kalmarek

----------------------------------------------------------------------------
        SCS v1.2.6 - Splitting Conic Solver
        (c) Brendan O'Donoghue, Stanford University, 2012-2016
----------------------------------------------------------------------------
Lin-sys: sparse-direct, nnz in A = 375437
eps = 1.00e-06, alpha = 1.80, max_iters = 20000, normalize = 1, scale = 5.00
Variables n = 93962, constraints m = 263096
Cones:  primal zero / dual free vars: 75173
        linear vars: 1
        sd vars: 187922, sd blks: 2

kalmarek

using Nemo

function power_by_cycles(a::perm, n::Int)
   if n <0
      return inv(a)^-n
   elseif n == 0
      return parent(a)()
   elseif n == 1
      return deepcopy(a)
   elseif n == 2

kalmarek

module DirectProduct

using Nemo

import Base: show, ==, hash
import Base: ×, *, inv

import Nemo: parent, parent_type, elem_type
import Nemo: elements, order, Group, GroupElem, Ring

kalmarek

using Nemo

function power_by_cycles(a::Nemo.perm, n::Int)
   if n <0
      return inv(a)^-n
   elseif n == 0
      return parent(a)()
   elseif n == 1
      return deepcopy(a)
   elseif n == 2

kalmarek

using Nemo
using BenchmarkTools

function perm_sample(N=1000, samplesize=10000, seed=1234)
    sample = Nemo.Generic.perm[]
    srand(seed)
    for i in 1:samplesize
        push!(sample, rand(PermutationGroup(N)))
    end
    return sample

kalmarek

----------------------------------------------------------------------------
	SCS v2.0.2 - Splitting Conic Solver
	(c) Brendan O'Donoghue, Stanford University, 2012-2017
----------------------------------------------------------------------------
Lin-sys: sparse-direct, nnz in A = 7232838
eps = 1.00e-14, alpha = 1.50, max_iters = 20000, normalize = 1, scale = 1.00
acceleration_lookback = 20, rho_x = 1.00e-03
Variables n = 13233, constraints m = 20463
Cones:	primal zero / dual free vars: 13621
	linear vars: 2

kalmarek

----------------------------------------------------------------------------
	SCS v2.0.2 - Splitting Conic Solver
	(c) Brendan O'Donoghue, Stanford University, 2012-2017
----------------------------------------------------------------------------
Lin-sys: sparse-direct, nnz in A = 7232838
eps = 1.00e-05, alpha = 1.50, max_iters = 5000, normalize = 1, scale = 1.00
acceleration_lookback = 1, rho_x = 1.00e-03
Variables n = 13233, constraints m = 20463
Cones:	primal zero / dual free vars: 13621
	linear vars: 2

kalmarek

module OrderStatistics

using StatsFuns
using Memoize

using IntervalArithmetic.Interval
import IntervalArithmetic.interval_from_midpoint_radius
import QuadGK.quadgk

export NormOrderStatistic, moment, expectation, expectationproduct

kalmarek

using Nemo
using Base.Test

const PREC = 200
const FF = AcbField(PREC)
const acb_struct = Nemo.acb_struct

import Base.*

function *(x::acb_struct, d::S, prec::Int=PREC) where S<:Int

kalmarek

doc"""
    elements!(G::PermGroup)
> Return an unsafe iterator over all permutations in `G`. Only one permutation
> is allocated and then modified in-place using the non-recursive
> [Heaps algorithm](https://en.wikipedia.org/wiki/Heap's_algorithm).
>
> Note: you need to explicitely copy permutations intended to be stored or
> modified.

# Examples: