remove DirectProducts and WreathProducts
These are part of the Groups.jl package
This commit is contained in:
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c6a56fcadb
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@ -1,248 +0,0 @@
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module DirectProducts
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using Nemo
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import Base: show, ==, hash, deepcopy_internal
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import Base: ×, *, inv
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import Nemo: parent, parent_type, elem_type
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import Nemo: elements, order, Group, GroupElem, Ring
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export DirectProductGroup, DirectProductGroupElem
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###############################################################################
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#
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# DirectProductGroup / DirectProductGroupElem
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#
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###############################################################################
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doc"""
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DirectProductGroup(factors::Vector{Group}) <: Group
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Implements direct product of groups as vector factors. The group operation is
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`*` distributed component-wise, with component-wise identity as neutral element.
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"""
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type DirectProductGroup <: Group
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factors::Vector{Group}
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operations::Vector{Function}
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end
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type DirectProductGroupElem <: GroupElem
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elts::Vector{GroupElem}
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parent::DirectProductGroup
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DirectProductGroupElem{T<:GroupElem}(a::Vector{T}) = new(a)
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end
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###############################################################################
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#
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# Type and parent object methods
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#
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###############################################################################
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elem_type(G::DirectProductGroup) = DirectProductGroupElem
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parent_type(::Type{DirectProductGroupElem}) = DirectProductGroup
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parent(g::DirectProductGroupElem) = g.parent
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###############################################################################
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#
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# DirectProductGroup / DirectProductGroupElem constructors
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#
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###############################################################################
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DirectProductGroup(G::Group, H::Group) = DirectProductGroup([G, H], Function[(*),(*)])
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DirectProductGroup(G::Group, H::Ring) = DirectProductGroup([G, H], Function[(*),(+)])
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DirectProductGroup(G::Ring, H::Group) = DirectProductGroup([G, H], Function[(+),(*)])
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DirectProductGroup(G::Ring, H::Ring) = DirectProductGroup([G, H], Function[(+),(+)])
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DirectProductGroup{T<:Ring}(X::Vector{T}) = DirectProductGroup(Group[X...], Function[(+) for _ in X])
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×(G::Group, H::Group) = DirectProductGroup(G,H)
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function DirectProductGroup{T<:Group, S<:Group}(G::Tuple{T, Function}, H::Tuple{S, Function})
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return DirectProductGroup([G[1], H[1]], Function[G[2],H[2]])
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end
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function DirectProductGroup(groups::Vector)
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for G in groups
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typeof(G) <: Group || throw("$G is not a group!")
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end
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ops = Function[typeof(G) <: Ring ? (+) : (*) for G in groups]
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return DirectProductGroup(groups, ops)
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end
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###############################################################################
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#
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# Parent object call overloads
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#
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###############################################################################
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(G::DirectProductGroup)() = G([H() for H in G.factors]; checked=false)
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function (G::DirectProductGroup)(g::DirectProductGroupElem; checked=true)
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if checked
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return G(g.elts)
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else
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g.parent = G
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return g
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end
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end
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doc"""
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(G::DirectProductGroup)(a::Vector; checked=true)
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> Constructs element of the direct product group `G` by coercing each element
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> of vector `a` to the corresponding factor of `G`. If `checked` flag is set to
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> `false` no checks on the correctness are performed.
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"""
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function (G::DirectProductGroup)(a::Vector; checked=true)
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length(a) == length(G.factors) || throw("Cannot coerce $a to $G: they have
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different number of factors")
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if checked
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for (F,g) in zip(G.factors, a)
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try
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F(g)
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catch
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throw("Cannot coerce to $G: $g cannot be coerced to $F.")
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end
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end
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end
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elt = DirectProductGroupElem([F(g) for (F,g) in zip(G.factors, a)])
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elt.parent = G
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return elt
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end
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###############################################################################
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#
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# Basic manipulation
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#
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###############################################################################
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function deepcopy_internal(g::DirectProductGroupElem, dict::ObjectIdDict)
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G = parent(g)
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return G(deepcopy(g.elts))
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end
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function hash(G::DirectProductGroup, h::UInt)
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return hash(G.factors, hash(G.operations, hash(DirectProductGroup,h)))
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end
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function hash(g::DirectProductGroupElem, h::UInt)
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return hash(g.elts, hash(g.parent, hash(DirectProductGroupElem, h)))
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end
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doc"""
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eye(G::DirectProductGroup)
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> Return the identity element for the given direct product of groups.
