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← Revision 9 as of 20081114 13:41:59 ⇥
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1. Characteristic Polynomial [:../charpoly: some benchmarks here]  1. Characteristic Polynomial [[../charpoly some benchmarks here]] 
Benchmarking Cyclotomic Linear Algebra
Systems:
 Magma2.14 and Magma2.13
 PARI2.3.3
 Sage3.0
Operating Systems / Hardware:
 32bit OS X intel 2.6Ghz core 2 duo natively
 64bit Linux running on 1.8Ghz Opteron natively
 32bit Linux running on 2.6Ghz core 2 duo (under vmware)
 64bit Linux running on 2.6Ghz core 2 duo (under vmware)
Benchmarks:
 Matrix addition
 Matrix vector product
 Matrix multiplication
 Determinant
 Rank
Characteristic Polynomial some benchmarks here
 Reduced row echelon form
 Sparse reduced row echelon form
 Solving A*x = b and A*X = B
 Kernel
 Rational decomposition
A good source of matrices that we care about:
Below, replace 23 by any of 23, 67, 89, 199, and p=2 in the last line below by any positive integer:
ModularSymbols_clear_cache() eps = DirichletGroup(23*3, CyclotomicField(11)).1^2 M = ModularSymbols(eps); M t = M.hecke_matrix(2)