Home       Trees       Indices       Help   
Package sage :: Package combinat :: Package species :: Module stream :: Class Stream_class
[hide private]
[frames] | no frames]

Class Stream_class

source code

                      object --+    
                               |    
structure.sage_object.SageObject --+
                                   |
                                  Stream_class



EXAMPLES:
    sage: from sage.combinat.species.stream import Stream
    sage: from itertools import izip
    sage: s = Stream(const=0)
    sage: len(s)
    1
    sage: [x for (x,i) in izip(s, range(4))]
    [0, 0, 0, 0]
    sage: len(s)
    1

    sage: s = Stream(const=4)
    sage: g = iter(s)
    sage: l1 = [x for (x,i) in izip(g, range(10))]
    sage: l = [4 for k in range(10)]
    sage: l == l1
    True

    sage: h = lambda l: 1 if len(l) < 2 else l[-1] + l[-2]
    sage: fib = Stream(h)
    sage: [x for (x,i) in izip(fib, range(11))]
    [1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89]

    sage: s = Stream()
    sage: l = Stream([1, 0])
    sage: y = Stream([0,1,0])
    sage: s.set_gen(iter(l + y * s * s))
    sage: [x for (x,i) in izip(s, range(6))]
    [1, 1, 2, 5, 14, 42]

    sage: r = [4, 3, 5, 2, 6, 1, 1, 1, 1, 1]
    sage: l = [4, 3, 5, 2, 6, 1]
    sage: s = Stream(l)
    sage: s[3] = -1
    sage: [x for (x,i) in izip(s, r)]
    [4, 3, 5, -1, 6, 1, 1, 1, 1, 1]
    sage: s[5] = -2
    sage: [x for (x,i) in izip(s, r)]
    [4, 3, 5, -1, 6, -2, 1, 1, 1, 1]
    sage: s[6] = -3
    sage: [x for (x,i) in izip(s, r)]
    [4, 3, 5, -1, 6, -2, -3, 1, 1, 1]
    sage: s[8] = -4
    sage: [x for (x,i) in izip(s, r)]
    [4, 3, 5, -1, 6, -2, -3, 1, -4, 1]
    sage: a = Stream(const=0)
    sage: a[2] = 3
    sage: [x for (x,i) in izip(a, range(4))]
    [0, 0, 3, 0]


Instance Methods [hide private]
 
__init__(self, gen=['4ti2-20061025', 'R-2.6.0', 'atlas-3.7.37', 'atlas-3.8.1', 'a..., const=['4ti2-20061025', 'R-2.6.0', 'atlas-3.7.37', 'atlas-3.8.1', 'a..., func=['4ti2-20061025', 'R-2.6.0', 'atlas-3.7.37', 'atlas-3.8.1', 'a...)
EXAMPLES:...		 source code
 
__setitem__(self, i, t)
Sets the ith entry of self to t.		 source code
 
set_gen(self, gen)
EXAMPLES: sage: from sage.combinat.species.stream import Stream sage: from itertools import izip sage: fib = Stream() sage: def g(): ...		 source code
 
map(self, f)
EXAMPLES:...		 source code
 
__getitem__(self, i)
Returns the ith entry of self.		 source code
 
__add__(self, s)
Returns the sum of two streams.		 source code
 
__mul__(self, s)
Returns the product of two streams.		 source code
 
_times_naive(self, s, n)
Returns the nth entry in the product of self and s via the naive multiplication algorithm.		 source code
 
__iter__(self)
EXAMPLES:...		 source code
 
__len__(self)
Returns the number of coefficients computed so far.		 source code
 
number_computed(self)
Returns the number of coefficients computed so far.		 source code
 
data(self)
Returns a list of all the coefficients computed so far.		 source code
 
is_constant(self)
Returns True if and only if...		 source code
 
stretch(self, k)
EXAMPLES:...		 source code
 
_stretch_aux(self, k)
EXAMPLES:...		 source code

Inherited from structure.sage_object.SageObject: __hash__, __new__, __repr__, _axiom_, _axiom_init_, _gap_, _gap_init_, _gp_, _gp_init_, _interface_, _interface_init_, _interface_is_cached_, _kash_, _kash_init_, _macaulay2_, _macaulay2_init_, _magma_, _magma_init_, _maple_, _maple_init_, _mathematica_, _mathematica_init_, _maxima_, _maxima_init_, _octave_, _octave_init_, _pari_, _pari_init_, _r_init_, _sage_, _singular_, _singular_init_, category, db, dump, dumps, plot, rename, reset_name, save, version

Inherited from object: __delattr__, __getattribute__, __reduce__, __reduce_ex__, __setattr__, __str__

Properties [hide private]

Inherited from object: __class__

Method Details [hide private]

