Merge branch 'master' into enh/julia-v0.6
This commit is contained in:
commit
822067b04c
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@ -1,7 +1,7 @@
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module GroupRings
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using Nemo
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import Nemo: Group, GroupElem, Ring, RingElem, parent, elem_type, parent_type
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import Nemo: Group, GroupElem, Ring, RingElem, parent, elem_type, parent_type, mul!, addeq!, divexact
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import Base: convert, show, hash, ==, +, -, *, //, /, length, norm, rationalize, deepcopy_internal, getindex, setindex!, eltype, one, zero
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@ -17,24 +17,31 @@ type GroupRing{Gr<:Group, T<:GroupElem} <: Ring
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basis_dict::Dict{T, Int}
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pm::Array{Int,2}
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function GroupRing{Gr, T}(G::Gr; initialise=true) where {Gr <: Group, T<:GroupElem}
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A = new(G)
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if initialise
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complete(A)
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end
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return A
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function GroupRing(G::Group, basis::Vector{T}; fastm::Bool=false)
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RG = new(G, basis, reverse_dict(basis))
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fastm && fastm!(RG)
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return RG
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end
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function GroupRing{Gr, T}(G::Gr, b::Vector{T}, b_d::Dict{T, Int}, pm::Array{Int,2}) where {Gr <: Group, T<:GroupElem}
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return new(G, b, b_d, pm)
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end
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function GroupRing(G::Gr, pm::Array{Int,2})
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RG = new(G)
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RG.pm = pm
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return RG
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end
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end
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GroupRing(G::Gr;initialise=true) where Gr <:Group = GroupRing{Gr, elem_type(G)}(G, initialise=initialise)
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GroupRing{Gr<:Group, T<:GroupElem}(G::Gr, basis::Vector{T}; fastm::Bool=true) =
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GroupRing{Gr, T}(G, basis, fastm=fastm)
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GroupRing(G::Gr, b::Vector{T}, b_d::Dict{T,Int}, pm::Array{Int,2}) where {Gr<:Group, T<:GroupElem} = GroupRing{Gr, T}(G, b, b_d, pm)
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GroupRing{Gr<:Group}(G::Gr, pm::Array{Int,2}) =
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GroupRing{Gr, elem_type(G)}(G, pm)
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type GroupRingElem{T<:Number} <: RingElem
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coeffs::AbstractVector{T}
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parent::GroupRing
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@ -53,7 +60,7 @@ type GroupRingElem{T<:Number} <: RingElem
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end
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end
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export GroupRing, GroupRingElem, complete, create_pm
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export GroupRing, GroupRingElem, complete!, create_pm, star
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###############################################################################
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#
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@ -61,12 +68,19 @@ export GroupRing, GroupRingElem, complete, create_pm
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#
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###############################################################################
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elem_type(::GroupRing) = GroupRingElem
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elem_type{T,S}(::Type{GroupRing{T,S}}) = GroupRingElem
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parent_type(::GroupRingElem) = GroupRing
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parent_type(::Type{GroupRingElem}) = GroupRing
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parent{T}(g::GroupRingElem{T}) = g.parent
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eltype(X::GroupRingElem) = eltype(X.coeffs)
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parent(g::GroupRingElem) = g.parent
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Base.promote_rule{T<:Number,S<:Number}(::Type{GroupRingElem{T}}, ::Type{GroupRingElem{S}}) = GroupRingElem{promote_type(T,S)}
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function convert{T<:Number}(::Type{T}, X::GroupRingElem)
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return GroupRingElem(convert(AbstractVector{T}, X.coeffs), parent(X))
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end
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###############################################################################
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#
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@ -78,34 +92,14 @@ function GroupRingElem{T<:Number}(c::AbstractVector{T}, RG::GroupRing)
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return GroupRingElem{T}(c, RG)
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end
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function convert{T<:Number}(::Type{T}, X::GroupRingElem)
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return GroupRingElem(convert(AbstractVector{T}, X.coeffs), parent(X))
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end
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function GroupRing(G::Group, pm::Array{Int,2})
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size(pm,1) == size(pm,2) || throw("pm must be square, got $(size(pm))")
