUM/leTyUsrFGd0hPLSO9R3Pw0meuezYM8Y1LXb0fWgKNQJxJwrm0aXDMLx2ov2LSf5tKeWX8snD\n",
-       "NY8k2bbs2FckeWgYhoPj9ouTvC/Jx0op5y2FnlLKuUn+XfqGoW7K6I7Sw+PVa/9iGIbly+lfleRt\n",
-       "wzB8Yvx+mzMaJvu+5W9wkrWs5FMz+jdai8uSvG2pMQzD+0opb83osRL3Lj95CrW/M6PJ+0uvvzmj\n",
-       "4Pm+JB/r7AOmQIiCOVBKOSej0PFQkr9e1v3GJD+U5Pcy+mM96QMZTUSe9LXj11ny6ozubO0av/aj\n",
-       "yRMPpVzzMFQp5bUZzRXaMZ4j9DkZ3T1JKeUrk5wzDMPdSf4m41V8Y9+V5JeHYfjg8tfsrWWyrKc4\n",
-       "PkzOh1pW31N57ngV3qSfTLIno2dzLX+Dda19GIYPlFL+Xyll53jY8+VJ/mQYhvvHP0NXH7D+hCiY\n",
-       "Dy/MaK7Ngxk9H+oJ4wnS35Nkd8ZDdBPuSfIDy45dluRYKeXqJJ+S5O7xsc8bhuHOkylyPER3Y5JN\n",
-       "kyVmNME9Sb45o3lDX5bRIwLeMJ7U/swkHxmG4baTef9ltXxrksuTfHaSnymlvCPJDyytXBw/rfvP\n",
-       "ll326ozC5Jcd5/Wen9Gw6TeUUs4ahuHHn/gBh+GeUsp/T7J3+XXTqD3JtyS5vpTygozuLH7zxOW9\n",
-       "fcA6K6O5k8CsjR+W+KGJYbjVXnfnMAxfO/5+S5L9Ga3E+/jKV05HKeU7hmH4tVm897I6viXJJ4Zh\n",
-       "+K1lx+eiPmDjW9WdqFrr1yX5vNbaT9daL05yS5JjGU94ba1JYnCShmF4oPPSVkp5+TAMf5DRhPI/\n",
-       "nVWAGvvUGb73pMszejzEcvNSH7DBnXDVSq31mUle2Fr76fGh3UmuaK1dmuSBjFbfALPzxiTfON7X\n",
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+      "image/png": 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a4Ji99kmDY88zY8peK66WeWQvSQ0w7CWpAYa9JDXAsJekBhj2ktQAw16SGmDYS1IDvM5e\nzfP6e7XAI3tJaoBhL0kNMOwlqQGO2Wuf55j8ZM3Xn97jfvXyyF6SGmDYS1IDDHtJaoBj9lqTZo8N\nOy4/fUvpY8fwV4+xjuyTnJ7kniT3Jdk2qaIkSZO15LBPsg74PeAM4FjgzUmOnVRhkqTJGefI/kTg\nvqp6oKr+HrgcOHsyZUmSJilVtbQVkzcAp1fVL/bTbwV+rKoumLXcVmBrP/nDwB1LL3fZHAp8ZaWL\nGMFaqHMt1AjWOWnWOVmvqKoDx9nAOCdoM2Tesz45qmo7sB0gya6q2jzGay4L65yctVAjWOekWedk\nJdk17jbGGcZ5EHjxwPSRwEPjlSNJmoZxwv4vgaOTHJVkf+Bc4NrJlCVJmqQlD+NU1dNJLgA+BqwD\nLq2qOxdYbftSX2+ZWefkrIUawTonzTona+w6l3yCVpK0dni7BElqgGEvSQ2YeNgneWOSO5M8k2Tz\nrLZ39LdWuCfJz86x/lFJbkpyb5Ir+pO/U9W/zq39Y3eSW+dYbneSz/XLjX0p1BLqvCjJlwdqPXOO\n5VbsNhZJ/muSu5PcnuTqJAfNsdyK9OVCfZPkgH5/uK/fDzcuV20DNbw4ySeT3NX/X3rbkGVOSfL4\nwL7wG8tdZ1/HvO9jOv+978/bk7xqBWp8xUA/3Zrk60nePmuZFenPJJcm2ZPkjoF5hyTZ2WfgziQH\nz7Huln6Ze5NsWfDFqmqiD+AY4BXAp4DNA/OPBW4DDgCOAu4H1g1Z/0rg3P75+4F/OekaF6j/t4Hf\nmKNtN3DoctYz6/UvAv7dAsus6/v2ZcD+fZ8fu4w1ngas75+/G3j3aunLUfoG+FfA+/vn5wJXrMD7\nfATwqv75gcDnh9R5CnDdcte22PcROBP4KN3v5ZwE3LTC9a4D/gZ46WroT+CngFcBdwzM+y1gW/98\n27D/Q8AhwAP9z4P75wfP91oTP7Kvqruq6p4hTWcDl1fVN6vqr4H76G658B1JArwa+FA/awdwzqRr\nnEv/+m8C/mS5XnMKVvQ2FlX18ap6up/8C7rfv1gtRumbs+n2O+j2w1P7/WLZVNXDVfXZ/vkTwF3A\ni5azhgk6G/ij6vwFcFCSI1awnlOB+6vqCytYw3dU1aeBr82aPbgPzpWBPwvsrKqvVdWjwE7g9Ple\naznH7F8EfGlg+kGevQP/APDYQFgMW2aafhJ4pKrunaO9gI8nubm/DcRKuKD/OnzpHF/vRunn5XIe\n3VHdMCvRl6P0zXeW6ffDx+n2yxXRDyOdANw0pPkfJbktyUeTvHJZC/uuhd7H1bQ/Qvdtba6DudXQ\nnwCHV9XD0H3wA4cNWWbR/bqk6+yT/F/ghUOaLqyqa+Zabci82dd9jnQLhqUYseY3M/9R/clV9VCS\nw4CdSe7uP5knZr46gfcBv0nXJ79JN+R03uxNDFl3otfXjtKXSS4EngYum2MzU+/LIVZ0H1ysJM8H\nPgy8vaq+Pqv5s3RDEU/2524+Ahy93DWy8Pu4mvpzf+B1wDuGNK+W/hzVovt1SWFfVa9Zwmqj3F7h\nK3Rf89b3R1UTuwXDQjUnWQ/8E+BH59nGQ/3PPUmuphsWmGhAjdq3Sf4QuG5I09RvYzFCX24BXguc\nWv0A45BtTL0vhxilb2aWebDfJ17As79mT12S/eiC/rKqump2+2D4V9UNSX4/yaFVtaw39RrhfVxN\nt1U5A/hsVT0yu2G19GfvkSRHVNXD/ZDXniHLPEh3nmHGkXTnSee0nMM41wLn9lc7HEX3qfmZwQX6\nYPgk8IZ+1hZgrm8Kk/Ya4O6qenBYY5LnJTlw5jndichlvYPnrLHO18/x+it6G4skpwO/Bryuqv52\njmVWqi9H6Ztr6fY76PbDT8z1gTUt/TmCS4C7qup35ljmhTPnEpKcSPd/+avLV+XI7+O1wC/0V+Wc\nBDw+M0SxAub85r4a+nPA4D44VwZ+DDgtycH9cO5p/by5TeHs8uvpPnW+CTwCfGyg7UK6qyHuAc4Y\nmH8D8IP985fRfQjcB/wf4IBJ1zhH3R8EfnnWvB8Ebhio67b+cSfdkMVyn7n/Y+BzwO39DnHE7Dr7\n6TPpruC4f7nr7N+3LwG39o/3z65xJftyWN8A76T7cAJ4br/f3dfvhy9bgff5J+i+kt8+0I9nAr88\ns48CF/R9dxvdifAfX4E6h76Ps+oM3R85ur/fdzcvd519Hf+ALrxfMDBvxfuT7sPnYeBbfW6eT3eO\n6Ebg3v7nIf2ym4EPDKx7Xr+f3gf884Vey9slSFID/A1aSWqAYS9JDTDsJakBhr0kNcCwl6QGGPaS\n1ADDXpIa8P8BEb7Ae9JKdQAAAAAASUVORK5CYII=\n"
