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# Abstract base class for Sage objects

Abstract base class for Sage objects

class `sage.structure.sage_object.``SageObject`

  Bases: `object`

  Base class for all (user-visible) objects in Sage

  Every object that can end up being returned to the user should inherit from `SageObject`.

  `_ascii_art_`()

    Return an ASCII art representation.

    To implement multi-line ASCII art output in a derived class you must override this method. Unlike `_repr_()`, which is sometimes used for the hash key, the output of `_ascii_art_()` may depend on settings and is allowed to change during runtime.

    OUTPUT:

    An `AsciiArt` object, see `sage.misc.ascii_art` for details.

    EXAMPLES:

    You can use the `ascii_art()` function to get the ASCII art representation of any object in Sage:

        sage: ascii_art(integral(exp(x+x^2)/(x+1), x))
          /
         |
         |   2
         |  x  + x
         | e
         | ------- dx
         |  x + 1
         |
        /

    Alternatively, you can use the `%display ascii_art/simple` magic to switch all output to ASCII art and back:

        sage: from sage.repl.interpreter import get_test_shell
        sage: shell = get_test_shell()
        sage: shell.run_cell('tab = StandardTableaux(3)[2]; tab')
        [[1, 2], [3]]
        sage: shell.run_cell('%display ascii_art')
        sage: shell.run_cell('tab')
        1  2
        3
        sage: shell.run_cell('Tableaux.global_options(ascii_art="table", convention="French")')
        sage: shell.run_cell('tab')
        +---+
        | 3 |
        +---+---+
        | 1 | 2 |
        +---+---+
        sage: shell.run_cell('%display simple')
        sage: shell.run_cell('Tableaux.global_options.reset()')

    TESTS:

        sage: 1._ascii_art_()
        1
        sage: type(_)
        <class 'sage.misc.ascii_art.AsciiArt'>

  `_cache_key`()

    Return a hashable key which identifies this objects for caching. The output must be hashable itself, or a tuple of objects which are hashable or define a `_cache_key`.

    This method will only be called if the object itself is not hashable.

    Some immutable objects (such as \(p\)-adic numbers) cannot implement a reasonable hash function because their `==` operator has been modified to return `True` for objects which might behave differently in some computations:

        sage: K.<a> = Qq(9)
        sage: b = a + O(3)
        sage: c = a + 3
        sage: b
        a + O(3)
        sage: c
        a + 3 + O(3^20)
        sage: b == c
        True
        sage: b == a
        True
        sage: c == a
        False

    If such objects defined a non-trivial hash function, this would break caching in many places. However, such objects should still be usable in caches. This can be achieved by defining an appropriate `_cache_key`:

        sage: hash(b)
        Traceback (most recent call last):
        ...
        TypeError: unhashable type: 'sage.rings.padics.padic_ZZ_pX_CR_element.pAdicZZpXCRElement'
        sage: @cached_method
        ....: def f(x): return x==a
        sage: f(b)
        True
        sage: f(c) # if b and c were hashable, this would return True
        False

        sage: b._cache_key()
        (..., ((0, 1),), 0, 1)
        sage: c._cache_key()
        (..., ((0, 1), (1,)), 0, 20)

    An implementation must make sure that for elements `a` and `b`, if `a != b`, then also `a._cache_key() != b._cache_key()`. In practice this means that the `_cache_key` should always include the parent as its first argument:

        sage: S.<a> = Qq(4)
        sage: d = a + O(2)
        sage: b._cache_key() == d._cache_key() # this would be True if the parents were not included
        False

  `category`()
  `db`(name, compress=True)

    Dumps self into the Sage database. Use db(name) by itself to reload.

    The database directory is `$HOME/.sage/db`

  `dump`(filename, compress=True)

    Same as self.save(filename, compress)

  `dumps`(compress=True)

    Dump `self` to a string `s`, which can later be reconstituted as `self` using `loads(s)`.

    There is an optional boolean argument `compress` which defaults to `True`.

    EXAMPLES:

        sage: O=SageObject(); O.dumps()
        'x\x9ck`J.NLO\xd5+.)*M.)-\x02\xb2\x80\xdc\xf8\xfc\xa4\xac\xd4\xe4\x12\xae` \xdb\x1f\xc2,d\xd4l,d\xd2\x03\x00\xb7X\x10\xf1'
        sage: O.dumps(compress=False)
        '\x80\x02csage.structure.sage_object\nSageObject\nq\x01)\x81q\x02.'

