Abstract Groups Type about furiousgenius

[aidevnn]

In other terms, the neutral must be a essential part of the definition and it must takes more attention.

FuriousGenius/src/Sn.jl

Lines 33 to 44 in e60d4cc

	struct Perm <: Elt
	baseGroup::Sn
	p::Vector{Int}
	eHash::UInt
	function Perm(sn::Sn, p::Vector{Int})
	new(sn, p, hash(p, sn.gHash))
	end
	function Perm(sn::Sn, cycles::Vector{Vector{Int}})
	p = CyclesToPermutation(sn.N, cycles)
	return Perm(sn, p)
	end
	end

FuriousGenius/src/Zn.jl

Lines 21 to 36 in e60d4cc

	struct ZnInt <: Elt
	baseGroup::Zn
	k::Int
	eHash::UInt
	function ZnInt(zn::Zn, k::Int)
	k0 = k % zn.mod
	if k0 < 0
	k0 += zn.mod
	end
	return new(zn, k0, hash(k0, zn.gHash))
	end
	function ZnInt(k::Int, mod::Int)
	zn = Zn(mod)
	return ZnInt(zn, k)
	end
	end

[aidevnn]

CGroup type is for DirectProduct, QuotientGroup and SemiDirectProduct. It is about to providing an inheritence operation from a superGroup to subGroups or to providing more operations like morphisms or group action over elements.

For example, QuotientGroup needs to apply a morphism over elements through a mapping and a Dictionary, and SemiDirectProduct needs to apply an action. They all deal with ConcreteGroup and now, it is well defined by taking more attention over Neutral inside the constructor.

The ambiguous issue about abstract types is solved.