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "display_png(x)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "<div class=\"alert alert-success\">\n",
     "It is important to note a subtle different between <code>display</code> and <code>display_png</code>. The former computes <em>all</em> representations of the object, and lets the notebook UI decide which to display. The later only computes the PNG representation.\n",
     "</div>"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Create a new Gaussian with different parameters:"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 7,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
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+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAEKCAYAAAAfGVI8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nLnYAAAAASUVORK5CYII=\n",
       "text/latex": [
        "$\\mathcal{N}(\\mu=0, \\sigma=2),\\ N=2000$"
       ],
       "text/plain": [
-       "<__main__.Gaussian at 0x106ab8c18>"
+       "<__main__.Gaussian at 0x116fe7668>"
       ]
      },
      "execution_count": 7,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "x2 = Gaussian(0, 2, 2000)\n",
     "x2"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "You can then compare the two Gaussians by displaying their histograms:"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 8,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": [
-       "iVBORw0KGgoAAAANSUhEUgAAAlEAAAGLCAYAAADnMccKAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
-       "AAALEgAACxIB0t1+/AAAGsJJREFUeJzt3X2QndddH/DvsUQs5cXIRoCNA9mGGIR5Dy9KiBMnMmnq\n",
-       "BAbamjOdYIOBafEMGd4MocEGUrAbG1Sgw7sLwWAI5bhT6tC0abCN4rQlSjEhmVAbG1yRRHgTYgsp\n",
-       "xEKOlKd/3LvmeiOvdo/26t6VPp9/ds9znufe32rvaL/znHOeU4ZhCAAAa3PWrAsAANiIhCgAgA5C\n",
-       "FABAByEKAKCDEAUA0EGIAgDoIEQBAHQQogAAOghRsIGVUraMv5ZSyq5Z1zMPSinnllK+atZ1AKc/\n",
-       "IQo2oFLKV5ZS3pPkQClla5IfTPIXp+i9P7eUclMp5d+XUv6glPIVp+J9n6KWraWUXy6lvHjp2DAM\n",
-       "B5K8opTyvFnVtRrHq32i77NLKb9SSvmuUsqvllIWTrYPWH9CFMypUsofl1JecZzjm5Jcn+Tnkrwo\n",
-       "yRcleWwYhvefgprOSnJtktcNw/A9SX4zydtKKdun/d7HqeU7k7w+yRVJyrLun0zyE6e6ptU6Qe1J\n",
-       "cluS24Zh+IUkv5rkd9ahD1hnQhTMoXEo+fKM/sgu97IkvzgMw68Ow/AnSb4/ya+fotIuSvI1ST5r\n",
-       "3P6dJM9I8o2n6P2fMAzDrwzD8ENJPnqcvseT3F9KedFaX7eUcnYp5UdKKftLKfeVUspE36tLKfeX\n",
-       "Un6/lPJPp1F7KeXzknzpMAz/c3zuO5N8finlczr7ntNbJ7AyIQrm08VJfiPJPy+lPG1Z38uS/GGS\n",
-       "lFLOS/IpwzB87BTV9XdJnp3kgiQZhuHo+Ni5p+j91+ItSV691ouGYTiS0Z2s25JcmImAOAzDm5L8\n",
-       "xjAMXz8Mw++tV6HLfEmSDyw79sGM7jr29H3NFGoEIkTBvPqKJD+S5ONJXrms7+xhGD4+/v5lSd59\n",
-       "qooahmH/MAzbh2H442Q0ByfJeUn+6FTVsAbvSfLCzmtfnOSOjIbEfnBZ3ydOpqhV+Iwkh5cdeyzJ\n",
-       "+Uk+vaPvM6dQI5Bk86wLAI7r3GEY9pdS3pTkqiT/JUlKKV+Q5P9OnPeFSf58+cWllG9J8vnDMFw3\n",
-       "bv/LJOcPw/ATE+dsS/LTOf6cnEk/MwzDe5+i77uSvGVpCOl4SinfkeS7M7p7tX1c7+NJXj4Mw4fX\n",
-       "sZYnGYbh4+PJ25uGYTi2mmsmfFWSmzK6k/OXpZQXD8PwjlLKjiz7955C7edm9O8z6fEkz0qytbMP\n",
-       "mAIhCubM+LEFS38MfzPJO0spnzkMw4eS/OMkbeL07UnedZyX+Wfja5d8U5KfnzxhGIa/TfLtJ1Hn\n",
-       "FyV5RZLLVjjnRzO6Q/L8jELGHyV5zTAMe9ezlhUsDTV+ZI3XbRqGYUjygVLK7yR5bZJ3ZHTn77cn\n",
-       "T5xC7Z80TyrJ05M8muMHtdX0AVNgOA/mz2VJ7kmSYRjeneT+JNeM+549DMPDE+c+LcnRyYvHq/cu\n",
-       "SXLXuL0lyQsynke1Hkopz8roTs0rh2E47h/p8V2zK5N8zzAMx8bzp/YlOZUTnR/PGv+fK6V8ZpLF\n",
-       "iUM/leTyUsrFGd0hPLSO9R3Pw0meuezYM8Y1LXb0fWgKNQJxJwrm0aXDMLx2ov2LSf5tKeWX8snD\n",
-       "NY8k2bbs2FckeWgYhoPj9ouTvC/Jx0op5y2FnlLKuUn+XfqGoW7K6I7Sw+PVa/9iGIbly+lfleRt\n",
-       "wzB8Yvx+mzMaJvu+5W9wkrWs5FMz+jdai8uSvG2pMQzD+0opb83osRL3Lj95CrW/M6PJ+0uvvzmj\n",
-       "4Pm+JB/r7AOmQIiCOVBKOSej0PFQkr9e1v3GJD+U5Pcy+mM96QMZTUSe9LXj11ny6ozubO0av/aj\n",
-       "yRMPpVzzMFQp5bUZzRXaMZ4j9DkZ3T1JKeUrk5wzDMPdSf4m41V8Y9+V5JeHYfjg8tfsrWWyrKc4\n",
