= Benchmarking Cyclotomic Linear Algebra =

Systems:
   * Magma-2.14 and Magma-2.13
   * PARI-2.3.3
   * Sage-3.0
  
Operating Systems / Hardware:
   * 32-bit OS X intel 2.6Ghz core 2 duo natively
   * 64-bit Linux running on 1.8Ghz Opteron natively
   * 32-bit Linux running on 2.6Ghz core 2 duo (under vmware)
   * 64-bit Linux running on 2.6Ghz core 2 duo (under vmware)

Benchmarks:
 1. Matrix addition
 1. Matrix vector product
 1. Matrix multiplication
 1. Determinant
 1. Rank
 1. Characteristic Polynomial [[../charpoly| some benchmarks here]]
 1. Reduced row echelon form
 1. Sparse reduced row echelon form
 1. Solving A*x = b and A*X = B
 1. Kernel
 1. 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)
}}}