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RG = GroupRing(G, initialise=false)
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RG.pm = pm
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return RG
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end
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function GroupRing(G::Group, basis::Vector)
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basis_dict = reverse_dict(basis)
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pm = try
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create_pm(basis, basis_dict)
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catch err
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isa(err, KeyError) && throw("Products are not supported on basis")
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throw(err)
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end
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return GroupRing(G, basis, basis_dict, pm)
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function GroupRing(G::Group; fastm::Bool=false)
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return GroupRing(G, [elements(G)...], fastm=fastm)
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end
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function GroupRing(G::Group, basis::Vector, pm::Array{Int,2})
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size(pm,1) == size(pm,2) || throw("pm must be of size (n,n), got
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$(size(pm))")
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eltype(basis) == elem_type(G) || throw("basis must consist of elements of $G")
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basis_dict = reverse_dict(basis)
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return GroupRing(G, basis, basis_dict, pm)
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size(pm,1) == size(pm,2) || throw("pm must be square, got $(size(pm))")
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eltype(basis) == elem_type(G) || throw("Basis must consist of elements of $G")
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return GroupRing(G, basis, reverse_dict(basis), pm)
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end
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###############################################################################
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@ -114,45 +108,71 @@ end
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#
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###############################################################################
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zero(RG::GroupRing, T::Type=Int) = RG(T)
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one(RG::GroupRing, T::Type=Int) = RG(RG.group(), T)
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one{R<:Nemo.Ring, S<:Nemo.RingElem}(RG::GroupRing{R,S}) = RG(eye(RG.group()))
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function (RG::GroupRing)(i::Int, T::Type=Int)
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elt = RG(T)
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elt[RG.group()] = i
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return elt
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end
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function (RG::GroupRing{R,S}){R<:Ring, S}(i::Int, T::Type=Int)
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elt = RG(T)
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elt[eye(RG.group())] = i
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return elt
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end
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function (RG::GroupRing)(T::Type=Int)
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isdefined(RG, :basis) || throw("Complete the definition of GroupRing first")
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isdefined(RG, :basis) || throw("Can not coerce without basis of GroupRing")
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return GroupRingElem(spzeros(T,length(RG.basis)), RG)
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end
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function (RG::GroupRing)(g::GroupElem, T::Type=Int)
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g = try
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RG.group(g)
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catch
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throw("Can't coerce $g to the underlying group of $RG")
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end
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g = RG.group(g)
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result = RG(T)
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result[g] = one(T)
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return result
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end
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function (RG::GroupRing)(x::AbstractVector)
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function (RG::GroupRing){T<:Number}(x::AbstractVector{T})
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isdefined(RG, :basis) || throw("Can not coerce without basis of GroupRing")
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length(x) == length(RG.basis) || throw("Can not coerce to $RG: lengths differ")
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result = RG(eltype(x))
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result.coeffs = x
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return result
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end
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function (RG::GroupRing{Gr,T}){Gr<:Nemo.Group, T<:Nemo.GroupElem}(V::Vector{T},
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S::Type=Rational{Int}; alt=false)
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res = RG(S)
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for g in V
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c = (alt ? sign(g)*one(S) : one(S))
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res[g] += c/length(V)
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end
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return res
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end
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function (RG::GroupRing)(X::GroupRingElem)
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RG == parent(X) || throw("Can not coerce!")
