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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)
}}}

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
  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)