ambient, basis, [check=None], [echelonize=False], [inner_product_matrix=True]) |
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:
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]
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.
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.
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.
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_