8.1.1.11 FreeModule_submodule_with_basis_pid Objects

class FreeModule_submodule_with_basis_pid
An $ R$ -submodule of $ K^n$ with distinguished basis, where $ K$ is the fraction field of a principal ideal domain $ R$ .
FreeModule_submodule_with_basis_pid( ambient, basis, [check=None], [echelonize=False], [inner_product_matrix=True])

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

ambient_vector_space,$  $ basis,$  $ change_ring,$  $ coordinate_vector,$  $ echelon_coordinate_vector,$  $ echelon_coordinates,$  $ echelon_to_user_matrix,$  $ echelonized_basis,$  $ is_ambient_vector_space,$  $ linear_combination_of_basis,$  $ user_to_echelon_matrix,$  $ vector_space

Further documentation:

change_ring( R)

Return the free module over R obtained by coercing each element of self into a vector over the fraction field of R, then taking the resulting R-module.

INPUT:
    R -- a principal ideal domain

sage: Q = RationalField()
sage: V = VectorSpace(Q, 3)
sage: W = V.subspace([V.gen(0) + Q('1/2')*V.gen(1)])
sage: W.change_ring(GF(7))
Vector space of degree 3 and dimension 1 over Finite field of size 7
Basis matrix:
[1 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.

echelon_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.

echelon_coordinates( v)

Write v in terms of the echelon 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.

Instances of class FreeModule_submodule_with_basis_pid also have the following special methods:

__cmp__,$  $ __repr__,$  $ _denominator,$  $ _latex_

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