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return RG(X.coeffs)
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end
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function (RG::GroupRing)(X::GroupRingElem, emb::Function)
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result = RG(eltype(X.coeffs))
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for g in parent(X).basis
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result[emb(g)] = X[g]
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end
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return result
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isdefined(RG, :basis) || throw("Can not coerce without basis of GroupRing")
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result = RG(eltype(X.coeffs))
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T = typeof(X.coeffs)
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result.coeffs = T(result.coeffs)
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for g in parent(X).basis
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result[emb(g)] = X[g]
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end
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return result
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end
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###############################################################################
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#
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# Basic manipulation
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# Basic manipulation && Array protocol
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#
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###############################################################################
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@ -161,7 +181,7 @@ function deepcopy_internal(X::GroupRingElem, dict::ObjectIdDict)
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end
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function hash(X::GroupRingElem, h::UInt)
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return hash(X.coeffs, hash(parent(X), h))
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return hash(full(X.coeffs), hash(parent(X), hash(GroupRingElem, h)))
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end
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function getindex(X::GroupRingElem, n::Int)
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@ -181,15 +201,12 @@ function setindex!(X::GroupRingElem, value, g::GroupElem)
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typeof(g) == elem_type(RG.group) || throw("$g is not an element of $(RG.group)")
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if !(g in keys(RG.basis_dict))
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g = (RG.group)(g)
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else
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X.coeffs[RG.basis_dict[g]] = value
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end
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X.coeffs[RG.basis_dict[g]] = value
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end
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eltype(X::GroupRingElem) = eltype(X.coeffs)
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one(RG::GroupRing) = RG(RG.group())
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zero(RG::GroupRing) = RG()
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Base.size(X::GroupRingElem) = size(X.coeffs)
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Base.linearindexing{T<:GroupRingElem}(::Type{T}) = Base.LinearFast()
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###############################################################################
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#
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@ -198,7 +215,7 @@ zero(RG::GroupRing) = RG()
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###############################################################################
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function show(io::IO, A::GroupRing)
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print(io, "Group Ring of [$(A.group)]")
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print(io, "Group Ring of $(A.group)")
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end
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function show(io::IO, X::GroupRingElem)
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@ -209,10 +226,14 @@ function show(io::IO, X::GroupRingElem)
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elseif isdefined(RG, :basis)
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non_zeros = ((X.coeffs[i], RG.basis[i]) for i in findn(X.coeffs))
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elts = ("$(sign(c)> 0? " + ": " - ")$(abs(c))*$g" for (c,g) in non_zeros)
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join(io, elts, "")
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str = join(elts, "")[2:end]
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if sign(first(non_zeros)[1]) > 0
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str = str[3:end]
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end
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print(io, str)
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else
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warn("Basis of the parent Group is not defined, showing coeffs")
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print(io, X.coeffs)
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show(io, MIME("text/plain"), X.coeffs)
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end
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end
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@ -237,8 +258,8 @@ function (==)(A::GroupRing, B::GroupRing)
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A.basis == B.basis || return false
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else
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warn("Bases of GroupRings are not defined, comparing products mats.")
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A.pm == B.pm || return false
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end
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A.pm == B.pm || return false
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return true
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end
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@ -250,6 +271,11 @@ end
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(-)(X::GroupRingElem) = GroupRingElem(-X.coeffs, parent(X))
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function mul!{T<:Number}(a::T, X::GroupRingElem{T})
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X.coeffs .*= a
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return X
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end
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mul{T<:Number}(a::T, X::GroupRingElem{T}) = GroupRingElem(a*X.coeffs, parent(X))
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function mul{T<:Number, S<:Number}(a::T, X::GroupRingElem{S})
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@ -282,16 +308,23 @@ end
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#
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###############################################################################
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function add{T<:Number}(X::GroupRingElem{T}, Y::GroupRingElem{T})
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parent(X) == parent(Y) || throw(ArgumentError(
|
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"Elements don't seem to belong to the same Group Ring!"))
|
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function addeq!{T}(X::GroupRingElem{T}, Y::GroupRingElem{T})
|
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X.coeffs .+= Y.coeffs
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return X
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end
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function add{T<:Number}(X::GroupRingElem{T}, Y::GroupRingElem{T}, check::Bool=true)
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if check
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parent(X) == parent(Y) || throw("Elements don't seem to belong to the same Group Ring!")
