Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

CHAPTER
FIFTEEN
SPARSE MATRICES OVER Z/NZ FOR
N SMALL
Sparse matrices over Z/nZ for n small
This is a compiled implementation of sparse matrices over Z/nZ for n small.
TODO: - move vectors into a Cython vector class - add _add_ and _mul_ methods.
EXAMPLES:
sage: a = matrix(Integers(37),3,3,range(9),sparse=True); a
[0 1 2]
[3 4 5]
[6 7 8]
sage: type(a)
sage: parent(a)
Full MatrixSpace of 3 by 3 sparse matrices over Ring of integers modulo 37
sage: a^2
[15 18 21]
[ 5 17 29]
[32 16 0]
sage: a+a
[ 0 2 4]
[ 6 8 10]
[12 14 16]
sage: b = a.new_matrix(2,3,range(6)); b
[0 1 2]
[3 4 5]
sage: a*b
Traceback (most recent call last):
...
TypeError: unsupported operand parent(s) for ’*’: ’Full MatrixSpace of 3 by 3 sparse matrices over Ri
sage: b*a
[15 18 21]
[ 5 17 29]
sage: TestSuite(a).run()
sage: TestSuite(b).run()
sage: a.echelonize(); a
[ 1 0 36]
[ 0 1 2]
[ 0 0 0]
299