-       "PkzOh1pW31N57ngV3qSfTLIno2dzLX+Dda19GIYPlFL+Xyll53jY8+VJ/mQYhvvHP0NXH7D+hCiY\n",
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      },
      "metadata": {},
      "output_type": "display_data"
     },
     {
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+      "image/png": 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GmQgkqXEmAklqnIlAkhq3btQVkxwCfAB4MvAjYEtVvSfJvsCHgY3AncAvV9UD44eqlbbx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\nLnYAAAAASUVORK5CYII=\n"
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "display_png(x)\n",
     "display_png(x2)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Note that like `print`, you can call any of the `display` functions multiple times in a cell."
    ]
   },
   {
    "cell_type": "markdown",
    "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 approach.  But in practice, you often need to work with existing classes that you can't easily modify. We now illustrate how to add rich output 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",
    "execution_count": 9,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
        "Polynomial([ 1.,  2.,  3.], [-10.,  10.], [-1,  1])"
       ]
      },
      "execution_count": 9,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "p = np.polynomial.Polynomial([1,2,3], [-10, 10])\n",
     "p"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Next, define a function that pretty-prints a polynomial as a LaTeX string:"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 10,
    "metadata": {
-    "collapsed": false
+    "collapsed": true
    },
    "outputs": [],
    "source": [
     "def poly_to_latex(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', $x \\in [%.2g,\\ %.2g]$' % tuple(p.domain)\n",
     "    return px+dom"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "This produces, on our polynomial ``p``, the following:"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 11,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
        "'$P(x)=1+2 x+3 x^2$, $x \\\\in [-10,\\\\ 10]$'"
       ]
      },
      "execution_count": 11,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "poly_to_latex(p)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "You can render this string using the `Latex` class:"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 12,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
       "text/latex": [
        "$P(x)=1+2 x+3 x^2$, $x \\in [-10,\\ 10]$"
       ],
       "text/plain": [
        "<IPython.core.display.Latex object>"
       ]
      },
      "execution_count": 12,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "from IPython.display import Latex\n",
     "Latex(poly_to_latex(p))"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "However, you can configure IPython to do this automatically by registering the `Polynomial` class and the `poly_to_latex` function with an IPython display formatter. Let's look at the default formatters provided by IPython:"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 13,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
+      "              text/plain : PlainTextFormatter\n",
+      "               text/html : HTMLFormatter\n",
+      "           text/markdown : MarkdownFormatter\n",
+      "           image/svg+xml : SVGFormatter\n",
       "               image/png : PNGFormatter\n",
       "         application/pdf : PDFFormatter\n",
-      "               text/html : HTMLFormatter\n",
       "              image/jpeg : JPEGFormatter\n",
-      "              text/plain : PlainTextFormatter\n",
-      "           text/markdown : MarkdownFormatter\n",
-      "        application/json : JSONFormatter\n",
-      "  application/javascript : JavascriptFormatter\n",