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end
|
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return GroupRingElem(X.coeffs+Y.coeffs, parent(X))
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end
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|
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function add{T<:Number, S<:Number}(X::GroupRingElem{T},
|
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Y::GroupRingElem{S})
|
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parent(X) == parent(Y) || throw(ArgumentError(
|
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"Elements don't seem to belong to the same Group Ring!"))
|
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Y::GroupRingElem{S}, check::Bool=true)
|
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if check
|
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parent(X) == parent(Y) || throw("Elements don't seem to belong to the same Group Ring!")
|
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end
|
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warn("Adding elements with different base rings!")
|
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return GroupRingElem(+(promote(X.coeffs, Y.coeffs)...), parent(X))
|
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end
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|
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@ -299,51 +332,143 @@ end
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(+)(X::GroupRingElem, Y::GroupRingElem) = add(X,Y)
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(-)(X::GroupRingElem, Y::GroupRingElem) = add(X,-Y)
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|
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function mul!{T<:Number}(X::AbstractVector{T}, Y::AbstractVector{T},
|
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pm::Array{Int,2}, result::AbstractVector{T})
|
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for (j,y) in enumerate(Y)
|
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if y != zero(eltype(Y))
|
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for (i, index) in enumerate(pm[:,j])
|
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if X[i] != zero(eltype(X))
|
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index == 0 && throw(ArgumentError("The product don't seem to belong to the span of basis!"))
|
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result[index] += X[i]*y
|
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doc"""
|
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mul!{T}(result::AbstractArray{T},
|
||||
X::AbstractVector,
|
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Y::AbstractVector,
|
||||
pm::Array{Int,2})
|
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> The most specialised multiplication for `X` and `Y` (`coeffs` of
|
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> `GroupRingElems`) using multiplication table `pm`.
|
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> Notes:
|
||||
> * this method will silently produce false results if `X[k]` is non-zero for
|
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> `k > size(pm,1)`.
|
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> * This method will fail if any zeros (i.e. uninitialised entries) are present
|
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> in `pm`.
|
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> * Use with extreme care!
|
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"""
|
||||
function mul!{T}(result::AbstractVector{T},
|
||||
X::AbstractVector,
|
||||
Y::AbstractVector,
|
||||
pm::Array{Int,2})
|
||||
z = zero(T)
|
||||
result .= z
|
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lY = length(Y)
|
||||
s = size(pm,1)
|
||||
|
||||
@inbounds for j in 1:lY
|
||||
if Y[j] != z
|
||||
for i in 1:s
|
||||
if X[i] != z
|
||||
pm[i,j] == 0 && throw(ArgumentError("The product don't seem to be supported on basis!"))
|
||||
result[pm[i,j]] += X[i]*Y[j]
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
function mul{T<:Number}(X::AbstractVector{T}, Y::AbstractVector{T},
|
||||
pm::Array{Int,2})
|
||||
result = zeros(X)
|
||||
mul!(X,Y,pm,result)
|
||||
return result
|
||||
end
|
||||
|
||||
function mul(X::AbstractVector, Y::AbstractVector, pm::Array{Int,2})
|
||||
T = promote_type(eltype(X), eltype(Y))
|
||||
result = zeros(T, deepcopy(X))
|
||||
mul!(X, Y, pm, result)
|
||||
doc"""
|
||||
mul!{T}(result::GroupRingElem{T},
|
||||
X::GroupRingElem,
|
||||
Y::GroupRingElem)
|
||||
> In-place multiplication for `GroupRingElem`s `X` and `Y`.
|
||||
> `mul!` will make use the initialised entries of `pm` attribute of
|
||||
> `parent(X)::GroupRing` (if available), and will compute and store in `pm` the
|
||||
> remaining products.
|
||||
> The method will fail with `KeyError` if product `X*Y` is not supported on
|
||||
> `parent(X).basis`.
