nyu

Author: PeterLuschny

demos/bfile.jl

@@ -25,6 +25,7 @@ function write_oeis_bfile(anum, range, seq, comments, targetdir)
         end
         println(file, n, " ", val)
     end
+    print("\n")
     close(file)
 end
 

docs/src/index.md

@@ -205,9 +205,6 @@ JacobiTheta4Powers
 KolakoskiList
 ```
 ```@docs
-LF097805
-```
-```@docs
 List
 ```
 ```@docs
@@ -481,6 +478,9 @@ RecTriangle
 Records
 ```
 ```@docs
+RecordsCached
+```
+```@docs
 ReflectPoly
 ```
 ```@docs
@@ -694,9 +694,6 @@ toΔ
 Ω
 ```
 ```@docs
-π
-```
-```@docs
 σ
 ```
 ```@docs

src/Compositions.jl

@@ -8,7 +8,7 @@ module Compositions
 using Nemo, IterTools, Triangles
 
 export ModuleCompositions
-export T097805, LF097805, V097805, M097805
+export T097805, L097805, V097805, M097805
 # The module SetPartitionsMType contains : P097805, L097805, TL097805,
 
 """
@@ -36,7 +36,7 @@ T097805(n) = RecTriangle(n, R097805)
 
 Lists the first ``n`` rows of A097805 by concatinating. This is the format for submissions to the OEIS.
 """
-LF097805(n) = vcat(T097805(n)...)
+L097805(n) = vcat(T097805(n)...)
 
 """
 
@@ -66,7 +66,7 @@ function demo()
     end
 
     println("\nLists the first 9 rows of L097805 by concatinating.")
-    println(LF097805(9))
+    println(L097805(9))
 
     #ShowAsMatrix(L097805(9))
     #println(M097805(9))
@@ -85,7 +85,7 @@ function demo()
     println("\nBenchmark the construction of the first 500 rows of A097805 based on Iteration.\n")
     #  0.111066 seconds (253.51 k allocations: 7.795 MiB)
     GC.gc()
-    @time LF097805(500)
+    @time L097805(500)
 
     println("\nBenchmark the construction of the first 500 rows of A097805 based on closed formula.")
     # Result: 0.479466 seconds (1.72 M allocations: 21.592 MiB)
@@ -109,7 +109,7 @@ L097805(500) :: 0.111066 seconds (253.51 k allocations: 7.795 MiB)
 """
 function perf()
     GC.gc()
-    @time LF097805(500)
+    @time L097805(500)
 end
 
 function main()

src/GaussFactorials.jl

@@ -98,13 +98,13 @@ V066570(n) = div(GaussFactorial(n, 1), GaussFactorial(n, n))
 
 Iterate over the indices of the first ``n`` record values of the Gauß factorial.
 """
-I193339(n) = Records(GaussFactorial, n, true, true, Dict())
+I193339(n) = Records(GaussFactorial, n, true, true)
 
 """
 
 Iterate over indices of the record values of the Gauß factorial which do not exceed ``n`` (``1 ≤ i ≤ n``).
 """
-F193339(n) = Records(GaussFactorial, n, false, true, Dict())
+F193339(n) = Records(GaussFactorial, n, false, true)
 
 """
 
@@ -125,13 +125,13 @@ V193339(n) = nth(I193339(n+1), n+1)
 
 Iterate over the first ``n`` record values of the Gauß factorial (``1 ≤ r``).
 """
-I193338(n) = Records(GaussFactorial, n, true, false, Dict())
+I193338(n) = Records(GaussFactorial, n, true, false)
 
 """
 
 Iterate over the record values of the Gauß factorial which do not exceed ``n`` (``1 ≤ i ≤ n``).
 """
-F193338(n) = Records(GaussFactorial, n, false, false, Dict())
+F193338(n) = Records(GaussFactorial, n, false, false)
 
 """
 

src/HighlyAbundant.jl

@@ -24,13 +24,13 @@ const ModuleHighlyAbundant = ""
 
 Iterate over the first ``n`` highly abundant numbers.
 """
-I002093(n) = Records(σ, n, true, true, Dict())
+I002093(n) = Records(σ, n, true, true)
 
 """
 
 Iterate over the highly abundant numbers which do not exceed ``n`` (``1 ≤ i ≤ n``).
 """
-F002093(n) = Records(σ, n, false, true, Dict())
+F002093(n) = Records(σ, n, false, true)
 
 """
 
@@ -52,13 +52,13 @@ V002093(n) = nth(I002093(n+1), n+1)
 