  `rename`(x=None)

    Change self so it prints as x, where x is a string.

    Note

    This is only supported for Python classes that derive from SageObject.

    EXAMPLES:

        sage: x = PolynomialRing(QQ, 'x', sparse=True).gen()
        sage: g = x^3 + x - 5
        sage: g
        x^3 + x - 5
        sage: g.rename('a polynomial')
        sage: g
        a polynomial
        sage: g + x
        x^3 + 2*x - 5
        sage: h = g^100
        sage: str(h)[:20]
        'x^300 + 100*x^298 - '
        sage: h.rename('x^300 + ...')
        sage: h
        x^300 + ...

    Real numbers are not Python classes, so rename is not supported:

        sage: a = 3.14
        sage: type(a)
        <type 'sage.rings.real_mpfr.RealLiteral'>
        sage: a.rename('pi')
        Traceback (most recent call last):
        ...
        NotImplementedError: object does not support renaming: 3.14000000000000

    Note

    The reason C-extension types are not supported by default is if they were then every single one would have to carry around an extra attribute, which would be slower and waste a lot of memory.

    To support them for a specific class, add a `cdef public __custom_name` attribute.

  `reset_name`()

    Remove the custrom name of an object.

    EXAMPLES:

        sage: P.<x> = QQ[]
        sage: P
        Univariate Polynomial Ring in x over Rational Field
        sage: P.rename('A polynomial ring')
        sage: P
        A polynomial ring
        sage: P.reset_name()
        sage: P
        Univariate Polynomial Ring in x over Rational Field

  `save`(filename=None, compress=True)

    Save self to the given filename.

    EXAMPLES:

        sage: f = x^3 + 5
        sage: f.save(os.path.join(SAGE_TMP, 'file'))
        sage: load(os.path.join(SAGE_TMP, 'file.sobj'))
        x^3 + 5

  `version`()

    The version of Sage.

    Call this to save the version of Sage in this object. If you then save and load this object it will know in what version of Sage it was created.

    This only works on Python classes that derive from SageObject.

`sage.structure.sage_object.``dumps`(obj, compress=True)

  Dump obj to a string s. To recover obj, use `loads(s)`.

  See also

  `dumps()`

  EXAMPLES:

      sage: a = 2/3
      sage: s = dumps(a)
      sage: print len(s)
      49
      sage: loads(s)
      2/3

`sage.structure.sage_object.``have_same_parent`(self, other)

  EXAMPLES:

      sage: from sage.structure.sage_object import have_same_parent
      sage: have_same_parent(1, 3)
      True
      sage: have_same_parent(1, 1/2)
      False
      sage: have_same_parent(gap(1), gap(1/2))
      True

`sage.structure.sage_object.``load`(compress=True, verbose=True, *filename)

  Load Sage object from the file with name filename, which will have an .sobj extension added if it doesn’t have one. Or, if the input is a filename ending in .py, .pyx, or .sage, load that file into the current running session. Loaded files are not loaded into their own namespace, i.e., this is much more like Python’s `execfile` than Python’s `import`.

  Note

  There is also a special Sage command (that is not available in Python) called load that you use by typing

      sage: load filename.sage           # not tested

  The documentation below is not for that command. The documentation for load is almost identical to that for attach. Type attach? for help on attach.

  This function also loads a `.sobj` file over a network by specifying the full URL. (Setting `verbose = False` suppresses the loading progress indicator.)

  Finally, if you give multiple positional input arguments, then all of those files are loaded, or all of the objects are loaded and a list of the corresponding loaded objects is returned.

  EXAMPLE:

      sage: u = 'http://sage.math.washington.edu/home/was/db/test.sobj'
      sage: s = load(u)                                                  # optional - internet
      Attempting to load remote file: http://sage.math.washington.edu/home/was/db/test.sobj
      Loading: [.]
      sage: s                                                            # optional - internet
      'hello SAGE'

  We test loading a file or multiple files or even mixing loading files and objects:

      sage: t=tmp_filename()+'.py'; open(t,'w').write("print 'hello world'")
      sage: load(t)
      hello world
      sage: load(t,t)
      hello world
      hello world
      sage: t2=tmp_filename(); save(2/3,t2)
      sage: load(t,t,t2)
      hello world
      hello world
      [None, None, 2/3]

`sage.structure.sage_object.``loads`(s, compress=True)

  Recover an object x that has been dumped to a string s using `s = dumps(x)`.

