Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
INPUT:
•n - matrix dimension (default: 200)
•min - minimal value for entries of matrix (default: 1)
•max - maximal value for entries of matrix (default: 100)
•system - either ‘sage’ or ‘magma’ (default: ‘sage’)
EXAMPLES:
sage: import sage.matrix.benchmark as b
sage: ts = b.det_ZZ(200)
sage: tm = b.det_ZZ(200, system=’magma’)
# optional - magma
sage.matrix.benchmark.det_hilbert_QQ(n=80, system=’sage’)
Runs the benchmark for calculating the determinant of the hilbert matrix over rationals of dimension n.
INPUT:
•n - matrix dimension (default: 300)
•system - either ‘sage’ or ‘magma’ (default: ‘sage’)
EXAMPLES:
sage: import sage.matrix.benchmark as b
sage: ts = b.det_hilbert_QQ(50)
sage: tm = b.det_hilbert_QQ(50, system=’magma’)
# optional - magma
sage.matrix.benchmark.echelon_QQ(n=100, min=0, max=9, system=’sage’)
Given a n x (2*n) matrix over QQ with random integer entries between min and max, compute the reduced row
echelon form.
INPUT:
•n - matrix dimension (default: 300)
•min - minimal value for entries of matrix (default: -9)
•max - maximal value for entries of matrix (default: 9)
•system - either ‘sage’ or ‘magma’ (default: ‘sage’)
EXAMPLES:
sage: import sage.matrix.benchmark as b
sage: ts = b.echelon_QQ(100)
sage: tm = b.echelon_QQ(100, system=’magma’)
# optional - magma
sage.matrix.benchmark.hilbert_matrix(n)
Returns the Hilbert matrix of size n over rationals.
EXAMPLES:
sage: import sage.matrix.benchmark as b
sage: b.hilbert_matrix(3)
[ 1 1/2 1/3]
[1/2 1/3 1/4]
[1/3 1/4 1/5]
sage.matrix.benchmark.inverse_QQ(n=100, min=0, max=9, system=’sage’)
Given a n x n matrix over QQ with random integer entries between min and max, compute the reduced row
echelon form.
415