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

           Gens --+        
                  |        
     object --+   |        
              |   |        
    VectorSpace --+        
                  |        
VectorSpace_generic --+    
                      |    
   VectorSpace_subspace --+
                          |
                         VectorSpace_subspace_with_basis


Method Summary
  __init__(self, basis, ambient)
  __repr__(self)
  basis(self)
  coordinates(self, v)
Write v in terms of the user basis for self.
  echelonized_basis(self)
  user_basis(self)
    Inherited from VectorSpace_subspace
  __contains__(self, v)
  ambient_space(self)
  dimension(self)
  generators(self)
  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)
  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

coordinates(self, v)

Write v in terms of the user basis for self.

Returns a list c such that if B is the basis for self, then 
        sum c[i] B[i] = v
If v is not in self, raises an ArithmeticError exception.
Overrides:
sage.linalg.vector_space.VectorSpace_generic.coordinates

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