  See also

  `dumps()`

  EXAMPLES:

      sage: a = matrix(2, [1,2,3,-4/3])
      sage: s = dumps(a)
      sage: loads(s)
      [   1    2]
      [   3 -4/3]

  If compress is True (the default), it will try to decompress the data with zlib and with bz2 (in turn); if neither succeeds, it will assume the data is actually uncompressed. If compress=False is explicitly specified, then no decompression is attempted.

      sage: v = [1..10]
      sage: loads(dumps(v, compress=False)) == v
      True
      sage: loads(dumps(v, compress=False), compress=True) == v
      True
      sage: loads(dumps(v, compress=True), compress=False)
      Traceback (most recent call last):
      ...
      UnpicklingError: invalid load key, 'x'.

`sage.structure.sage_object.``picklejar`(obj, dir=None)

  Create pickled sobj of obj in dir, with name the absolute value of the hash of the pickle of obj. This is used in conjunction with `unpickle_all()`.

  To use this to test the whole Sage library right now, set the environment variable `SAGE_PICKLE_JAR`, which will make it so dumps will by default call picklejar with the default dir. Once you do that and doctest Sage, you’ll find that the `SAGE_ROOT`/tmp/ contains a bunch of pickled objects along with corresponding txt descriptions of them. Use the `unpickle_all()` to see if they unpickle later.

  INPUTS:

  - `obj` – a pickleable object
  - `dir` – a string or None; if None then `dir` defaults to `SAGE_ROOT/tmp/pickle_jar`

  EXAMPLES:

      sage: dir = tmp_dir()
      sage: sage.structure.sage_object.picklejar(1, dir)
      sage: sage.structure.sage_object.picklejar('test', dir)
      sage: len(os.listdir(dir))   # Two entries (sobj and txt) for each object
      4

  TESTS:

  Test an unaccessible directory:

      sage: import os
      sage: os.chmod(dir, 0o000)
      sage: try:
      ...   uid = os.getuid()
      ... except AttributeError:
      ...    uid = -1
      sage: if uid==0:
      ...     raise OSError('You must not run the doctests as root, geez!')
      ... else: sage.structure.sage_object.picklejar(1, dir + '/noaccess')
      Traceback (most recent call last):
      ...
      OSError: ...
      sage: os.chmod(dir, 0o755)

`sage.structure.sage_object.``register_unpickle_override`(module, name, callable, call_name=None)

  Python pickles include the module and class name of classes. This means that rearranging the Sage source can invalidate old pickles. To keep the old pickles working, you can call register_unpickle_override with an old module name and class name, and the Python callable (function, class with __call__ method, etc.) to use for unpickling. (If this callable is a value in some module, you can specify the module name and class name, for the benefit of `explain_pickle()` when called with `in_current_sage=True`).)

  EXAMPLES:

      sage: from sage.structure.sage_object import unpickle_override, register_unpickle_override
      sage: unpickle_global('sage.rings.integer', 'Integer')
      <type 'sage.rings.integer.Integer'>

  Now we horribly break the pickling system:

      sage: register_unpickle_override('sage.rings.integer', 'Integer', Rational, call_name=('sage.rings.rational', 'Rational'))
      sage: unpickle_global('sage.rings.integer', 'Integer')
      <type 'sage.rings.rational.Rational'>

  and we reach into the internals and put it back:

      sage: del unpickle_override[('sage.rings.integer', 'Integer')]
      sage: unpickle_global('sage.rings.integer', 'Integer')
      <type 'sage.rings.integer.Integer'>

  In many cases, unpickling problems for old pickles can be resolved with a simple call to `register_unpickle_override`, as in the example above and in many of the `sage` source files. However, if the underlying data structure has changed significantly then unpickling may fail and it will be necessary to explicitly implement unpickling methods for the associated objects. The python pickle protocol is described in detail on the web and, in particular, in the python pickling documentation. For example, the following excerpt from this documentation shows that the unpickling of classes is controlled by their `__setstate__()` method.

      object.__setstate__(state)

          Upon unpickling, if the class also defines the method :meth:`__setstate__`, it is
          called with the unpickled state. If there is no :meth:`__setstate__` method,
          the pickled state must be a dictionary and its items are assigned to the new
          instance's dictionary. If a class defines both :meth:`getstate__` and
          :meth:`__setstate__`, the state object needn't be a dictionary and these methods
          can do what they want.