|
||||
"""
|
||||
function mul!{T}(result::GroupRingElem{T}, X::GroupRingElem, Y::GroupRingElem)
|
||||
if result === X
|
||||
result = deepcopy(result)
|
||||
end
|
||||
|
||||
z = zero(T)
|
||||
result.coeffs .= z
|
||||
|
||||
RG = parent(X)
|
||||
|
||||
lX = length(X.coeffs)
|
||||
lY = length(Y.coeffs)
|
||||
|
||||
if isdefined(RG, :pm)
|
||||
s = size(RG.pm)
|
||||
findlast(X.coeffs) <= s[1] || throw("Element in X outside of support of RG.pm")
|
||||
findlast(Y.coeffs) <= s[2] || throw("Element in Y outside of support of RG.pm")
|
||||
|
||||
for j in 1:lY
|
||||
if Y.coeffs[j] != z
|
||||
for i in 1:lX
|
||||
if X.coeffs[i] != z
|
||||
if RG.pm[i,j] == 0
|
||||
RG.pm[i,j] = RG.basis_dict[RG.basis[i]*RG.basis[j]]
|
||||
end
|
||||
result.coeffs[RG.pm[i,j]] += X[i]*Y[j]
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
else
|
||||
for j::Int in 1:lY
|
||||
if Y.coeffs[j] != z
|
||||
for i::Int in 1:lX
|
||||
if X.coeffs[i] != z
|
||||
result[RG.basis[i]*RG.basis[j]] += X[i]*Y[j]
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
return result
|
||||
end
|
||||
|
||||
function *{T<:Number}(X::GroupRingElem{T}, Y::GroupRingElem{T})
|
||||
parent(X) == parent(Y) || throw(ArgumentError(
|
||||
"Elements don't seem to belong to the same Group Ring!"))
|
||||
RG = parent(X)
|
||||
isdefined(RG, :pm) || complete(RG)
|
||||
result = mul(X.coeffs, Y.coeffs, RG.pm)
|
||||
return GroupRingElem(result, RG)
|
||||
function *{T<:Number}(X::GroupRingElem{T}, Y::GroupRingElem{T}, check::Bool=true)
|
||||
if check
|
||||
parent(X) == parent(Y) || throw("Elements don't seem to belong to the same Group Ring!")
|
||||
end
|
||||
if isdefined(parent(X), :basis)
|
||||
result = parent(X)(similar(X.coeffs))
|
||||
result = mul!(result, X, Y)
|
||||
else
|
||||
result = mul!(similar(X.coeffs), X.coeffs, Y.coeffs, parent(X).pm)
|
||||
result = GroupRingElem(result, parent(X))
|
||||
end
|
||||
return result
|
||||
end
|
||||
|
||||
function *{T<:Number, S<:Number}(X::GroupRingElem{T}, Y::GroupRingElem{S})
|
||||
parent(X) == parent(Y) || throw("Elements don't seem to belong to the same
|
||||
Group Ring!")
|
||||
warn("Multiplying elements with different base rings!")
|
||||
RG = parent(X)
|
||||
isdefined(RG, :pm) || complete(RG)
|
||||
result = mul(X.coeffs, Y.coeffs, RG.pm)
|
||||
return GroupRingElem(result, RG)
|
||||
function *{T<:Number, S<:Number}(X::GroupRingElem{T}, Y::GroupRingElem{S}, check::Bool=true)
|
||||
if true
|
||||
parent(X) == parent(Y) || throw("Elements don't seem to belong to the same Group Ring!")
|
||||
end
|
||||
|
||||
TT = typeof(first(X.coeffs)*first(Y.coeffs))
|
||||
warn("Multiplying elements with different base rings! Promoting the result to $TT.")
|
||||
|
||||
if isdefined(parent(X), :basis)
|
||||
result = parent(X)(similar(X.coeffs))
|
||||
result = convert(TT, result)
|
||||
result = mul!(result, X, Y)
|
||||
else
|
||||
result = convert(TT, similar(X.coeffs))
|
||||
result = mul!(result, X.coeffs, Y.coeffs, parent(X).pm)
|
||||
result = GroupRingElem(result, parent(X))
|
||||
end
|
||||
return result
|
||||
end
|
||||
|
||||
|
||||
|
||||
function divexact{T}(X::GroupRingElem{T}, Y::GroupRingElem{T})
|
||||
if length(Y) != 1
|
||||
throw("Can not divide by a non-primitive element: $(Y)!")