__init__(self, gen=['4ti2-20061025', 'R-2.6.0', 'atlas-3.7.37', 'atlas-3.8.1', 'a..., const=['4ti2-20061025', 'R-2.6.0', 'atlas-3.7.37', 'atlas-3.8.1', 'a..., func=['4ti2-20061025', 'R-2.6.0', 'atlas-3.7.37', 'atlas-3.8.1', 'a...)
(Constructor)

source code  

EXAMPLES:
    sage: from sage.combinat.species.stream import Stream_class, Stream
    sage: s = Stream_class(const=4)
    sage: loads(dumps(s))
    <class 'sage.combinat.species.stream.Stream_class'>

    sage: list(sorted(s.__dict__.iteritems()))
    [('_constant', 4),
     ('_gen', None),
     ('_last_index', 0),
     ('_list', [4]),
     ('end_reached', True)]

     sage: s = Stream(ZZ)
     sage: list(sorted(s.__dict__.iteritems()))
     [('_constant', None),
      ('_gen', <generator object at 0x...>),
      ('_last_index', -1),
      ('_list', []),
      ('end_reached', False)]
Overrides: object.__init__

__setitem__(self, i, t)
(Index assignment operator)

source code  

Sets the ith entry of self to t.

EXAMPLES:
    sage: from sage.combinat.species.stream import Stream

    sage: s = Stream(const=0)
    sage: s[5]
    0
    sage: s.data()
    [0]
    sage: s[5] = 5
    sage: s[5]
    5
    sage: s.data()
    [0, 0, 0, 0, 0, 5]

    sage: s = Stream(ZZ)
    sage: s[10]
    -5
    sage: s.data()
    [0, 1, -1, 2, -2, 3, -3, 4, -4, 5, -5]
    sage: s[10] = 10
    sage: s.data()
    [0, 1, -1, 2, -2, 3, -3, 4, -4, 5, 10]

set_gen(self, gen)

source code  

EXAMPLES:
    sage: from sage.combinat.species.stream import Stream
    sage: from itertools import izip
    sage: fib = Stream()
    sage: def g():
    ...          yield 1
    ...          yield 1
    ...          n = 0
    ...          while True:
    ...              yield fib[n] + fib[n+1]
    ...              n += 1

    sage: fib.set_gen(g())
    sage: [x for (x,i) in izip(fib, range(11))]
    [1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89]


    sage: l = [4,3,5,2,6,1]
    sage: s = Stream(l)
    sage: s[3]
    2
    sage: len(s)
    4
    sage: g = iter(l)
    sage: s.set_gen(g)
    sage: s[5]
    3
    sage: len(s)
    6

map(self, f)

source code  

EXAMPLES:
    sage: from sage.combinat.species.stream import Stream
    sage: s = Stream(ZZ)
    sage: square = lambda x: x^2
    sage: ss = s.map(square)
    sage: [ss[i] for i in range(10)]
    [0, 1, 1, 4, 4, 9, 9, 16, 16, 25]

TESTS:
    sage: from itertools import izip
    sage: f = lambda l: 0 if len(l) == 0 else l[-1] + 1
    sage: o = Stream(f)
    sage: [x for (x,i) in izip(o, range(10))]
    [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
    sage: double = lambda z: 2*z
    sage: t = o.map(double)
    sage: [x for (x,i) in izip(t, range(10))]
    [0, 2, 4, 6, 8, 10, 12, 14, 16, 18]

    sage: double = lambda z: 2*z
    sage: o = Stream([0,1,2,3])
    sage: [x for (x,i) in izip(o, range(6))]
    [0, 1, 2, 3, 3, 3]
    sage: t = o.map(double)
    sage: [x for (x,i) in izip(t, range(6))]
    [0, 2, 4, 6, 6, 6]

__getitem__(self, i)
(Indexing operator)

source code  

Returns the ith entry of self.

EXAMPLES:
    sage: from sage.combinat.species.stream import Stream
    sage: s = Stream(ZZ)
    sage: [s[i] for i in range(10)]
    [0, 1, -1, 2, -2, 3, -3, 4, -4, 5]
    sage: s[1]
    1

    sage: s = Stream([1,2,3])
    sage: [s[i] for i in range(10)]
    [1, 2, 3, 3, 3, 3, 3, 3, 3, 3]

    sage: s = Stream(QQ)
    sage: s[10]
    -3/2

__add__(self, s)
(Addition operator)

source code  

Returns the sum of two streams.

EXAMPLES:
    sage: from sage.combinat.species.stream import Stream
    sage: s = Stream(ZZ)
    sage: ss = s + s
    sage: [ss[i] for i in range(10)]
    [0, 2, -2, 4, -4, 6, -6, 8, -8, 10]

__mul__(self, s)

source code  

Returns the product of two streams.