  By implementing a `__setstate__()` method for a class it should be possible to fix any unpickling problems for the class. As an example of what needs to be done, we show how to unpickle a `CombinatorialObject` object using a class which also inherits from `Element`. This exact problem often arises when refactoring old code into the element framework. First we create a pickle to play with:

      sage: from sage.structure.element import Element
      sage: class SourPickle(CombinatorialObject): pass
      sage: class SweetPickle(CombinatorialObject,Element): pass
      sage: import __main__
      sage: __main__.SourPickle=SourPickle
      sage: __main__.SweetPickle=SweetPickle  # a hack to allow us to pickle command line classes
      sage: gherkin = dumps( SourPickle([1,2,3]) )

  Using `register_unpickle_override()` we try to sweeten our pickle, but we are unable to eat it:

      sage: from sage.structure.sage_object import register_unpickle_override
      sage: register_unpickle_override('__main__','SourPickle',SweetPickle)
      sage: loads( gherkin )
      Traceback (most recent call last):
      ...
      KeyError: 0

  The problem is that the `SweetPickle` has inherited a `__setstate__()` method from `Element` which is not compatible with unpickling for `CombinatorialObject`. We can fix this by explicitly defining a new `__setstate__()` method:

      sage: class SweeterPickle(CombinatorialObject,Element):
      ...       def __setstate__(self, state):
      ...           if isinstance(state, dict):   # a pickle from CombinatorialObject is just its instance dictionary
      ...               self._set_parent(Tableaux())      # this is a fudge: we need an appropriate parent here
      ...               self.__dict__ = state
      ...           else:
      ...               self._set_parent(state[0])
      ...               self.__dict__ = state[1]
      ...
      sage: __main__.SweeterPickle = SweeterPickle
      sage: register_unpickle_override('__main__','SourPickle',SweeterPickle)
      sage: loads( gherkin )
      [1, 2, 3]
      sage: loads(dumps( SweeterPickle([1,2,3]) ))   # check that pickles work for SweeterPickle
      [1, 2, 3]

  The `state` passed to `__setstate__()` will usually be something like the instance dictionary of the pickled object, however, with some older classes such as `CombinatorialObject` it will be a tuple. In general, the `state` can be any python object. `Sage` provides a special tool, `explain_pickle()`, which can help in figuring out the contents of an old pickle. Here is a second example.

      sage: class A(object):
      ...      def __init__(self,value):
      ...          self.original_attribute = value
      ...      def __repr__(self):
      ...          return 'A(%s)'%self.original_attribute
      sage: class B(object):
      ...      def __init__(self,value):
      ...          self.new_attribute = value
      ...      def __setstate__(self,state):
      ...          try:
      ...              self.new_attribute = state['new_attribute']
      ...          except KeyError:      # an old pickle
      ...              self.new_attribute = state['original_attribute']
      ...      def __repr__(self):
      ...          return 'B(%s)'%self.new_attribute
      sage: import __main__
      sage: __main__.A=A; __main__.B=B  # a hack to allow us to pickle command line classes
      sage: A(10)
      A(10)
      sage: loads( dumps(A(10)) )
      A(10)
      sage: sage.misc.explain_pickle.explain_pickle( dumps(A(10)) )
      pg_A = unpickle_global('__main__', 'A')
      si = unpickle_newobj(pg_A, ())
      pg_make_integer = unpickle_global('sage.rings.integer', 'make_integer')
      unpickle_build(si, {'original_attribute':pg_make_integer('a')})
      si
      sage: from sage.structure.sage_object import register_unpickle_override
      sage: register_unpickle_override('__main__', 'A', B)
      sage: loads( dumps(A(10)) )
      B(10)
      sage: loads( dumps(B(10)) )
      B(10)