       "              text/latex : LatexFormatter\n",
-      "           image/svg+xml : SVGFormatter\n"
+      "        application/json : JSONFormatter\n",
+      "  application/javascript : JavascriptFormatter\n"
      ]
     }
    ],
    "source": [
     "ip = get_ipython()\n",
     "for mime, formatter in ip.display_formatter.formatters.items():\n",
     "    print('%24s : %s' % (mime, formatter.__class__.__name__))"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "The `formatters` attribute is a dictionary keyed by MIME types. To define a custom LaTeX display function, you want a handle on the `text/latex` formatter:"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 14,
    "metadata": {
-    "collapsed": false
+    "collapsed": true
    },
    "outputs": [],
    "source": [
     "ip = get_ipython()\n",
     "latex_f = ip.display_formatter.formatters['text/latex']"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "The formatter object has a couple of methods for registering custom display functions for existing types."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 15,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
       "Help on method for_type in module IPython.core.formatters:\n",
       "\n",
       "for_type(typ, func=None) method of IPython.core.formatters.LatexFormatter instance\n",
       "    Add a format function for a given type.\n",
       "    \n",
       "    Parameters\n",
       "    -----------\n",
       "    typ : type or '__module__.__name__' string for a type\n",
       "        The class of the object that will be formatted using `func`.\n",
       "    func : callable\n",
       "        A callable for computing the format data.\n",
       "        `func` will be called with the object to be formatted,\n",
       "        and will return the raw data in this formatter's format.\n",
       "        Subclasses may use a different call signature for the\n",
       "        `func` argument.\n",
       "        \n",
       "        If `func` is None or not specified, there will be no change,\n",
       "        only returning the current value.\n",
       "    \n",
       "    Returns\n",
       "    -------\n",
       "    oldfunc : callable\n",
       "        The currently registered callable.\n",
       "        If you are registering a new formatter,\n",
       "        this will be the previous value (to enable restoring later).\n",
       "\n"
      ]
     }
    ],
    "source": [
     "help(latex_f.for_type)"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 16,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
       "Help on method for_type_by_name in module IPython.core.formatters:\n",
       "\n",
       "for_type_by_name(type_module, type_name, func=None) method of IPython.core.formatters.LatexFormatter instance\n",
       "    Add a format function for a type specified by the full dotted\n",
       "    module and name of the type, rather than the type of the object.\n",
       "    \n",
       "    Parameters\n",
       "    ----------\n",
       "    type_module : str\n",
       "        The full dotted name of the module the type is defined in, like\n",
       "        ``numpy``.\n",
       "    type_name : str\n",
       "        The name of the type (the class name), like ``dtype``\n",
       "    func : callable\n",
       "        A callable for computing the format data.\n",
       "        `func` will be called with the object to be formatted,\n",
       "        and will return the raw data in this formatter's format.\n",
       "        Subclasses may use a different call signature for the\n",
       "        `func` argument.\n",
       "        \n",
