5.1.1.2 VectorSpace_ambient Objects

class VectorSpace_ambient
The VectorSpace_ambient class defines functionality for both dense and sparse ambient vector spaces over an arbitrary base field. This class derives from VectorSpace_generic.
VectorSpace_ambient( base_field, degree, [sparse=False])

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

Instances of class VectorSpace_ambient have the following methods (in addition to inherited methods and special methods):

ambient_space,$  $ basis,$  $ dimension,$  $ echelonized_basis,$  $ is_ambient

These methods are defined as follows:

ambient_space( )

basis( )

sage: from sage.rings.rings import RationalField
sage: V = VectorSpace(RationalField(), 2); V
Full Vector space of degree 2 over Rational Field
sage: V.basis()
[(1 0), (0 1)]

dimension( )

echelonized_basis( )

sage: from sage.rings.rings import RationalField
sage: V = VectorSpace(RationalField(), 2); V
Full Vector space of degree 2 over Rational Field
sage: V.basis()
[(1 0), (0 1)]

is_ambient( )

Instances of class VectorSpace_ambient also have the following special methods:

__contains__( x)

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