Add encode and pc_group for encoding finite pc groups into integers and back

src/Groups/pcgroup.jl

@@ -923,3 +923,91 @@ function collector(::Type{T}, G::PcGroup) where T <: IntegerUnion
 end
 
 collector(G::PcGroup) = collector(ZZRingElem, G)
+
+# GAP wrappers for group encoding / decoding
+
+"""
+    code_pcgroup(G::PcGroup)
+
+Return a `ZZRingElem` representing the polycyclic group `G`, using the same
+encoding as GAP's `CodePcGroup` and Magma's `SmallGroupEncoding`.
+Currently only defined for `PcGroup`, not `SubPcGroup`.
+
+# Examples
+```jldoctest
+julia> G = pc_group(small_group(12, 2))
+Pc group of order 12
+
+julia> code = code_pcgroup(G)
+266
+
+julia> H = pcgroup_code(code, order(G))
+Pc group of order 12
+
+julia> code_pcgroup(G) == code_pcgroup(H)
+true
+```
+"""
+function code_pcgroup(G::PcGroup)
+  return ZZ(GAP.Globals.CodePcGroup(GapObj(G))::GapInt)
+end
+
+"""
+    pcgroup_code(code)
+
+Given a code (either a single integer or an integer vector), return the polycyclic group it encodes.
+The accepted codes and resulting groups match those of GAP's PcGroupCode and Magma's SmallGroupDecoding.
+
+# Examples
+```jldoctest
+julia> G = pc_group(small_group(12, 2))
+Pc group of order 12
+
+julia> code = code_pcgroup(G)
+266
+
+julia> H1 = pcgroup_code(code, order(G))
+Pc group of order 12
+
+julia> H2 = pcgroup_code(code, G)
+Pc group of order 12
+
+julia> code_pcgroup(G) == code_pcgroup(H1)
+true
+
+julia> code_pcgroup(G) == code_pcgroup(H2)
+true
+
+julia> vec_code = code_pcgroup(G)  
+266
+
+julia> vec_code = vec(code_pcgroup(G)) 
+1-element Vector{Int64}:
+ 266
+
+julia> H3 = pcgroup_code(vec_code, order(G))
+Pc group of order 12
+
+julia> code_pcgroup(H3) == code_pcgroup(G)
+true
+```
+"""
+# 1. Integer code + size object
+function pcgroup_code(code, size)
+  PcGroup(GAP.Globals.PcGroupCode(Int(code), Int(size)))
+end
+
+# 2. Integer code + PcGroup
+function pcgroup_code(code, G::PcGroup)
+  pcgroup_code(code, order(G))
+end
+
+# 3. Vector of integers code + size object
+function pcgroup_code(code::Vector{<:Integer}, size)
+  PcGroup(GAP.Globals.PcGroupCode(code, Int(size)))
+end
+
+# 4. Vector of integers code + PcGroup
+function pcgroup_code(code::Vector{<:Integer}, G::PcGroup)
+  pcgroup_code(code, order(G))
+end

src/exports.jl

@@ -412,6 +412,7 @@ export cobases
 export cochain_complex
 export cocircuits
 export cocycle_matroid
+export code_pcgroup
 export codim
 export codomain
 export codomain_covering
@@ -1409,6 +1410,7 @@ export partitions
 export patches
 export pbw_algebra
 export pc_group
+export pcgroup_code
 export pcore
 export pentagonal_hexecontahedron
 export pentagonal_icositetrahedron

test/Groups/pcgroup.jl

@@ -150,3 +150,20 @@ end
     @test is_bijective(f)
   end
 end
+
+@testset "pcgroup code and reconstruction" begin
+  groups = [
+      cyclic_group(6),
+      cyclic_group(12),
+      dihedral_group(10),
+      small_group(PcGroup, 12, 2)
+  ]
+
+  for G in groups
+      code = code_pcgroup(G)  
+      H = pcgroup_code(code, G)  
+      @test hom(G, H, gens(H)) isa Map
+      @test order(G) == order(H)
+      @test code_pcgroup(H) == code
+  end
+end