       "        If `func` is None or unspecified, there will be no change,\n",
       "        only returning the current value.\n",
       "    \n",
       "    Returns\n",
       "    -------\n",
       "    oldfunc : callable\n",
       "        The currently registered callable.\n",
       "        If you are registering a new formatter,\n",
       "        this will be the previous value (to enable restoring later).\n",
       "\n"
      ]
     }
    ],
    "source": [
     "help(latex_f.for_type_by_name)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "In this case, we will use `for_type_by_name` to register `poly_to_latex` as the display function for the `Polynomial` type:"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 17,
    "metadata": {
-    "collapsed": false
+    "collapsed": true
    },
    "outputs": [],
    "source": [
     "latex_f.for_type_by_name('numpy.polynomial.polynomial',\n",
     "                                 'Polynomial', poly_to_latex)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Once the custom display function has been registered, all NumPy `Polynomial` instances will be represented by their LaTeX form instead:"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 18,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
       "text/latex": [
        "$P(x)=1+2 x+3 x^2$, $x \\in [-10,\\ 10]$"
       ],
       "text/plain": [
        "Polynomial([ 1.,  2.,  3.], [-10.,  10.], [-1,  1])"
       ]
      },
      "execution_count": 18,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "p"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 19,
-   "metadata": {
-    "collapsed": false
-   },
+   "metadata": {},
    "outputs": [
     {
      "data": {
       "text/latex": [
        "$P(x)=-20+71 x+-15 x^2+x^3$, $x \\in [-1,\\ 1]$"
       ],
       "text/plain": [
        "Polynomial([-20.,  71., -15.,   1.], [-1,  1], [-1,  1])"
       ]
      },
      "execution_count": 19,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "p2 = np.polynomial.Polynomial([-20, 71, -15, 1])\n",
     "p2"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
+    "## Custom Mimetypes with `_repr_mimebundle_`\n",
+    "\n",
+    "Available on IPython 5.4+ and 6.1+.\n",
+    "\n",
+    "For objects needing full control over the `repr` protocol may decide to implement the `_repr_mimebundle_(include, exclude)` method.\n",
+    "Unlike the other `_repr_*_` methods must return many representation of the object in a mapping object which keys are _mimetypes_ and value are associated data. The `_repr_mimebundle_()` method, may also return a second mapping from _mimetypes_ to metadata. \n",
+    "\n",
+    "Example:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "class Gaussian(object):\n",
+    "    \"\"\"A simple object holding data sampled from a Gaussian distribution.\n",
+    "    \"\"\"\n",
+    "    def __init__(self, mean=0.0, 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",
+    "        \n",
+    "    def _figure_data(self, format):\n",
+    "        fig, ax = plt.subplots()\n",
+    "        ax.hist(self.data, bins=50)\n",
+    "        ax.set_xlim(-10.0,10.0)\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",
+    "    def _compute_mathml(self):\n",
+    "        return \"\"\"\n",
+    "        <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n",
+    "          <mrow class=\"MJX-TeXAtom-ORD\">\n",
+    "            <mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">N</mi>\n",
+    "          </mrow>\n",
+    "          <mo stretchy=\"false\">(</mo>\n",
+    "          <mi>&#x03BC;<!-- μ --></mi>\n",
+    "          <mo>=</mo>\n",
+    "          <mn>{mu}</mn>\n",
+    "          <mo>,</mo>\n",