  Pickling for python classes and extension classes, such as cython, is different – again this is discussed in the python pickling documentation. For the unpickling of extension classes you need to write a `__reduce__()` method which typically returns a tuple `(f, args,...)` such that `f(*args)` returns (a copy of) the original object. The following code snippet is the `__reduce__()` method from `sage.rings.integer.Integer`.

      def __reduce__(self):
          'Including the documentation properly causes a doc-test failure so we include it as a comment:'
          #* '''
          #* This is used when pickling integers.
          #*
          #* EXAMPLES::
          #*
          #*     sage: n = 5
          #*     sage: t = n.__reduce__(); t
          #*     (<built-in function make_integer>, ('5',))
          #*     sage: t[0](*t[1])
          #*     5
          #*     sage: loads(dumps(n)) == n
          #*     True
          #* '''
          # This single line below took me HOURS to figure out.
          # It is the *trick* needed to pickle Cython extension types.
          # The trick is that you must put a pure Python function
          # as the first argument, and that function must return
          # the result of unpickling with the argument in the second
          # tuple as input. All kinds of problems happen
          # if we don't do this.
          return sage.rings.integer.make_integer, (self.str(32),)

`sage.structure.sage_object.``save`(obj, filename=None, compress=True, **kwds)

  Save `obj` to the file with name `filename`, which will have an `.sobj` extension added if it doesn’t have one, or if `obj` doesn’t have its own `save()` method, like e.g. Python tuples.

  For image objects and the like (which have their own `save()` method), you may have to specify a specific extension, e.g. `.png`, if you don’t want the object to be saved as a Sage object (or likewise, if `filename` could be interpreted as already having some extension).

  Warning

  This will replace the contents of the file if it already exists.

  EXAMPLES:

      sage: a = matrix(2, [1,2,3,-5/2])
      sage: objfile = os.path.join(SAGE_TMP, 'test.sobj')
      sage: objfile_short = os.path.join(SAGE_TMP, 'test')
      sage: save(a, objfile)
      sage: load(objfile_short)
      [   1    2]
      [   3 -5/2]
      sage: E = EllipticCurve([-1,0])
      sage: P = plot(E)
      sage: save(P, objfile_short)   # saves the plot to "test.sobj"
      sage: save(P, filename=os.path.join(SAGE_TMP, "sage.png"), xmin=-2)
      sage: save(P, os.path.join(SAGE_TMP, "filename.with.some.wrong.ext"))
      Traceback (most recent call last):
      ...
      ValueError: allowed file extensions for images are '.eps', '.pdf', '.png', '.ps', '.sobj', '.svg'!
      sage: print load(objfile)
      Graphics object consisting of 2 graphics primitives
      sage: save("A python string", os.path.join(SAGE_TMP, 'test'))
      sage: load(objfile)
      'A python string'
      sage: load(objfile_short)
      'A python string'

  TESTS:

  Check that trac ticket #11577 is fixed:

      sage: filename = os.path.join(SAGE_TMP, "foo.bar")  # filename containing a dot
      sage: save((1,1),filename)            # saves tuple to "foo.bar.sobj"
      sage: load(filename)
      (1, 1)

`sage.structure.sage_object.``unpickle_all`(dir=None, debug=False, run_test_suite=False)

  Unpickle all sobj’s in the given directory, reporting failures as they occur. Also printed the number of successes and failure.

  INPUT:

  - `dir` – a string; the name of a directory (or of a .tar.bz2 file that decompresses to a directory) full of pickles. (default: the standard pickle jar)
  - `debug` – a boolean (default: False) whether to report a stacktrace in case of failure
  - `run_test_suite` – a boolean (default: False) whether to run `TestSuite(x).run()` on the unpickled objects

  EXAMPLES:

      sage: dir = tmp_dir()
      sage: sage.structure.sage_object.picklejar('hello', dir)
      sage: sage.structure.sage_object.unpickle_all(dir)
      Successfully unpickled 1 objects.
      Failed to unpickle 0 objects.

