Package sage :: Package linalg :: Module vector_space :: Class VectorSpace_ambient
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Type VectorSpace_ambient

           Gens --+    
                  |    
     object --+   |    
              |   |    
    VectorSpace --+    
                  |    
VectorSpace_generic --+
                      |
         object --+   |
                  |   |
              _uniq --+
                      |
                     VectorSpace_ambient


Ambient vector space:
        base_field -- a field
        degree -- int >= 0, the degree of the vector space 
                  (number of components of vectors).
        sparse -- whether or not vectors are given a sparse representation 
                  (default to False)

Method Summary
  __init__(self, base_field, degree, sparse)
Create the space of all vectors of given degree over base_field.
  __contains__(self, x)
  __repr__(self)
  ambient_space(self)
  basis(self)
EXAMPLES:
  dimension(self)
  echelonized_basis(self)
EXAMPLES:
  is_ambient(self)
    Inherited from VectorSpace_generic
  __add__(self, other)
  __call__(self, entries, coerce_entries, copy, check_element)
  __cmp__(self, right)
  base_field(self)
  base_ring(self)
  coordinates(self, v)
Write v in terms of the basis for self.
  degree(self)
  gen(self, n)
  is_dense(self)
  is_full(self)
  is_sparse(self)
  matrix(self)
  ngens(self)
  random(self, X, prob, coerce)
Returns a random element of self.
  random_element(self, X, prob, coerce)
Returns a random element of self.
  subspace(self, gens)
Create a subspace of self.
  subspace_with_basis(self, basis)
Create a subspace of self with given basis.
  vector(self, x, coerce_entries, copy, check_element)
  vector_space(self, degree)
  zero_vector(self)
    Inherited from VectorSpace
  __new__(cls, *args, **kwds)
(Static method)
    Inherited from object
  __delattr__(...)
x.__delattr__('name') <==> del x.name
  __getattribute__(...)
x.__getattribute__('name') <==> x.name
  __hash__(x)
x.__hash__() <==> hash(x)
  __reduce__(...)
helper for pickle
  __reduce_ex__(...)
helper for pickle
  __setattr__(...)
x.__setattr__('name', value) <==> x.name = value
  __str__(x)
x.__str__() <==> str(x)
    Inherited from Gens
  __getattr__(self, attrname)
  __getitem__(self, n)
  __getslice__(self, n, m)
  gens(self)
  list(self)

Instance Method Details

__init__(self, base_field, degree, sparse=False)
(Constructor)

Create the space of all vectors of given degree over base_field.
INPUT:
    base_field -- a field
    degree -- int >= 0, the degree of the vector space 
              (number of components of vectors).
    sparse -- whether or not matrices are given a sparse representation 
              (default to False)
Overrides:
sage.linalg.vector_space.VectorSpace_generic.__init__ (inherited documentation)

basis(self)

EXAMPLES:
>>> from sage.rings.rings import RationalField
>>> V = VectorSpace(RationalField(), 2); V
Full Vector space of degree 2 over Rational Field

>>> V.basis()
[(1 0), (0 1)]
Overrides:
sage.linalg.vector_space.VectorSpace_generic.basis

echelonized_basis(self)

EXAMPLES:
>>> from sage.rings.rings import RationalField
>>> V = VectorSpace(RationalField(), 2); V
Full Vector space of degree 2 over Rational Field

>>> V.basis()
[(1 0), (0 1)]
Overrides:
sage.linalg.vector_space.VectorSpace_generic.basis

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