Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
[3 4 5]
[6 7 8]
sage: v = m.dense_rows(); v
[(0, 1, 2), (3, 4, 5), (6, 7, 8)]
sage: v is m.dense_rows()
False
sage: m.dense_rows(copy=False) is m.dense_rows(copy=False)
True
sage: m[0,0] = 10
sage: m.dense_rows()
[(10, 1, 2), (3, 4, 5), (6, 7, 8)]
TESTS:
Check that the returned rows are immutable as per trac ticket #14874:
sage: m = Mat(ZZ,3,3)(range(9))
sage: v = m.dense_rows()
sage: map(lambda x: x.is_mutable(), v)
[False, False, False]
lift()
Return lift of self to the covering ring of the base ring R, which is by definition the ring returned by calling
cover_ring() on R, or just R itself if the cover_ring method is not defined.
EXAMPLES:
sage: M = Matrix(Integers(7), 2, 2, [5, 9, 13, 15]) ; M
[5 2]
[6 1]
sage: M.lift()
[5 2]
[6 1]
sage: parent(M.lift())
Full MatrixSpace of 2 by 2 dense matrices over Integer Ring
The field QQ doesn’t have a cover_ring method:
sage: hasattr(QQ, ’cover_ring’)
False
So lifting a matrix over QQ gives back the same exact matrix.
sage: B = matrix(QQ, 2, [1..4])
sage: B.lift()
[1 2]
[3 4]
sage: B.lift() is B
True
matrix_from_columns(columns)
Return the matrix constructed from self using columns with indices in the columns list.
EXAMPLES:
sage: M = MatrixSpace(Integers(8),3,3)
sage: A = M(range(9)); A
[0 1 2]
[3 4 5]
[6 7 0]
sage: A.matrix_from_columns([2,1])
105