base_field, dimension, degree, [sparse=None], [inner_product_matrix=False]) |
category,
intersection,
is_subspace,
submodule,
submodule_with_basis,
vector_space,
zero_submodule,
zero_subspace
Further documentation:
) |
Return the category to which this vector space belongs.
other) |
Return the intersection of self and other, which must be R-submodules of a common ambient vector space.
sage: V = VectorSpace(RationalField(),3) sage: W1 = V.subspace([V.gen(0), V.gen(0) + V.gen(1)]) sage: W2 = V.subspace([V.gen(1), V.gen(2)]) sage: W1.intersection(W2) Vector space of degree 3 and dimension 1 over Rational Field Basis matrix: [0 1 0] sage: W2.intersection(W1) Vector space of degree 3 and dimension 1 over Rational Field Basis matrix: [0 1 0] sage: V.intersection(W1) Vector space of degree 3 and dimension 2 over Rational Field Basis matrix: [1 0 0] [0 1 0] sage: W1.intersection(V) Vector space of degree 3 and dimension 2 over Rational Field Basis matrix: [1 0 0] [0 1 0] sage: Z = V.subspace([]) sage: W1.intersection(Z) Vector space of degree 3 and dimension 0 over Rational Field Basis matrix: []
other) |
True if this vector space is a subspace of other.
sage: V = VectorSpace(RationalField(),3) sage: W = V.subspace([V.gen(0), V.gen(0) + V.gen(1)]) sage: W2 = V.subspace([V.gen(1)]) sage: W.is_subspace(V) True sage: W2.is_subspace(V) True sage: W.is_subspace(W2) False sage: W2.is_subspace(W) True
Instances of class FreeModule_generic_field also have the following special methods:
__add__,
__mul__,
__rmul__
Further documentation:
other) |
Return the product of this module by the number other, which is the module spanned by other times each basis vector.
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