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 1. Characteristic Polynomial  1. Characteristic Polynomial [[../charpoly| some benchmarks here]]

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
  2. Matrix vector product
  3. Matrix multiplication
  4. Determinant
  5. Rank

  6. Characteristic Polynomial some benchmarks here

  7. Reduced row echelon form
  8. Sparse reduced row echelon form
  9. Solving A*x = b and A*X = B
  10. Kernel
  11. 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)

cyclo/benchmark (last edited 2008-11-14 13:41:59 by anonymous)