8.1.1.1 FreeModule_ambient Objects

class FreeModule_ambient
Ambient free module over a commutative ring.
FreeModule_ambient( base_ring, rank, [sparse=None], [inner_product_matrix=False])

Create the free module of given rank over the given base_ring.

INPUT:
    base_ring -- a commutative ring
    rank -- a non-negative integer

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

basis,$  $ change_ring,$  $ coordinate_vector,$  $ echelon_coordinate_vector,$  $ is_ambient,$  $ linear_combination_of_basis

Further documentation:

change_ring( R)

Return the ambient free module over R of the same rank as self.

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.

linear_combination_of_basis( v)

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

Instances of class FreeModule_ambient also have the following special methods:

__cmp__,$  $ __repr__,$  $ _latex_

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