Pi

Author: PeterLuschny

Project.toml

@@ -5,6 +5,7 @@ version = "0.2.0"
 [deps]
 Atom = "c52e3926-4ff0-5f6e-af25-54175e0327b1"
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
+DataStructures = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
 Dates = "ade2ca70-3891-5945-98fb-dc099432e06a"
 DocStringExtensions = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"

demos/DistributedQueens.jl

@@ -2,9 +2,9 @@ module QueensAlwaysPuzzleMe
 
 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
+# For some background see https://wp.me/paipV7-E and https://oeis.org/A319284
 
 function solve!(profile, level, size, start, cols, diag4, diag1)
 

docs/src/index.md

@@ -88,6 +88,9 @@ CantorMachine
 CantorPairing
 ```
 ```@docs
+CardinalityOfSetPartitionsWithShape
+```
+```@docs
 Central
 ```
 ```@docs
@@ -418,6 +421,9 @@ PartitionNumberList
 Pascal
 ```
 ```@docs
+Pi
+```
+```@docs
 Poly
 ```
 ```@docs
@@ -529,6 +535,9 @@ SetPartitions
 Sfactorial
 ```
 ```@docs
+ShapePartitions
+```
+```@docs
 ShowAsMatrix
 ```
 ```@docs
@@ -715,6 +724,9 @@ toΔ
 Ω
 ```
 ```@docs
+π
+```
+```@docs
 σ
 ```
 ```@docs
@@ -940,6 +952,9 @@ L000735
 L000739
 ```
 ```@docs
+L000796
+```
+```@docs
 G000957
 ```
 ```@docs

docs/src/modules.md

@@ -456,6 +456,16 @@ For example consider the case n = 4. There are five integer partitions of 4:
 
 See also [A260876](https://oeis.org/A260876).
 
+   🔶  [SpigotPi](https://github.com/OpenLibMathSeq/IntegerSequences.jl/blob/master/src/SpigotPi.jl)
+
+Computes the first n decimal digits of Pi, uses a variant of the spigot algorithm valid as long as the number of digits <= 54900.
+
+Based on ideas of A. Sale (1968). Algorithm due to D. Saada (1988) and S. Rabinowitz (1991). Proof due to S. Rabinowitz and S. Wagon (1995).
+
+https://www.maa.org/sites/default/files/pdf/pubs/amm_supplements/Monthly_Reference_12.pdf
+
+* Pi, π, L000796
+
    🔶  [StirlingLahNumbers](https://github.com/OpenLibMathSeq/IntegerSequences.jl/blob/master/src/StirlingLahNumbers.jl)
 
 

src/BuildSequences.jl

@@ -35,7 +35,6 @@ docsrcdir = joinpath(docdir, "src")
 @info("The following modules are included in IntegerSequences.jl:")
 
 exclude = [
-    "SetPartitionsByShape.jl",
     "TemplateModule.jl",
     "BuildSequences.jl",
     "IntegerSequences.jl",
@@ -221,7 +220,7 @@ function build_seq()
     println(olm, "__precompile__()")
 
     println(olm, "module IntegerSequences")
-    println(olm, "using Nemo, IterTools, HTTP, DocStringExtensions")
+    println(olm, "using Nemo, IterTools, DataStructures, HTTP, DocStringExtensions")
     # println(olm, "import AbstractAlgebra.lead")
 
     for l in eachline(sor, keep = true)
@@ -252,10 +251,7 @@ function build_test()
     println(o, "srcdir ∉ LOAD_PATH && push!(LOAD_PATH, srcdir)")
 
     println(o, "module runtests")
-    println(
-        o,
-        "using Nemo, Test, SeqTests, IntegerSequences, IterTools"
-    )
+    println(o, "using Nemo, Test, SeqTests, IntegerSequences, IterTools, DataStructures")
 
     path = joinpath(tstdir, "runtests.jl")
     i = open(path, "r")
@@ -331,7 +327,7 @@ function build_perf()
     println(o, "srcdir ∉ LOAD_PATH && push!(LOAD_PATH, srcdir)")
 
     println(o, "module perftests")
-    println(o, "using IntegerSequences, Dates, InteractiveUtils")
+    println(o, "using IntegerSequences, DataStructures, Dates, InteractiveUtils")
 
     println(o, "InteractiveUtils.versioninfo()")
     println(o, "start = Dates.now()")

src/GeneralizedBinomial.jl

@@ -7,7 +7,7 @@ module GeneralizedBinomial
 using Nemo, PrimesIterator, NumberTheory, Products, Triangles
 
 export ModuleGeneralizedBinomial
-export Binomial, Pascal, T007318
+export Binomial, Pascal, T007318, Multinomial
 
 """
 
@@ -94,6 +94,21 @@ function Binomial(n::Int, k::Int)
     ZZ(0)
 end
 
+"""
+
+Return the multinomial coefficient of a list.
+"""
+function Multinomial(lst::Array{Int})
+    s = 0
+    result = ZZ(1)
+    for c in lst
+        s += c
+        result *= binom(s, c)
+    end
+    result
+end
+
+
 #START-TEST-########################################################
 
 using Test

src/IntPartitions.jl

@@ -5,8 +5,10 @@
 
 module IntPartitions
 
+using GeneralizedBinomial
+
 export ModuleIntPartitions
-export IntegerPartitions, PartitionNumber, Multinomial
+export IntegerPartitions, PartitionNumber
 export PartOrder, byNumPart, byMaxPart
 export PartitionCoefficientsByLength, PartitionCoefficientsByBiggestPart
 export V000041, I072233, L072233, L036038, L078760, L005651, L262071, L292222
@@ -219,19 +221,6 @@ Return a list of the number of partitions of ``n`` into ``k`` parts.
 """
 L072233(n) = collect(I072233(n))
 
-"""
-
-Return the multinomial coefficient of a list.
-"""
-function Multinomial(lst::Array{Int})
-    s = 0
-    result = 1
-    for c in lst
-        s += c
-        result *= binomial(s, c)
-    end
-    result
-end
 
 """