LLL jump

julia> using Hecke

julia> K, a = number_field(x^4-10*x^2+1, cached = false)

julia> OK = (maximal_order(K))

julia> E = EquationOrder(K)

julia> P = prime_decomposition(E, 13)[1][1]^C

julia> P = prime_decomposition(E, 13)[1][1]^C

julia> Q = P; for i in 1:20
         global Q = Q^2; @show i
         M = basis_matrix(Q)
         @show nbits(maximum(abs, M))
         @time lll(M)
       end
i = 1
nbits(maximum(abs, M)) = 8
  0.000073 seconds (121 allocations: 10.781 KiB)
i = 2
nbits(maximum(abs, M)) = 15
  0.000046 seconds (124 allocations: 10.844 KiB)
i = 3
nbits(maximum(abs, M)) = 30
  0.000048 seconds (130 allocations: 11.109 KiB)
i = 4
nbits(maximum(abs, M)) = 60
  0.000053 seconds (143 allocations: 11.672 KiB)
i = 5
nbits(maximum(abs, M)) = 119
  0.000104 seconds (240 allocations: 15.922 KiB)
i = 6
nbits(maximum(abs, M)) = 237
  0.000253 seconds (452 allocations: 25.430 KiB)
i = 7
nbits(maximum(abs, M)) = 474
  0.000306 seconds (628 allocations: 53.023 KiB)
i = 8
nbits(maximum(abs, M)) = 948
  0.000591 seconds (1.29 k allocations: 115.047 KiB)
i = 9
nbits(maximum(abs, M)) = 1895
  0.000796 seconds (2.00 k allocations: 184.641 KiB)
i = 10
nbits(maximum(abs, M)) = 3790
  0.001480 seconds (3.91 k allocations: 343.430 KiB)
i = 11
nbits(maximum(abs, M)) = 7579
  0.010938 seconds (7.77 k allocations: 746.781 KiB, 70.67% gc time)
i = 12
nbits(maximum(abs, M)) = 15158
  0.007789 seconds (15.83 k allocations: 1.865 MiB)
i = 13
nbits(maximum(abs, M)) = 30315
  0.043569 seconds (60.17 k allocations: 8.265 MiB)
i = 14
nbits(maximum(abs, M)) = 60629
  0.031775 seconds (58.62 k allocations: 14.802 MiB, 13.49% gc time)
i = 15
nbits(maximum(abs, M)) = 121257
  0.211259 seconds (196.61 k allocations: 76.224 MiB, 4.27% gc time)
i = 16
nbits(maximum(abs, M)) = 242513
  0.875391 seconds (397.89 k allocations: 275.843 MiB, 2.13% gc time)
i = 17
nbits(maximum(abs, M)) = 485025
  2.073985 seconds (826.89 k allocations: 2.884 GiB, 9.61% gc time)
i = 18
nbits(maximum(abs, M)) = 970049
  2.373175 seconds (952.51 k allocations: 4.553 GiB, 12.64% gc time)
i = 19
nbits(maximum(abs, M)) = 1940097
 29.525222 seconds (3.43 M allocations: 57.138 GiB, 12.67% gc time)
i = 20
nbits(maximum(abs, M)) = 3880193
 38.771705 seconds (3.87 M allocations: 75.772 GiB, 13.42% gc time)