Fix some combinatorics (#3860)

* Make sure the combinatorics functions work for every integer type

* Fix `is_standard` for negative values

* Fix documentation of Schur polynomials

* Fix `schur_polynomial`

* Change one-line/terse printing of tableaux

docs/src/Combinatorics/EnumerativeCombinatorics/schur_polynomials.md

@@ -1,6 +1,6 @@
 # Schur polynomials
 
-Given a partition $\lambda$ of $n$, the **Schur polynomial** is defined to be
+Given a partition $\lambda$ with $n$ parts, the **Schur polynomial** is defined to be
 the polynomial
 
 $$s_\lambda := \sum x_1^{m_1}\dots x_n^{m_n}$$

src/Combinatorics/EnumerativeCombinatorics/partitions.jl

@@ -227,10 +227,9 @@ function Base.iterate(P::Partitions{T}) where T
     return partition(T[1], check=false), (T[1], 1, 0)
   end
 
-  d = fill( T(1), n )
+  d = fill(T(1), Int(n))
   d[1] = n
   return partition(d[1:1], check=false), (d, 1, 1)
-
 end
 
 @inline function Base.iterate(P::Partitions{T}, state::Tuple{Vector{T}, Int, Int}) where T
@@ -381,7 +380,7 @@ function Base.iterate(P::PartitionsFixedNumParts{T}) where T
   only_distinct_parts = P.distinct_parts
 
   if n == 0 && k == 0
-    return partition(T[], check=false), (T[], T[], 0, 0, 1, false)
+    return partition(T[], check=false), (T[], T[], T(0), T(0), 1, false)
   end
 
   # This iterator should be empty
@@ -391,17 +390,17 @@ function Base.iterate(P::PartitionsFixedNumParts{T}) where T
 
   if n == k && lb == 1
     only_distinct_parts && k > 1 && return nothing
-    return partition(T[1 for i in 1:n], check=false), (T[], T[], 0, 0, 1, false)
+    return partition(T[1 for i in 1:n], check=false), (T[], T[], T(0), T(0), 1, false)
   end
 
   if k == 1 && lb <= n <= ub
-    return partition(T[n], check=false), (T[], T[], 0, 0, 1, false)
+    return partition(T[n], check=false), (T[], T[], T(0), T(0), 1, false)
   end
 
   x = zeros(T,k)
   y = zeros(T,k)
   jj = only_distinct_parts*k*(k-1)
-  N = n - k*lb - div(jj,2)
+  N = T(n - k*lb - div(jj,2))
   L2 = ub-lb
   0 <= N <= k*L2 - jj || return nothing
 
@@ -410,7 +409,7 @@ function Base.iterate(P::PartitionsFixedNumParts{T}) where T
   end
 
   i = 1
-  L2 = L2 - only_distinct_parts*(k-1)
+  L2 = L2 - only_distinct_parts*T(k-1)
 
   while N > L2
     N -= L2
@@ -421,15 +420,15 @@ function Base.iterate(P::PartitionsFixedNumParts{T}) where T
   return partition(x[1:k], check = false), (x, y, N, L2, i, true)
 end
 
-@inline function Base.iterate(P::PartitionsFixedNumParts{T}, state::Tuple{Vector{T}, Vector{T}, T, IntegerUnion, Int, Bool}) where T
+@inline function Base.iterate(P::PartitionsFixedNumParts{T}, state::Tuple{Vector{T}, Vector{T}, T, T, Int, Bool}) where T
   k = P.k
   x, y, N, L2, i, flag = state
 
   N == 0 && return nothing
 
   if flag
     if i < k && N > 1
-      N = 1
+      N = T(1)
       x[i] = x[i] - 1
       i += 1
       x[i] = y[i] + 1
@@ -442,12 +441,11 @@ end
       flag = false
     end
   end
-
   if !flag
     lcycle = false
     for j in i - 1:-1:1
-      L2 = x[j] - y[j] - 1
-      N = N + 1
+      L2 = x[j] - y[j] - T(1)
+      N = N + T(1)
       if N <= (k-j)*L2
         x[j] = y[j] + L2
         lcycle = true
@@ -457,7 +455,6 @@ end
       x[i] = y[i]
       i = j
     end
-
     lcycle || return nothing
     while N > L2
       N -= L2
@@ -769,7 +766,7 @@ end
       x[i] = m
       i -= 1
       i == 0 && break # inner while loop
-      r = ii[i]
+      r = Int(ii[i])
       N = N + x[i] - m
       m = y[i]
     end

src/Combinatorics/EnumerativeCombinatorics/schur_polynomials.jl

@@ -120,7 +120,7 @@ function schur_polynomial_cbf(R::ZZMPolyRing, lambda::Partition{T}, n::Int = len
   end
 
   #calculate sub_dets[2:n] using Laplace extension
-  exp = zeros(Int, n)
+  exp = zeros(Int, ngens(R))
   for i = 2:n
     for (columnview, ) in sub_dets[i]
       d = R() #the alternating sum of minors
@@ -134,8 +134,11 @@ function schur_polynomial_cbf(R::ZZMPolyRing, lambda::Partition{T}, n::Int = len
 
