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Package sage :: Package linalg :: Module vector_space :: Class VectorSpace_ambient |
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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 | |
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Create the space of all vectors of given degree over base_field. | |
__contains__(self,
x)
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__repr__(self)
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ambient_space(self)
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EXAMPLES: | |
dimension(self)
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EXAMPLES: | |
is_ambient(self)
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Inherited from VectorSpace_generic | |
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Write v in terms of the basis for self. | |
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Returns a random element of self. | |
Returns a random element of self. | |
Create a subspace of self. | |
Create a subspace of self with given basis. | |
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Inherited from VectorSpace | |
(Static method) | |
Inherited from object | |
x.__delattr__('name') <==> del x.name | |
x.__getattribute__('name') <==> x.name | |
x.__hash__() <==> hash(x) | |
helper for pickle | |
helper for pickle | |
x.__setattr__('name', value) <==> x.name = value | |
x.__str__() <==> str(x) | |
Inherited from Gens | |
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Instance Method Details |
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__init__(self,
base_field,
degree,
sparse=False)
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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)] |
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)] |
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