5.1.1.5 VectorSpace_subspace_with_basis Objects

class VectorSpace_subspace_with_basis
The VectorSpace_subspace_with_basis class derives from VectorSpace_subspace and provides additional functionality for subspaces with a specified basis, which need not be in echelon form.
VectorSpace_subspace_with_basis( basis, [ambient=None])

Instances of class VectorSpace_subspace_with_basis have the following functions (in addition to inherited functions and special functions):

basis,$  $ change_ring,$  $ coordinate_vector,$  $ coordinates,$  $ echelonized_basis,$  $ linear_combination_of_basis,$  $ user_basis

Further documentation:

change_ring( R)

Change this vector space to be a vector space over R by coercing the basis vectors into R. The basis vectors must coerce into R or this command will fail.

sage: V = VectorSpace(QQ,3)
sage: W = V.subspace_with_basis([2*V._0 + QQ('1/2')*V._1])
sage: W.change_ring(GF(7))
Vector space of degree 3, dimension 1 over Finite field of size
7
User basis matrix:
[2 4 0]

coordinate_vector( v)

Write v in terms of the user basis for self.

Returns a vector 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.

coordinates( v)

Write v in terms of the 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.

linear_combination_of_basis( v)

Return the linear combination of the basis for self obtained from the coordinates of v.

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