 Iterate over the first ``n`` record values of sigma.
 """
-I034885(n) = Records(σ, n, true, false, Dict())
+I034885(n) = Records(σ, n, true, false)
 
 """
 
 Iterate over the record values of sigma the indices of which do not exceed ``n`` (``1 ≤ r ≤ n``).
 """
-F034885(n) = Records(σ, n, false, false, Dict())
+F034885(n) = Records(σ, n, false, false)
 
 """
 

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 2019-11-06 01:35:53
-# 63b05410-002d-11ea-3957-070f416b5206
+# Version of: UTC 2019-11-06 13:47:27
+# 966f98f0-0093-11ea-1a21-434e877baaf5
 
 # 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!
@@ -80,7 +80,6 @@ InvOrthoPoly,
 JacobiTheta3Powers,
 JacobiTheta4Powers,
 KolakoskiList,
-LF097805,
 List,
 ModuleAbundant,
 ModuleAndreNumbers,
@@ -172,6 +171,7 @@ RamanujanTau,
 RamanujanTauList,
 RecTriangle,
 Records,
+RecordsCached,
 ReflectPoly,
 RiordanProduct,
 RiordanSquare,
@@ -243,7 +243,6 @@ oeis_writebfile,
 takeFirst,
 toΔ,
 Ω,
-π,
 σ,
 σ2,
 τ,
@@ -2621,7 +2620,7 @@ T097805(n) = RecTriangle(n, R097805)
 Lists the first ``n`` rows of A097805 by concatinating. This is the format for submissions to the OEIS.
 $(SIGNATURES)
 """
-LF097805(n) = vcat(T097805(n)...)
+L097805(n) = vcat(T097805(n)...)
 """
 
 Return the triangular array as a square matrix.
@@ -4468,13 +4467,13 @@ V066570(n) = div(GaussFactorial(n, 1), GaussFactorial(n, n))
 Iterate over the indices of the first ``n`` record values of the Gauß factorial.
 $(SIGNATURES)
 """
-I193339(n) = Records(GaussFactorial, n, true, true, Dict())
+I193339(n) = Records(GaussFactorial, n, true, true)
 """
 
 Iterate over indices of the record values of the Gauß factorial which do not exceed ``n`` (``1 ≤ i ≤ n``).
 $(SIGNATURES)
 """
-F193339(n) = Records(GaussFactorial, n, false, true, Dict())
+F193339(n) = Records(GaussFactorial, n, false, true)
 """
 
 Return the indices of the first ``n`` record values of the Gauß factorial as an array.
@@ -4492,13 +4491,13 @@ V193339(n) = nth(I193339(n+1), n+1)
 Iterate over the first ``n`` record values of the Gauß factorial (``1 ≤ r``).
 $(SIGNATURES)
 """
-I193338(n) = Records(GaussFactorial, n, true, false, Dict())
+I193338(n) = Records(GaussFactorial, n, true, false)
 """
 
 Iterate over the record values of the Gauß factorial which do not exceed ``n`` (``1 ≤ i ≤ n``).
 $(SIGNATURES)
 """
-F193338(n) = Records(GaussFactorial, n, false, false, Dict())
+F193338(n) = Records(GaussFactorial, n, false, false)
 """
 
 Return the first ``n`` record values of the Gauß factorial as an array.
@@ -4668,13 +4667,13 @@ const ModuleHighlyAbundant = ""
 Iterate over the first ``n`` highly abundant numbers.
 $(SIGNATURES)
 """
-I002093(n) = Records(σ, n, true, true, Dict())
+I002093(n) = Records(σ, n, true, true)
 """
 
 Iterate over the highly abundant numbers which do not exceed ``n`` (``1 ≤ i ≤ n``).
 $(SIGNATURES)
 """
-F002093(n) = Records(σ, n, false, true, Dict())
+F002093(n) = Records(σ, n, false, true)
 """
 
 Return the first ``n`` highly abundant numbers as an array.
@@ -4692,13 +4691,13 @@ V002093(n) = nth(I002093(n+1), n+1)
 Iterate over the first ``n`` record values of sigma.
 $(SIGNATURES)
 """
-I034885(n) = Records(σ, n, true, false, Dict())
+I034885(n) = Records(σ, n, true, false)
 """
 
 Iterate over the record values of sigma the indices of which do not exceed ``n`` (``1 ≤ r ≤ n``).
 $(SIGNATURES)
 """
-F034885(n) = Records(σ, n, false, false, Dict())
+F034885(n) = Records(σ, n, false, false)
 """
 