+    "          <mi>&#x03C3;<!-- σ --></mi>\n",
+    "          <mo>=</mo>\n",
+    "          <mn>{sigma}</mn>\n",
+    "          <mo stretchy=\"false\">)</mo>\n",
+    "          <mo>,</mo>\n",
+    "          <mtext>&#xA0;</mtext>\n",
+    "          <mi>N</mi>\n",
+    "          <mo>=</mo>\n",
+    "          <mn>{N}</mn>\n",
+    "        </math>\n",
+    "        \"\"\".format(N=self.size, mu=self.mean, sigma=self.std)\n",
+    "        \n",
+    "    def _repr_mimebundle_(self, include, exclude, **kwargs):\n",
+    "        \"\"\"\n",
+    "        repr_mimebundle shoudl accept include, exclude and **kwargs\n",
+    "        \"\"\"\n",
+    "        if self._png_data is None:\n",
+    "            self._png_data = self._figure_data('png')\n",
+    "        math = r'$\\mathcal{N}(\\mu=%.2g, \\sigma=%.2g),\\ N=%d$' % (self.mean,\n",
+    "                                                                 self.std, self.size)\n",
+    "        data = {'image/png':self._png_data,\n",
+    "                'text/latex':math,\n",
+    "                'application/mathml+xml': self._compute_mathml()\n",
+    "                }\n",
+    "        if include:\n",
+    "            data = {k:v for (k,v) in data.items() if k in include}\n",
+    "        if exclude:\n",
+    "            data = {k:v for (k,v) in data.items() if k not in exclude}\n",
+    "        return data"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/mathml+xml": "\n        <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n          <mrow class=\"MJX-TeXAtom-ORD\">\n            <mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">N</mi>\n          </mrow>\n          <mo stretchy=\"false\">(</mo>\n          <mi>&#x03BC;<!-- μ --></mi>\n          <mo>=</mo>\n          <mn>0.0</mn>\n          <mo>,</mo>\n          <mi>&#x03C3;<!-- σ --></mi>\n          <mo>=</mo>\n          <mn>1</mn>\n          <mo stretchy=\"false\">)</mo>\n          <mo>,</mo>\n          <mtext>&#xA0;</mtext>\n          <mi>N</mi>\n          <mo>=</mo>\n          <mn>1000</mn>\n        </math>\n        ",
+      "image/png": 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uesPj7av3nn1VHaiq+4Y8tRX4UFV9t6r+FbifwS0Xvi9JgJcA13eLdgOX913jUrr9vx74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\nDfgfS9fLKUqMYTsAAAAASUVORK5CYII=\n",
+      "text/latex": [
+       "$\\mathcal{N}(\\mu=0, \\sigma=1),\\ N=1000$"
+      ],
+      "text/plain": [
+       "<__main__.Gaussian at 0x11a614e80>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# that is deffinitively wrong as it shoudl show the PNG. \n",
+    "display(Gaussian())"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "In the above example, the 3 mimetypes are embeded in the notebook document this allowing custom extensions and converters to display the representation(s) of their choice.\n",
+    "\n",
+    "For example, converting this noetebook to _epub_ may decide to use the MathML representation as most ebook reader cannot run mathjax (unlike browsers). \n",
+    "\n",
+    "\n",
+    "### Implementation guidelines\n",
+    "\n",
+    "The `_repr_mimebundle_` methods is also given two keywords parameters :  `include` and `exclude`. Each can be a  containers (e.g.:`list`, `set` ...) of mimetypes to return or `None`, This allows implementation to avoid computing potentially unnecessary and expensive mimetypes representations. \n",
+    "\n",
+    "When `include` is non-empty (empty `list` or None), `_repr_mimebundle_` may decide to returns only the mimetypes in include.\n",
+    "When `exclude` is non-empty, `_repr_mimebundle_` may decide to not return any mimetype in exclude. \n",
+    "If both `include` and `exclude` and overlap, mimetypes present in exclude may not be returned. \n",
