dem

Author: PeterLuschny

.gitignore

@@ -1,3 +1,4 @@
+Manifest.toml
 local/*
 docs/build/*
 .vscode/*

Project.toml

@@ -3,16 +3,18 @@ uuid = "b4b868b0-69a7-11e9-2db0-173b4e8e576c"
 version = "0.2.0"
 
 [deps]
+Atom = "c52e3926-4ff0-5f6e-af25-54175e0327b1"
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 Dates = "ade2ca70-3891-5945-98fb-dc099432e06a"
 DocStringExtensions = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
 HTTP = "cd3eb016-35fb-5094-929b-558a96fad6f3"
 InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 IterTools = "c8e1da08-722c-5040-9ed9-7db0dc04731e"
+Juno = "e5e0dc1b-0480-54bc-9374-aad01c23163d"
 Nemo = "2edaba10-b0f1-5616-af89-8c11ac63239a"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [compat]
-Nemo = ">= 0.14.3"
+Nemo = ">= 0.15.1"
 julia = ">= 1.2.0"

demos/DistributedQueens.jl

@@ -1,8 +1,10 @@
 module QueensAlwaysPuzzleMe
 
-using Distributed
+using Distributed, BenchmarkTools
 
 # For some background see: https://wp.me/paipV7-E
+# There is also a simple (i.e. not distributed) version:
+# https://github.com/PeterLuschny/IntegerSequences.jl/blob/master/demos/SimpleQueens.jl
 
 function solve!(profile, level, size, start, cols, diag4, diag1)
 
@@ -57,22 +59,42 @@ function queens(n::Int)
     [profile[n-i+1] for i = 0:n]
 end
 
-function demo(up_to)
-    # The number of threads used for multithreading.
-    println(Base.Sys.CPU_THREADS)
-    println(Threads.nthreads())
-
+function ProfileQueens(up_to)
     for n in 0:up_to
-        print("elapsed: ")
-        @time profile = queens(n)
-        println("size:      ", n)
-        println("profile:   ", profile)
-        println("nodes:     ", sum(profile))
-        println("solutions: ", profile[n+1])
-        println()
+        profile = queens(n)
+        #show_profile(n, profile)
     end
 end
 
-demo(10)
+"""
+julia> show_profile(7, queens(7))
+    size:      7
+    profile:   [1, 7, 30, 76, 140, 164, 94, 40]
+    nodes:     552
+    solutions: 40
+"""
+function show_profile(n, p)
+    println("size:      ", n)
+    println("profile:   ", p)
+    println("nodes:     ", sum(p))
+    println("solutions: ", p[n+1])
+    println()
+end
+
+"""
+julia> BechmarkQueens()
+    Number of cpu-threads : 4
+    Number of threads used: 4
+    95.699 ms (589 allocations: 48.88 KiB)
+"""
+function BechmarkQueens()
+    println("Number of cpu-threads : ", Base.Sys.CPU_THREADS)
+    println("Number of threads used: ", Threads.nthreads())
+    println()
+
+    @btime ProfileQueens(12)
+end
+
+BechmarkQueens()
 
 end # module

demos/SimpleQueens.jl

@@ -1,6 +1,9 @@
 module QueensAlwaysMakeProblems
 
 # For some background see: https://wp.me/paipV7-E
+# There is also a 'distributed' version:
+# https://github.com/PeterLuschny/IntegerSequences.jl/blob/master/demos/DistributedQueens.jl
+
 
 function solve!(profile, level, size, start, cols, diag4, diag1)
 