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"""
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eye(G::DirectProductGroup) = G()
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###############################################################################
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#
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# String I/O
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#
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###############################################################################
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function show(io::IO, G::DirectProductGroup)
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println(io, "Direct product of groups")
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join(io, G.factors, ", ", " and ")
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end
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function show(io::IO, g::DirectProductGroupElem)
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print(io, "("*join(g.elts,",")*")")
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end
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###############################################################################
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#
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# Comparison
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#
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###############################################################################
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function (==)(G::DirectProductGroup, H::DirectProductGroup)
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G.factors == H.factors || return false
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G.operations == H.operations || return false
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return true
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end
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doc"""
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==(g::DirectProductGroupElem, h::DirectProductGroupElem)
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> Return `true` if the given elements of direct products are equal, otherwise return `false`.
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"""
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function (==)(g::DirectProductGroupElem, h::DirectProductGroupElem)
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parent(g) == parent(h) || return false
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g.elts == h.elts || return false
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return true
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end
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###############################################################################
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#
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# Binary operators
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#
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###############################################################################
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function direct_mult(g::DirectProductGroupElem, h::DirectProductGroupElem)
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parent(g) == parent(h) || throw("Can't multiply elements from different groups: $g, $h")
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G = parent(g)
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return G([op(a,b) for (op,a,b) in zip(G.operations, g.elts, h.elts)])
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end
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doc"""
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*(g::DirectProductGroupElem, h::DirectProductGroupElem)
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> Return the direct-product group operation of elements, i.e. component-wise
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> operation as defined by `operations` field of the parent object.
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"""
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(*)(g::DirectProductGroupElem, h::DirectProductGroupElem) = direct_mult(g,h)
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###############################################################################
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#
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# Inversion
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#
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###############################################################################
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doc"""
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inv(g::DirectProductGroupElem)
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> Return the inverse of the given element in the direct product group.
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"""
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# TODO: dirty hack around `+` operation
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function inv(g::DirectProductGroupElem)
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G = parent(g)
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return G([(op == (*) ? inv(elt): -elt) for (op,elt) in zip(G.operations, g.elts)])
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end
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###############################################################################
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#
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# Misc
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#
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###############################################################################
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doc"""
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elements(G::DirectProductGroup)
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> Returns `Task` that produces all elements of group `G` (provided that factors
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> implement the elements function).
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"""
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# TODO: can Base.product handle generators?
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# now it returns nothing's so we have to collect ellements...
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function elements(G::DirectProductGroup)
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cartesian_prod = Base.product([collect(elements(H)) for H in G.factors]...)
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return (G(collect(elt)) for elt in cartesian_prod)
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end
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doc"""
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order(G::DirectProductGroup)
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> Returns the order (number of elements) in the group.
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"""
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order(G::DirectProductGroup) = prod([order(H) for H in G.factors])
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end # of module DirectProduct
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@ -1,236 +0,0 @@
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module WreathProducts
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using Nemo
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using DirectProducts
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import Base: convert, deepcopy_internal, show, isequal, ==, hash, size, inv
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import Base: +, -, *, //
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import Nemo: Group, GroupElem, elem_type, parent_type, parent, elements, order
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###############################################################################
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#
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# WreathProduct / WreathProductElem
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#
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###############################################################################
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doc"""
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WreathProduct <: Group
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> Implements Wreath product of a group N by permutation (sub)group P < Sₖ,
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> usually written as $N \wr P$.
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> The multiplication inside wreath product is defined as
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> (n, σ) * (m, τ) = (n*ψ(σ)(m), σ*τ),
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> where ψ:P → Aut(Nᵏ) is the permutation representation of Sₖ restricted to P.
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# Arguments:
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* `::Group` : the single factor of group N
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* `::PermutationGroup` : full PermutationGroup
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"""
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type WreathProduct <: Group
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N::DirectProductGroup
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P::PermutationGroup
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function WreathProduct(G::Group, P::PermutationGroup)
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N = DirectProductGroup(typeof(G)[G for _ in 1:P.n])
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return new(N, P)
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end
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end
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type WreathProductElem <: GroupElem
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n::DirectProductGroupElem
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p::perm
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parent::WreathProduct
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function WreathProductElem(n::DirectProductGroupElem, p::perm)
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length(n.elts) == parent(p).n
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return new(n, p)
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end
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end
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export WreathProduct, WreathProductElem
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###############################################################################
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#
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# Type and parent object methods
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#
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###############################################################################
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elem_type(::WreathProduct) = WreathProductElem
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parent_type(::WreathProductElem) = WreathProduct
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parent(g::WreathProductElem) = g.parent
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###############################################################################
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#
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# WreathProduct / WreathProductElem constructors
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#
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###############################################################################
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# converts???
