Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
INPUT:
•A - matrix window
•cutoff - size at which algorithm reverts to naive Gaussian elimination and multiplication must be at least
1.
OUTPUT: The list of pivot columns
EXAMPLE:
sage: A = matrix(QQ, 7, [5, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 3, 1, 0, -1, 0, 0, -1
sage: B = A.__copy__(); B._echelon_strassen(1); B
[ 1 0 0 0 0 0 0]
[ 0 1 0 -1 0 1 0]
[ 0 0 1 0 0 0 0]
[ 0 0 0 0 1 0 0]
[ 0 0 0 0 0 0 1]
[ 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0]
sage: C = A.__copy__(); C._echelon_strassen(2); C == B
True
sage: C = A.__copy__(); C._echelon_strassen(4); C == B
True
sage: n = 32; A = matrix(Integers(389),n,range(n^2))
sage: B = A.__copy__(); B._echelon_in_place_classical()
sage: C = A.__copy__(); C._echelon_strassen(2)
sage: B == C
True
TESTS:
sage: A = matrix(Integers(7), 4, 4, [1,2,0,3,0,0,1,0,0,1,0,0,0,0,0,1])
sage: B = A.__copy__(); B._echelon_in_place_classical()
sage: C = A.__copy__(); C._echelon_strassen(2)
sage: B == C
True
sage: A = matrix(Integers(7), 4, 4, [1,0,5,0,2,0,3,6,5,1,2,6,4,6,1,1])
sage: B = A.__copy__(); B._echelon_in_place_classical()
sage: C = A.__copy__(); C._echelon_strassen(2) #indirect doctest
sage: B == C
True
AUTHORS:
•Robert Bradshaw
sage.matrix.strassen.strassen_window_multiply(C, A, B, cutoff )
Multiplies the submatrices specified by A and B, places result in C. Assumes that A and B have compatible
dimensions to be multiplied, and that C is the correct size to receive the product, and that they are all defined
over the same ring.
Uses strassen multiplication at high levels and then uses MatrixWindow methods at low levels. EXAMPLES:
The following matrix dimensions are chosen especially to exercise the eight possible parity combinations that
could occur while subdividing the matrix in the strassen recursion. The base case in both cases will be a (4x5)
matrix times a (5x6) matrix.
sage: A = MatrixSpace(Integers(2^65), 64, 83).random_element()
sage: B = MatrixSpace(Integers(2^65), 83, 101).random_element()
273