       #multiply by the factorized term
       factor = MPolyBuildCtx(R)
-      exp = zeros(Int, n)
-      exp[columnview] .= exp_incr[i]
+      exp = zeros(Int, ngens(R))
+      for j in 1:n
+        columnview[j] || continue
+        exp[j] = exp_incr[i]
+      end
       push_term!(factor, one(ZZ), exp)
       sub_dets[i][columnview] = mul!(d, d, finish(factor))
     end

src/Combinatorics/EnumerativeCombinatorics/tableaux.jl

@@ -58,8 +58,7 @@ young_tableau(v::Vector{Vector{T}}; check::Bool = true) where T <: IntegerUnion
 data(tab::YoungTableau) = tab.t
 
 function Base.show(io::IO, tab::YoungTableau)
-  print(io, "Young tableau")
-  # TODO: is there meaningful information to add in one-line mode?
+  print(io, data(tab))
 end
 
 function Base.show(io::IO, ::MIME"text/plain", tab::YoungTableau)
@@ -591,7 +590,7 @@ function is_standard(tab::YoungTableau)
   numbs = falses(n)
   for i = 1:length(s)
     for j = 1:s[i]
-      if tab[i][j] > n
+      if tab[i][j] < 1 || tab[i][j] > n
         return false
       end
       numbs[tab[i][j]] = true

src/Combinatorics/EnumerativeCombinatorics/types.jl

@@ -78,10 +78,10 @@ struct CompositionsFixedNumParts{T<:IntegerUnion}
     if k > n
       # 1 does not have any weak compositions into 0 parts, so this will
       # produce an empty iterator
-      nk = 1
+      nk = T(1)
       kk = 0
     else
-      nk = n - k
+      nk = n - T(k)
       kk = k
     end
     return new{T}(n, k, weak_compositions(nk, kk))
@@ -165,7 +165,7 @@ struct PartitionsFixedNumParts{T<:IntegerUnion}
     if lb == 0
       lb = 1
     end
-    return new{T}(n, convert(T, k), T(lb), T(ub), only_distinct_parts)
+    return new{T}(n, Int(k), T(lb), T(ub), only_distinct_parts)
   end
 
 end

test/Combinatorics/EnumerativeCombinatorics/compositions.jl

@@ -1,24 +1,25 @@
-@testset "compositions" begin
+@testset "Compositions with integer type $T" for T in [Int, Int8, ZZRingElem]
   # Check some stupid cases
-  @test number_of_compositions(0, 0) == 1
-  @test number_of_compositions(0, 1) == 0
-  @test number_of_compositions(1, 0) == 0
-  @test number_of_compositions(0) == 1
+  @test number_of_compositions(T(0), T(0)) == 1
+  @test number_of_compositions(T(0), T(1)) == 0
+  @test number_of_compositions(T(1), T(0)) == 0
+  @test number_of_compositions(T(0)) == 1
 
   # First few number of compositions from https://oeis.org/A011782
   nums = [1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648, 4294967296, 8589934592]
 
   # Check if number_of_compositions is correct in these examples
-  @test [number_of_compositions(n) for n in 0:length(nums) - 1] == nums
+  @test [number_of_compositions(T(n)) for n in 0:length(nums) - 1] == nums
 
   # Complete check of compositions for small cases
   for n in 0:5
     # We'll piece together all compositions of n by the compositions
     # of n into k parts for 0 <= k <= n
     allcomps = []
     for k in 0:n
-      C = collect(compositions(n, k))
-      @test length(C) == number_of_compositions(n, k)
+      C = @inferred collect(compositions(T(n), T(k)))
+      @test C isa Vector{Oscar.Composition{T}}
+      @test length(C) == number_of_compositions(T(n), T(k))
 
       # Check if each composition consists of k parts and sums up to n
       for c in C
@@ -37,19 +38,25 @@
     @test allcomps == unique(allcomps)
 
     # Number of compositions needs to be correct
-    @test length(allcomps) == number_of_compositions(n)
+    @test length(allcomps) == number_of_compositions(T(n))
 
     # Finally, check compositions(n) function
-    allcomps2 = collect(compositions(n))
+    allcomps2 = @inferred collect(compositions(T(n)))
+    @test allcomps2 isa Vector{Oscar.Composition{T}}
     @test allcomps2 == unique(allcomps2)
     @test Set(allcomps) == Set(allcomps2)
   end
+
+  # Test the case k > n
+  C = @inferred collect(compositions(T(2), T(3)))
+  @test C isa Vector{Oscar.Composition{T}}
+  @test isempty(C)
 end
 
-@testset "Ascending compositions" begin
+@testset "Ascending compositions with integer type $T" for T in [Int, Int8, ZZRingElem]
   for n in 0:20
-    C = collect(ascending_compositions(n))
-    @test length(C) == number_of_partitions(n)
+    C = @inferred collect(ascending_compositions(T(n)))
+    @test length(C) == number_of_partitions(T(n))
     @test C == unique(C)
     for lambda in C
       @test sum(lambda) == n