  When run with no arguments `unpickle_all()` tests that all of the “standard” pickles stored in the pickle_jar at `SAGE_ROOT/local/share/sage/ext/pickle_jar/pickle_jar.tar.bz2` can be unpickled.

      sage: sage.structure.sage_object.unpickle_all()  # (4s on sage.math, 2011)
      doctest:... DeprecationWarning: ...
      See http://trac.sagemath.org/... for details.
      Successfully unpickled ... objects.
      Failed to unpickle 0 objects.

  Check that unpickling a second time works (see trac ticket #5838):

      sage: sage.structure.sage_object.unpickle_all()
      Successfully unpickled ... objects.
      Failed to unpickle 0 objects.

  When it is not possible to unpickle a pickle in the pickle_jar then `unpickle_all()` prints the following error message which warns against removing pickles from the pickle_jar and directs the user towards `register_unpickle_override()`. The following code intentionally breaks a pickle to illustrate this:

      sage: from sage.structure.sage_object import register_unpickle_override, unpickle_all, unpickle_global
      sage: class A(CombinatorialObject,sage.structure.element.Element):
      ...       pass # to break a pickle
      sage: tableau_unpickler=unpickle_global('sage.combinat.tableau','Tableau_class')
      sage: register_unpickle_override('sage.combinat.tableau','Tableau_class',A) # breaking the pickle
      sage: unpickle_all()  # todo: not tested
      ...
      Failed:
      _class__sage_combinat_crystals_affine_AffineCrystalFromClassicalAndPromotion_with_category_element_class__.sobj
      _class__sage_combinat_crystals_tensor_product_CrystalOfTableaux_with_category_element_class__.sobj
      _class__sage_combinat_crystals_tensor_product_TensorProductOfCrystalsWithGenerators_with_category__.sobj
      _class__sage_combinat_tableau_Tableau_class__.sobj
      ----------------------------------------------------------------------
      ** This error is probably due to an old pickle failing to unpickle.
      ** See sage.structure.sage_object.register_unpickle_override for
      ** how to override the default unpickling methods for (old) pickles.
      ** NOTE: pickles should never be removed from the pickle_jar!
      ----------------------------------------------------------------------
      Successfully unpickled 583 objects.
      Failed to unpickle 4 objects.
      sage: register_unpickle_override('sage.combinat.tableau','Tableau_class',tableau_unpickler) # restore to default

  Todo

  Create a custom-made `SourPickle` for the last example.

  If you want to find lots of little issues in Sage then try the following:

      sage: print "x"; sage.structure.sage_object.unpickle_all(run_test_suite = True) # todo: not tested

  This runs `TestSuite` tests on all objects in the Sage pickle jar. Some of those objects seem to unpickle properly, but do not pass the tests because their internal data structure is messed up. In most cases though it is just that their source file misses a TestSuite call, and therefore some misfeatures went unnoticed (typically Parents not implementing the `an_element` method).

  Note

  Every so often the standard pickle jar should be updated by running the doctest suite with the environment variable `SAGE_PICKLE_JAR` set, then copying the files from `SAGE_ROOT/tmp/pickle_jar*` into the standard pickle jar.

  Warning

  Sage’s pickle jar helps to ensure backward compatibility in sage. Pickles should only be removed from the pickle jar after the corresponding objects have been properly deprecated. Any proposal to remove pickles from the pickle jar should first be discussed on sage-devel.

`sage.structure.sage_object.``unpickle_global`(module, name)

  Given a module name and a name within that module (typically a class name), retrieve the corresponding object. This normally just looks up the name in the module, but it can be overridden by register_unpickle_override. This is used in the Sage unpickling mechanism, so if the Sage source code organization changes, register_unpickle_override can allow old pickles to continue to work.

  EXAMPLES:

      sage: from sage.structure.sage_object import unpickle_override, register_unpickle_override
      sage: unpickle_global('sage.rings.integer', 'Integer')
      <type 'sage.rings.integer.Integer'>

  Now we horribly break the pickling system:

      sage: register_unpickle_override('sage.rings.integer', 'Integer', Rational, call_name=('sage.rings.rational', 'Rational'))
      sage: unpickle_global('sage.rings.integer', 'Integer')
      <type 'sage.rings.rational.Rational'>

  and we reach into the internals and put it back:

      sage: del unpickle_override[('sage.rings.integer', 'Integer')]
      sage: unpickle_global('sage.rings.integer', 'Integer')
      <type 'sage.rings.integer.Integer'>

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