|
||||
else
|
||||
idx = findfirst(Y)
|
||||
c = Y[idx]
|
||||
c != 0 || throw("Can not invert: $c not found in $Y")
|
||||
g = parent(Y).basis[idx]
|
||||
return X*1//c*parent(Y)(inv(g))
|
||||
end
|
||||
end
|
||||
|
||||
###############################################################################
|
||||
|
|
@ -354,7 +479,7 @@ end
|
|||
|
||||
function star{T}(X::GroupRingElem{T})
|
||||
RG = parent(X)
|
||||
isdefined(RG, :basis) || complete(RG)
|
||||
isdefined(RG, :basis) || throw("*-involution without basis is not possible")
|
||||
result = RG(T)
|
||||
for (i,c) in enumerate(X.coeffs)
|
||||
if c != zero(T)
|
||||
|
|
@ -393,16 +518,15 @@ function reverse_dict(iter)
|
|||
end
|
||||
|
||||
function create_pm{T<:GroupElem}(basis::Vector{T}, basis_dict::Dict{T, Int},
|
||||
limit=length(basis); twisted=false)
|
||||
limit::Int=length(basis); twisted::Bool=false)
|
||||
product_matrix = zeros(Int, (limit,limit))
|
||||
for i in 1:limit
|
||||
Threads.@threads for i in 1:limit
|
||||
x = basis[i]
|
||||
if twisted
|
||||
x = inv(x)
|
||||
end
|
||||
for j in 1:limit
|
||||
w = x*(basis[j])
|
||||
product_matrix[i,j] = basis_dict[w]
|
||||
product_matrix[i,j] = basis_dict[x*(basis[j])]
|
||||
end
|
||||
end
|
||||
return product_matrix
|
||||
|
|
@ -410,22 +534,34 @@ end
|
|||
|
||||
create_pm{T<:GroupElem}(b::Vector{T}) = create_pm(b, reverse_dict(b))
|
||||
|
||||
function complete(A::GroupRing)
|
||||
if !isdefined(A, :basis)
|
||||
A.basis = [elements(A.group)...]
|
||||
function complete!(RG::GroupRing)
|
||||
if !isdefined(RG, :basis)
|
||||
RG.basis = [elements(RG.group)...]
|
||||
end
|
||||
if !isdefined(A, :basis_dict)
|
||||
A.basis_dict = reverse_dict(A.basis)
|
||||
|
||||
fastm!(RG, fill=true)
|
||||
|
||||
for linidx in find(RG.pm .== 0)
|
||||
i,j = ind2sub(size(RG.pm), linidx)
|
||||
RG.pm[i,j] = RG.basis_dict[RG.basis[i]*RG.basis[j]]
|
||||
end
|
||||
if !isdefined(A, :pm)
|
||||
A.pm = try
|
||||
create_pm(A.basis, A.basis_dict)
|
||||
return RG
|
||||
end
|
||||
|
||||
function fastm!(RG::GroupRing; fill::Bool=false)
|
||||
isdefined(RG, :basis) || throw("For baseless Group Rings You need to provide pm.")
|
||||
isdefined(RG, :pm) && return RG
|
||||
if fill
|
||||
RG.pm = try
|
||||
create_pm(RG.basis, RG.basis_dict)
|
||||
catch err
|
||||
isa(err, KeyError) && throw("Product is not supported on basis")
|
||||
isa(err, KeyError) && throw("Product is not supported on basis, $err.")
