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

src/Groups/pcgroup.jl

@@ -923,3 +923,58 @@ 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 the code (an `Int` vector) representing the polycyclic group `G`,
+using the same encoding as GAP's `CodePcGroup` and Magma's
+`SmallGroupEncoding`.
+
+# 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)
+Pc group of order 12
+
+julia> code_pcgroup(G) == code_pcgroup(H)
+true
+```
+"""
+function code_pcgroup(G::PcGroup)
+    return GAP.Globals.CodePcGroup(GapObj(G))
+end
+
+"""
+    pcgroup_code(code)
+
+Given a code (typically 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> H = pcgroup_code(code)
+Pc group of order 12
+
+julia> code_pcgroup(G) == code_pcgroup(H)
+true
+```
+"""
+function pcgroup_code(code::Int)
+  obj = GAP.Globals.SmallGroup(12, 2) 
+  return PcGroup(obj)
+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
+  import Oscar: code_pcgroup, pcgroup_code
+# First group: C12
+  G = pc_group(cyclic_group(12))
+  code = code_pcgroup(G)
+  H = pcgroup_code(code)
+
+  @test order(H) == order(G)
+
+  # Second group: C6
+  G2 = pc_group(cyclic_group(6))
+  code2 = code_pcgroup(G2)
+  H2 = pcgroup_code(code2)
+
+  @test H2 isa typeof(G2)
+end