Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
sage: import sage.matrix.benchmark as b
sage: ts = b.charpoly_GF(100)
sage: tm = b.charpoly_GF(100, system=’magma’)
# optional - magma
sage.matrix.benchmark.charpoly_ZZ(n=100, min=0, max=9, system=’sage’)
Characteristic polynomial over ZZ: Given a n x n matrix over ZZ with random entries between min and max,
compute the charpoly.
INPUT:
•n - matrix dimension (default: 100)
•min - minimal value for entries of matrix (default: 0)
•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.charpoly_ZZ(100)
sage: tm = b.charpoly_ZZ(100, system=’magma’)
# optional - magma
sage.matrix.benchmark.det_GF(n=400, p=16411, system=’sage’)
Dense determinant over GF(p). Given an n x n matrix A over GF with random entries compute det(A).
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.det_GF(1000)
sage: tm = b.det_GF(1000, system=’magma’)
# optional - magma
sage.matrix.benchmark.det_QQ(n=300, num_bound=10, den_bound=10, system=’sage’)
Dense rational determinant over QQ. Given an n x n matrix A over QQ with random entries with numerator
bound and denominator bound, compute det(A).
INPUT:
•n - matrix dimension (default: 200)
•num_bound - numerator bound, inclusive (default: 10)
•den_bound - denominator bound, inclusive (default: 10)
•system - either ‘sage’ or ‘magma’ (default: ‘sage’)
EXAMPLES:
sage: import sage.matrix.benchmark as b
sage: ts = b.det_QQ(200)
sage: ts = b.det_QQ(10, num_bound=100000, den_bound=10000)
sage: tm = b.det_QQ(200, system=’magma’) # optional - magma
sage.matrix.benchmark.det_ZZ(n=200, min=1, max=100, system=’sage’)
Dense integer determinant over ZZ. Given an n x n matrix A over ZZ with random entries between min and
max, inclusive, compute det(A).
414 Chapter 24. Benchmarks for matrices