+    "\n",
+    "If implementations decide to ignore the `include` and `exclude` logic and always returns a full mimebundles, the IPython kernel will take care of removing non-desired representations.\n",
+    "\n",
+    "The `_repr_mimebundle_` method should accept arbitrary keyword arguments for future compatiility.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\mathcal{N}(\\mu=0, \\sigma=1),\\ N=1000$"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "display(Gaussian(), include={'text/latex'}) # only show latex"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/mathml+xml": "\n        <math xmlns=\"http://www.w3.org/1998/Math/MathML\">\n          <mrow class=\"MJX-TeXAtom-ORD\">\n            <mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">N</mi>\n          </mrow>\n          <mo stretchy=\"false\">(</mo>\n          <mi>&#x03BC;<!-- μ --></mi>\n          <mo>=</mo>\n          <mn>0.0</mn>\n          <mo>,</mo>\n          <mi>&#x03C3;<!-- σ --></mi>\n          <mo>=</mo>\n          <mn>1</mn>\n          <mo stretchy=\"false\">)</mo>\n          <mo>,</mo>\n          <mtext>&#xA0;</mtext>\n          <mi>N</mi>\n          <mo>=</mo>\n          <mn>1000</mn>\n        </math>\n        ",
+      "text/latex": [
+       "$\\mathcal{N}(\\mu=0, \\sigma=1),\\ N=1000$"
+      ],
+      "text/plain": [
+       "<__main__.Gaussian at 0x116fe7550>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "display(Gaussian(), exclude={'image/png'}) # exclude png"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<__main__.Gaussian at 0x11a8a0b38>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "display(Gaussian(), include={'text/plain', 'image/png'}, exclude={'image/png'}) # keep only plain/text"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
     "## More complex display with `_ipython_display_`"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "Rich output special methods and functions can only display one object or MIME type at a time. Sometimes this is not enough if you want to display multiple objects or MIME types at once. An example of this would be to use an HTML representation to put some HTML elements in the DOM and then use a JavaScript representation to add events to those elements.\n",
     "\n",
     "**IPython 2.0** recognizes another display method, `_ipython_display_`, which allows your objects to take complete control of displaying themselves. If this method is defined, IPython will call it, and make no effort to display the object using the above described `_repr_*_` methods for custom display functions. It's a way for you to say \"Back off, IPython, I can display this myself.\" Most importantly, your `_ipython_display_` method can make multiple calls to the top-level `display` functions to accomplish its goals.\n",
     "\n",
     "Here is an object that uses `display_html` and `display_javascript` to make a plot using the [Flot](http://www.flotcharts.org/) JavaScript plotting library:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 25,
    "metadata": {
-    "collapsed": false
+    "collapsed": true
    },
    "outputs": [],
    "source": [
     "import json\n",
     "import uuid\n",
     "from IPython.display import display_javascript, display_html, display\n",
     "\n",
     "class FlotPlot(object):\n",
     "    def __init__(self, x, y):\n",
     "        self.x = x\n",
     "        self.y = y\n",
     "        self.uuid = str(uuid.uuid4())\n",
     "    \n",
     "    def _ipython_display_(self):\n",
     "        json_data = json.dumps(list(zip(self.x, self.y)))\n",
     "        display_html('<div id=\"{}\" style=\"height: 300px; width:80%;\"></div>'.format(self.uuid),\n",
     "            raw=True\n",