 Return the first ``n`` record values of sigma as an array.
@@ -7140,7 +7139,7 @@ const ModuleRecordSearch = ""
 The type object to construct an iterated search for records in sequences.
 $(SIGNATURES)
 """
-struct Records
+struct RecordsCached
 "function representing the sequence"
 fun::Function
 "search limit OR search length"
@@ -7152,17 +7151,16 @@ index::Bool
 "the records"
 records
 end
-Base.iterate(::Records) = (ZZ(1), (ZZ(1), ZZ(0), ZZ(1)))
+Base.iterate(::RecordsCached) = (ZZ(1), (ZZ(1), ZZ(0), ZZ(1)))
 """
 
 Return the value or the index of the next record.
 $(SIGNATURES)
 """
-function Base.iterate(R::Records, state)
+function Base.iterate(R::RecordsCached, state)
 h, n, s = state
 if (R.below ? s : n) >= R.lim
-println()
-println(R.records)
+println(); println(R.records)
 return nothing
 end
 while true
@@ -7174,6 +7172,38 @@ end
 n += 1
 end
 end
+Base.length(R::RecordsCached) = R.lim
+Base.eltype(R::RecordsCached) = fmpz
+"""
+
+The type object to construct an iterated search for records in sequences.
+$(SIGNATURES)
+"""
+struct Records
+"function representing the sequence"
+fun::Function
+"search limit OR search length"
+lim::Int
+"true ↦ search all below lim, false ↦ search length items"
+below::Bool
+"true ↦ return index of record, false ↦ return value of record"
+index::Bool
+end
+Base.iterate(::Records) = (ZZ(1), (ZZ(1), ZZ(0), ZZ(1)))
+"""
+
+Return the value or the index of the next record.
+$(SIGNATURES)
+"""
+function Base.iterate(R::Records, state)
+h, n, s = state
+(R.below ? s : n) >= R.lim && return nothing
+while true
+v = R.fun(n)
+v > h && return (R.index ? n : v, (v, n + 1, s + 1))
+n += 1
+end
+end
 Base.length(R::Records) = R.lim
 Base.eltype(R::Records) = fmpz
 # *** RiordanSquares.jl ****************
@@ -7415,6 +7445,11 @@ Alias for is_oeis_installed.
 $(SIGNATURES)
 """
 data_installed() = is_oeis_installed()
+"""
+
+Perform tests for an array of sequences of given type assuming the given offset.
+$(SIGNATURES)
+"""
 function SeqTest(seqarray, kind, offset = 0)
 if kind == 'V'
 return SeqVTest(seqarray, offset)
@@ -7495,6 +7530,11 @@ ShowAsΔ(S)
 end
 end
 end
+"""
+
+Test to generate sequences from a given list of sequences.
+$(SIGNATURES)
+"""
 function GenerateAllTest(A::Array{Function,1})
 err = String[]
 for a ∈ A
@@ -7518,9 +7558,7 @@ elseif startswith(stra, "is")
 elseif startswith(stra, 'I')
 collect(a(6)) |> println
 elseif startswith(stra, 'F')
-w = fmpz[]
-for r ∈ a(20) push!(w, r) end
-println(w)
+collect(IterTools.takewhile(k -> k <= 20, a(21))) |> println
 elseif startswith(stra, 'P')
 for k ∈ 0:4 a(k) |> println end
 elseif startswith(stra, 'R')
@@ -7537,7 +7575,12 @@ else
 [a(2, k) for k ∈ 0:6] |> println
 end
 else
-"??? \n" |> print
+if applicable(a, 1)
+[a(k) for k ∈ 0:6] |> println
+else
+[a(0, k) for k ∈ 0:6] |> println
+[a(2, k) for k ∈ 0:6] |> println
+end
 end
 catch
 "ERROR!" |> println
@@ -7546,7 +7589,8 @@ end
 end
 numerr = length(err)
 if numerr > 0
-@warn(numerr, " errors found:\n", err)
+@warn(numerr, " errors found:")
+for e ∈ err println(e) end
 end
 return numerr
 end
@@ -8123,13 +8167,13 @@ P097805(n) = OrderedSetPolynomials(0, n)
 
 Return the number of ordered set partitions of an ``n``-set which are of shape type ``0``.
 ```julia-repl
-julia> L097805(3)
+julia> TL097805(3)
 4-element Array{Nemo.fmpz,1}:
 [0, 1, 2, 1]
 ```
 $(SIGNATURES)
 """
-L097805(n) = Coeffs(OrderedSetPolynomials(0, n))
+TL097805(n) = Coeffs(OrderedSetPolynomials(0, n))
 """
 
 Return the first ``len`` rows of the triangle of compositions of ``n``.