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

src/Groups/pcgroup.jl

@@ -923,3 +923,57 @@ 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 = 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::IntegerUnion, order::IntegerUnion)
+
+Given an integer `code` and an integer `order`, return the polycyclic group it encodes.
+Both `code` and `order` can be of type `Int`, `BigInt`, or `ZZRingElem`. Internally, these are converted to `GapInt` before calling the GAP function `PcGroupCode`.
+The accepted codes and resulting groups match those of GAP's `PcGroupCode` and Magma's `SmallGroupDecoding`.
+
+# Examples
+```jldoctest
+julia> G = 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 pcgroup_code(code::IntegerUnion, order::IntegerUnion)
+  return PcGroup(GAP.Globals.PcGroupCode(GAP.GapInt(BigInt(code)),GAP.GapInt(BigInt(order))))
+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, order(G))
+      @test hom(G, H, gens(H)) isa Map
+      @test order(G) == order(H)
+      @test code_pcgroup(H) == code
+  end
+end