     "        )\n",
     "        display_javascript(\"\"\"\n",
     "        require([\"//cdnjs.cloudflare.com/ajax/libs/flot/0.8.2/jquery.flot.min.js\"], function() {\n",
     "          var line = JSON.parse(\"%s\");\n",
     "          console.log(line);\n",
     "          $.plot(\"#%s\", [line]);\n",
     "        });\n",
     "        \"\"\" % (json_data, self.uuid), raw=True)\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {
-    "collapsed": false
-   },
+   "execution_count": 26,
+   "metadata": {},
    "outputs": [
     {
      "data": {
       "text/html": [
-       "<div id=\"4ad544ff-a161-4493-ba2c-f99531e317bd\" style=\"height: 300px; width:80%;\"></div>"
+       "<div id=\"c6929609-3cb6-4443-9574-d9f71791a987\" style=\"height: 300px; width:80%;\"></div>"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     },
     {
      "data": {
       "application/javascript": [
        "\n",
        "        require([\"//cdnjs.cloudflare.com/ajax/libs/flot/0.8.2/jquery.flot.min.js\"], function() {\n",
        "          var line = JSON.parse(\"[[0.0, 0.0], [0.20408163265306123, 0.20266793654820095], [0.40816326530612246, 0.39692414892492234], [0.6122448979591837, 0.5747060412161791], [0.8163265306122449, 0.7286347834693503], [1.0204081632653061, 0.8523215697196184], [1.2244897959183674, 0.9406327851124867], [1.4285714285714286, 0.9899030763721239], [1.6326530612244898, 0.9980874821347183], [1.836734693877551, 0.9648463089837632], [2.0408163265306123, 0.8915592304110037], [2.2448979591836737, 0.7812680235262639], [2.4489795918367347, 0.6385503202266021], [2.6530612244897958, 0.469329612777201], [2.857142857142857, 0.28062939951435684], [3.0612244897959187, 0.0802816748428135], [3.2653061224489797, -0.12339813736217871], [3.4693877551020407, -0.3219563150726187], [3.673469387755102, -0.5071517094845144], [3.8775510204081636, -0.6712977935519321], [4.081632653061225, -0.8075816909683364], [4.285714285714286, -0.9103469443107828], [4.4897959183673475, -0.9753282860670456], [4.6938775510204085, -0.9998286683840896], [4.8979591836734695, -0.9828312039256306], [5.1020408163265305, -0.9250413717382029], [5.3061224489795915, -0.8288577363730427], [5.510204081632653, -0.6982723955653996], [5.714285714285714, -0.5387052883861563], [5.918367346938775, -0.35677924089893803], [6.122448979591837, -0.16004508604325057], [6.326530612244898, 0.04333173336868346], [6.530612244897959, 0.2449100710119793], [6.73469387755102, 0.4363234264718193], [6.938775510204081, 0.6096271964908323], [7.142857142857143, 0.7576284153927202], [7.346938775510204, 0.8741842988197335], [7.551020408163265, 0.9544571997387519], [7.755102040816327, 0.9951153947776636], [7.959183673469388, 0.9944713672636168], [8.16326530612245, 0.9525518475314604], [8.36734693877551, 0.8710967034823207], [8.571428571428571, 0.7534867274396376], [8.775510204081632, 0.6046033165061543], [8.979591836734695, 0.43062587038273736], [9.183673469387756, 0.23877531564403087], [9.387755102040817, 0.03701440148506237], [9.591836734693878, -0.1662827938487564], [9.795918367346939, -0.3626784288265488], [10.0, -0.5440211108893699]]\");\n",
        "          console.log(line);\n",
-       "          $.plot(\"#4ad544ff-a161-4493-ba2c-f99531e317bd\", [line]);\n",
+       "          $.plot(\"#c6929609-3cb6-4443-9574-d9f71791a987\", [line]);\n",
        "        });\n",
        "        "
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "import numpy as np\n",
     "x = np.linspace(0,10)\n",
     "y = np.sin(x)\n",
     "FlotPlot(x, np.sin(x))"
    ]
   }
  ],
  "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": "3.4.2"
+   "version": "3.6.0"
   }
  },
  "nbformat": 4,
- "nbformat_minor": 0
+ "nbformat_minor": 1
 }