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:
- Matrix addition
- Matrix vector product
- Matrix multiplication
- Determinant
- Rank
- Characteristic Polynomial [:../charpoly: 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)