EXAMPLES:
  We can use a stream to represent the polynomial 1+x and use it to compute the
  coefficients of (1+x)^2.
  
    sage: from sage.combinat.species.stream import Stream
    sage: s = Stream([1,1,0])
    sage: ss = s*s
    sage: [ss[i] for i in range(5)]
    [1, 2, 1, 0, 0]

_times_naive(self, s, n)

source code  

Returns the nth entry in the product of self and s via the naive multiplication
algorithm.  Note that this requires that all entries for self and s in range(n+1)
be computed.

EXAMPLES:
    sage: from sage.combinat.species.stream import Stream
    sage: s = Stream([1,1,0])
    sage: s._times_naive(s, 0)
    1
    sage: s._times_naive(s, 1)
    2
    sage: s._times_naive(s, 2)
    1

__iter__(self)

source code  

EXAMPLES:
    sage: from sage.combinat.species.stream import Stream
    sage: s = Stream([1,2,3])
    sage: g = iter(s)
    sage: [g.next() for i in range(5)]
    [1, 2, 3, 3, 3]

__len__(self)
(Length operator)

source code  

Returns the number of coefficients computed so far.

EXAMPLES:
    sage: from sage.combinat.species.stream import Stream
    sage: l = [4,3,5,7,4,1,9,7]
    sage: s = Stream(l)
    sage: s[3]
    7
    sage: len(s)
    4
    sage: s[3]
    7
    sage: len(s)
    4
    sage: s[1]
    3
    sage: len(s)
    4
    sage: s[4]
    4
    sage: len(s)
    5


TESTS:
    sage: l = ['Hello', ' ', 'World', '!']
    sage: s = Stream(l)
    sage: len(s)
    0
    sage: s[2]
    'World'
    sage: len(s)
    3
    sage: u = ""
    sage: for i in range(len(s)): u += s[i]
    sage: u
    'Hello World'
    sage: v = ""
    sage: for i in range(10): v += s[i]
    sage: v
    'Hello World!!!!!!!'
    sage: len(s)
    4

number_computed(self)

source code  

Returns the number of coefficients computed so far.

EXAMPLES:
    sage: from sage.combinat.species.stream import Stream
    sage: l = [4,3,5,7,4,1,9,7]
    sage: s = Stream(l)
    sage: s[3]
    7
    sage: len(s)
    4
    sage: s[3]
    7
    sage: len(s)
    4
    sage: s[1]
    3
    sage: len(s)
    4
    sage: s[4]
    4
    sage: len(s)
    5


TESTS:
    sage: l = ['Hello', ' ', 'World', '!']
    sage: s = Stream(l)
    sage: len(s)
    0
    sage: s[2]
    'World'
    sage: len(s)
    3
    sage: u = ""
    sage: for i in range(len(s)): u += s[i]
    sage: u
    'Hello World'
    sage: v = ""
    sage: for i in range(10): v += s[i]
    sage: v
    'Hello World!!!!!!!'
    sage: len(s)
    4

data(self)

source code  

Returns a list of all the coefficients computed so far.

EXAMPLES:
    sage: from sage.combinat.species.stream import Stream, _integers_from
    sage: s = Stream(_integers_from(3))
    sage: s.data()
    []
    sage: s[5]
    8
    sage: s.data()
    [3, 4, 5, 6, 7, 8]

is_constant(self)

source code  

Returns True if and only if

EXAMPLES:
    sage: from sage.combinat.species.stream import Stream
    sage: s = Stream([1,2,3])
    sage: s.is_constant()
    False
    sage: s[3]
    3
    sage: s.data()
    [1, 2, 3]
    sage: s.is_constant()
    True

TESTS:
    sage: l = [2,3,5,7,11,0]
    sage: s = Stream(l)
    sage: s.is_constant()
    False
    sage: s[3]
    7
    sage: s.is_constant()
    False
    sage: s[5]
    0
    sage: s.is_constant()
    False
    sage: s[6]
    0
    sage: s.is_constant()
    True

    sage: s = Stream(const='I am constant.')
    sage: s.is_constant()
    True

stretch(self, k)

source code  

EXAMPLES:
    sage: from sage.combinat.species.stream import Stream
    sage: s = Stream(range(1, 10))
    sage: s2 = s.stretch(2)
    sage: [s2[i] for i in range(10)]
    [1, 0, 2, 0, 3, 0, 4, 0, 5, 0]

_stretch_aux(self, k)

source code  

EXAMPLES:
    sage: from sage.combinat.species.stream import Stream
    sage: s = Stream(range(1, 10))
    sage: g = s._stretch_aux(2)
    sage: [g.next() for i in range(10)]
    [1, 0, 2, 0, 3, 0, 4, 0, 5, 0]

   Home       Trees       Indices       Help   
Generated by Epydoc 3.0beta1 on Thu Jul 17 04:23:38 2008 http://epydoc.sourceforge.net