Rename and add tests for the partitions function

As there is already an integer_partitions function in Base which
does basically the same thing, it is better to have this as an
extra method of it.

Author: andrioni

src/Catalan.jl

@@ -2,6 +2,8 @@ module Catalan
 
 using Polynomial
 
+import Base: integer_partitions
+
 export  bell,
         catalan,
         derangement,
@@ -16,8 +18,7 @@ export  bell,
         multinomial,
         primorial,
         stirlings1,
-        subfactorial,
-        partitions
+        subfactorial
 
 include("youngdiagrams.jl")
 
@@ -152,14 +153,18 @@ function stirlings1(n::Integer, k::Integer)
 end
 
 # Lists the partitions of the number n, the order is consistent with GAP
-function partitions(n)
-    if n == 1
+function integer_partitions(n::Integer)
+    if n < 0
+        throw(DomainError())
+    elseif n == 0
+        return Vector{Int}[]
+    elseif n == 1
         return Vector{Int}[[1]]
     end
 
     list = Vector{Int}[]
 
-    for p in partitions(n-1)
+    for p in integer_partitions(n-1)
         push!(list, [p, 1])
         if length(p) == 1 || p[end] < p[end-1]
             push!(list, [p[1:end-1], p[end]+1])
@@ -169,4 +174,4 @@ function partitions(n)
     list
 end
 
-end
+end # module

test/Catalan_test.jl

@@ -45,3 +45,7 @@ using Base.Test
 @test bell(7) == 877
 @test bell(42) == BigInt("35742549198872617291353508656626642567")
 @test_fails bell(-1)
+
+# integer_partitions
+@test integer_partitions(5) == {[1, 1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1], [3, 1, 1], [3, 2], [4, 1], [5]}
+@test_fails integer_partitions(-1)