Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
sage.matrix.benchmark.matrix_multiply_ZZ(n=300, min=-9, max=9, system=’sage’,
times=1)
Matrix multiplication over ZZ Given an n x n matrix A over ZZ with random entries between min and max,
inclusive, compute A * (A+1).
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’)
•times - number of experiments (default: 1)
EXAMPLES:
sage: import sage.matrix.benchmark as b
sage: ts = b.matrix_multiply_ZZ(200)
sage: tm = b.matrix_multiply_ZZ(200, system=’magma’)
# optional - magma
sage.matrix.benchmark.nullspace_GF(n=300, p=16411, system=’sage’)
Given a n+1 x n matrix over GF(p) with random entries, compute the nullspace.
INPUT:
•n - matrix dimension (default: 300)
•p - prime number (default: 16411)
•system - either ‘magma’ or ‘sage’ (default: ‘sage’)
EXAMPLES:
sage: import sage.matrix.benchmark as b
sage: ts = b.nullspace_GF(300)
sage: tm = b.nullspace_GF(300, system=’magma’)
# optional - magma
sage.matrix.benchmark.nullspace_RDF(n=300, min=0, max=10, system=’sage’)
Nullspace over RDF: Given a n+1 x n matrix over RDF with random entries between min and max, compute the
nullspace.
INPUT:
•n - matrix dimension (default: 300)
•min - minimal value for entries of matrix (default: 0)
•max - maximal value for entries of matrix (default: 10‘)
•system - either ‘sage’ or ‘magma’ (default: ‘sage’)
EXAMPLES:
sage: import sage.matrix.benchmark as b
sage: ts = b.nullspace_RDF(100) # long time
sage: tm = b.nullspace_RDF(100, system=’magma’)
# optional - magma
sage.matrix.benchmark.nullspace_RR(n=300, min=0, max=10, system=’sage’)
Nullspace over RR: Given a n+1 x n matrix over RR with random entries between min and max, compute the
nullspace.
INPUT:
418 Chapter 24. Benchmarks for matrices