docs/src/developerguide.md

@@ -119,7 +119,7 @@ this short notations for the rising and the falling factorial powers are support
     FallingFactorial(n::Int, k::Int) = ∏(n - k + 1, n)
 ```
 
-## Muliti-dimensional sequences
+## Multi-dimensional sequences
 
 ### The concept of a sequence
 

docs/src/index.md

@@ -334,6 +334,9 @@ ModuleSetPartitions
 ModuleSetPartitionsMType
 ```
 ```@docs
+ModuleSetPartitionsMType
+```
+```@docs
 ModuleStirlingNumbers
 ```
 ```@docs

docs/src/modules.md

@@ -235,7 +235,7 @@ GammaHyp: ``(a, b, c, d)`` ↦ ``Γ(a) `` Hypergeometric``1F1(b, c, d).``
    🔶  [IntPartitions](https://github.com/OpenLibMathSeq/IntegerSequences.jl/blob/master/src/IntPartitions.jl)
 
 
-All integer partitions are listet by two orderings:
+All integer partitions are listed by two orderings:
 IntegerPartitions(n, byNumPart)
 IntegerPartitions(n, byMaxPart)
 
@@ -416,6 +416,13 @@ Return the numbers of partitions of an ``n``-set into nonempty subsets.
 * SetNumber(n::Int, m::Int)
 Return the numbers of partitions of an ``n``-set into ``m`` nonempty subsets.
 
+   🔶  [SetPartitionsByShape](https://github.com/OpenLibMathSeq/IntegerSequences.jl/blob/master/src/SetPartitionsByShape.jl)
+
+
+general Definition
+
+* exported functions
+
    🔶  [SetPartitionsMType](https://github.com/OpenLibMathSeq/IntegerSequences.jl/blob/master/src/SetPartitionsMType.jl)
 
 

src/IntPartitions.jl

@@ -13,7 +13,7 @@ export V000041, I072233, L072233, L036038, L078760, L005651, L262071, L292222
 
 """
 
-All integer partitions are listet by two orderings:
+All integer partitions are listed by two orderings:
    IntegerPartitions(n, byNumPart)
    IntegerPartitions(n, byMaxPart)
 

src/IntegerSequences.jl

@@ -2,8 +2,8 @@
 # Copyright Peter Luschny. License is MIT.
 # This file includes parts from Combinatorics.jl in modified form.
 
-# Version of: UTC 2019-10-24 09:31:01
-# 3af04a00-f630-11e9-1ccb-3f8b137e1871
+# Version of: UTC 2019-10-26 10:41:45
+# 71458000-f7cc-11e9-0078-e76d536f0017
 
 # Do not edit this file, it is generated from the modules and will be overwritten!
 # Edit the modules in the src directory and build this file with BuildSequences.jl!
@@ -123,6 +123,7 @@ ModuleSeqUtils,
 ModuleSeriesExpansion,
 ModuleSetPartitions,
 ModuleSetPartitionsMType,
+ModuleSetPartitionsMType,
 ModuleStirlingNumbers,
 ModuleSwingFactorial,
 ModuleTriangles,
@@ -4764,7 +4765,7 @@ end
 # *** IntPartitions.jl ****************
 """
 
-All integer partitions are listet by two orderings:
+All integer partitions are listed by two orderings:
    IntegerPartitions(n, byNumPart)
    IntegerPartitions(n, byMaxPart)
 
@@ -7881,6 +7882,45 @@ Return the numbers of partitions of an ``n``-set into nonempty subsets.
 $(SIGNATURES)
 """
 SetNumber(n::Int) = Int(Nemo.bell(n))
+# *** SetPartitionsByShape.jl ****************
+"""
+
+general Definition
+
+* exported functions
+"""
+const ModuleSetPartitionsMType = ""
+function P(m, n)
+R, x = PolynomialRing(ZZ, "x")
+function recP(m, n, x)
+n == 0 && return R(1)
+sum(binomial(m*n, m*k)*recP(m, n-k, x)*x for k in 1:n)
+end
+n == 0 && return [ZZ(1)]
+p = recP(m, n, x)
+[coeff(p, k) for k in 0:n]
+end
+function xmSetPartitions(m, n, k)
+shapes = (map(x -> x*m, p) for p in IntegerPartitions(n, k))
+p = []
+if shapes != Nothing
+for s in shapes
+if s != Nothing
+vcat(p, [p for p in SetPartitions(s)]) |>println
+end end
+end
+end
+function SP_byLength(m, n)
+n == 0 && return [n]
+[sum(mSetPartitions(m, n, k)) for k in 1:n]
+end
+function SP_byShape(m, n)
+[p for k in 1:n for p in mSetPartitions(m, n, k)]
+end
+RowSum(m, n)  = sum(SP_byLength(m, n))
+ARowSum(m, n) = sum((-1)^k*sum(mSetPartitions(m, n, k)) for k in 0:n)
+Diagonal(m,n) = mSetPartitions(m, n, n)[0]
+Central(m, n) = SP_byLength(m, 2n)[n]
 # *** SetPartitionsMType.jl ****************
 """
 

src/QueensProblems.jl

@@ -70,6 +70,7 @@ Returns the profile of the backtrack tree for the n queens problem.
 """
 L319284(n) = Queens(n)
 
+
 #START-TEST-########################################################
 
 using Test
@@ -97,8 +98,7 @@ end
 
 """
 
-L319284(15)
-    18.731622 seconds (4 allocations: 480 bytes)
+L319284(15) :: 18.731622 seconds (4 allocations: 480 bytes)
 """
 function perf()
     @time L319284(15)