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###############################################################################
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#
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# Parent object call overloads
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#
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###############################################################################
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function (G::WreathProduct)(g::WreathProductElem)
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try
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G.N(g.n)
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catch
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throw("Can't coerce $(g.n) to $(G.N) factor of $G")
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end
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try
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G.P(g.p)
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catch
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throw("Can't coerce $(g.p) to $(G.P) factor of $G")
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end
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elt = WreathProductElem(G.N(g.n), G.P(g.p))
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elt.parent = G
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return elt
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end
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doc"""
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(G::WreathProduct)(n::DirectProductGroupElem, p::perm)
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> Creates an element of wreath product `G` by coercing `n` and `p` to `G.N` and
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> `G.P`, respectively.
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"""
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function (G::WreathProduct)(n::DirectProductGroupElem, p::perm)
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result = WreathProductElem(n,p)
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result.parent = G
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return result
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end
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(G::WreathProduct)() = G(G.N(), G.P())
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doc"""
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(G::WreathProduct)(p::perm)
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> Returns the image of permutation `p` in `G` via embedding `p -> (id,p)`.
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"""
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(G::WreathProduct)(p::perm) = G(G.N(), p)
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doc"""
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(G::WreathProduct)(n::DirectProductGroupElem)
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> Returns the image of `n` in `G` via embedding `n -> (n,())`. This is the
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> embedding that makes sequence `1 -> N -> G -> P -> 1` exact.
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"""
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(G::WreathProduct)(n::DirectProductGroupElem) = G(n, G.P())
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###############################################################################
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#
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# Basic manipulation
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#
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###############################################################################
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function deepcopy_internal(g::WreathProductElem, dict::ObjectIdDict)
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G = parent(g)
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return G(deepcopy(g.n), deepcopy(g.p))
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end
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function hash(G::WreathProduct, h::UInt)
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return hash(G.N, hash(G.P, hash(WreathProduct, h)))
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end
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function hash(g::WreathProductElem, h::UInt)
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return hash(g.n, hash(g.p, hash(parent(g), h)))
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end
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###############################################################################
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#
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# String I/O
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#
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###############################################################################
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function show(io::IO, G::WreathProduct)
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print(io, "Wreath Product of $(G.N.factors[1]) and $(G.P)")
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end
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function show(io::IO, g::WreathProductElem)
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# println(io, "Element of WreathProduct over $T of size $(size(X)):")
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# show(io, "text/plain", matrix_repr(X))
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print(io, "($(g.n)≀$(g.p))")
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end
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###############################################################################
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#
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# Comparison
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#
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###############################################################################
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function (==)(G::WreathProduct, H::WreathProduct)
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G.N == H.N || return false
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G.P == H.P || return false
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return true
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end
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function (==)(g::WreathProductElem, h::WreathProductElem)
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parent(g) == parent(h) || return false
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g.n == h.n || return false
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g.p == h.p || return false
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return true
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end
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###############################################################################
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#
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# Binary operators
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#
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###############################################################################
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function wreath_multiplication(g::WreathProductElem, h::WreathProductElem)
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parent(g) == parent(h) || throw("Can not multiply elements from different
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groups!")
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G = parent(g)
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w=G.N((h.n).elts[inv(g.p).d])
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return G(g.n*w, g.p*h.p)
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end
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doc"""
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*(g::WreathProductElem, h::WreathProductElem)
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> Return the wreath product group operation of elements, i.e.
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>
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> g*h = (g.n*g.p(h.n), g.p*h.p),
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>
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> where g.p(h.n) denotes the action of `g.p::perm` on
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> `h.n::DirectProductGroupElem` via standard permutation of coordinates.
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"""
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(*)(g::WreathProductElem, h::WreathProductElem) = wreath_multiplication(g,h)
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###############################################################################
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#
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# Inversion
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#
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###############################################################################
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doc"""
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inv(g::WreathProductElem)
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> Returns the inverse of element of a wreath product, according to the formula
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> g^-1 = (g.n, g.p)^-1 = (g.p^-1(g.n^-1), g.p^-1).
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"""
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function inv(g::WreathProductElem)
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G = parent(g)
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w = G.N(inv(g.n).elts[g.p.d])
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return G(w, inv(g.p))
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end
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###############################################################################
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#
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# Misc
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#
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###############################################################################
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matrix_repr(g::WreathProductElem) = Any[matrix_repr(g.p) g.n]
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function elements(G::WreathProduct)
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iter = Base.product(collect(elements(G.N)), collect(elements(G.P)))
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return (G(n)*G(p) for (n,p) in iter)
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end
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order(G::WreathProduct) = order(G.P)*order(G.N)
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end # of module WreatProduct
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