|
||||
throw(err)
|
||||
end
|
||||
else
|
||||
RG.pm = zeros(Int, length(RG.basis), length(RG.basis))
|
||||
end
|
||||
return A
|
||||
return RG
|
||||
end
|
||||
|
||||
end # of module GroupRings
|
||||
|
|
|
|||
|
|
@ -10,14 +10,19 @@ using Nemo
|
|||
@test isa(GroupRing(G), Nemo.Ring)
|
||||
@test isa(GroupRing(G), GroupRing)
|
||||
|
||||
RG = GroupRing(G, initialise=false)
|
||||
@test isdefined(RG, :pm) == false
|
||||
@test isdefined(RG, :basis) == false
|
||||
@test isdefined(RG, :basis_dict) == false
|
||||
|
||||
@test isa(complete(RG), GroupRing)
|
||||
@test size(RG.pm) == (6,6)
|
||||
RG = GroupRing(G)
|
||||
@test isdefined(RG, :basis) == true
|
||||
@test length(RG.basis) == 6
|
||||
@test isdefined(RG, :basis_dict) == true
|
||||
@test isdefined(RG, :pm) == false
|
||||
|
||||
RG = GroupRing(G, fastm=true)
|
||||
@test isdefined(RG, :pm) == true
|
||||
@test RG.pm == zeros(Int, (6,6))
|
||||
|
||||
@test isa(complete!(RG), GroupRing)
|
||||
@test all(RG.pm .> 0)
|
||||
@test RG.pm == GroupRings.fastm!(GroupRing(G, fastm=false), fill=true).pm
|
||||
|
||||
@test RG.basis_dict == GroupRings.reverse_dict(elements(G))
|
||||
|
||||
|
|
@ -37,7 +42,7 @@ using Nemo
|
|||
@testset "GroupRing constructors FreeGroup" begin
|
||||
using Groups
|
||||
F = FreeGroup(3)
|
||||
S = generators(F)
|
||||
S = gens(F)
|
||||
append!(S, [inv(s) for s in S])
|
||||
S = unique(S)
|
||||
|
||||
|
|
@ -53,18 +58,22 @@ using Nemo
|
|||
B = GroupRing(F, basis, d, pm)
|
||||
@test A == B
|
||||
|
||||
g = B()
|
||||
s = S[2]
|
||||
g[s] = 1
|
||||
@test g == B(s)
|
||||
@test g[s^2] == 0
|
||||
@test_throws KeyError g[s^10]
|
||||
end
|
||||
|
||||
@testset "GroupRingElems constructors/basic manipulation" begin
|
||||
G = PermutationGroup(3)
|
||||
RG = GroupRing(G, initialise=true)
|
||||
RG = GroupRing(G, fastm=true)
|
||||
a = rand(6)
|
||||
@test isa(GroupRingElem(a, RG), GroupRingElem)
|
||||
@test isa(RG(a), GroupRingElem)
|
||||
|
||||
for g in elements(G)
|
||||
@test isa(RG(g), GroupRingElem)
|
||||
end
|
||||
@test all(isa(RG(g), GroupRingElem) for g in elements(G))
|
||||
|
||||
@test_throws String GroupRingElem([1,2,3], RG)
|
||||
@test isa(RG(G([2,3,1])), GroupRingElem)
|
||||
|
|
@ -77,7 +86,8 @@ using Nemo
|
|||
@test a[5] == 1
|
||||
@test a[p] == 1
|
||||
|
||||
@test string(a) == " + 1*[2, 3, 1]"
|
||||
@test string(a) == "1*[2, 3, 1]"
|
||||
@test string(-a) == "- 1*[2, 3, 1]"
|
||||
|
||||
@test RG([0,0,0,0,1,0]) == a
|
||||
|
||||
|
|
@ -89,14 +99,15 @@ using Nemo
|
|||
@test a[1] == 2
|
||||
@test a[s] == 2
|
||||
|
||||
@test string(a) == " + 2*[1, 2, 3] + 1*[2, 3, 1]"
|
||||
@test string(a) == "2*[1, 2, 3] + 1*[2, 3, 1]"
|
||||
@test string(-a) == "- 2*[1, 2, 3] - 1*[2, 3, 1]"
|
||||
|
||||
@test length(a) == 2
|
||||
end
|
||||
|
||||
@testset "Arithmetic" begin
|
||||
G = PermutationGroup(3)
|
||||
RG = GroupRing(G)
|
||||
RG = GroupRing(G, fastm=true)
|
||||
a = RG(ones(Int, order(G)))
|
||||
|
||||
@testset "scalar operators" begin
|
||||
|
|
@ -157,6 +168,9 @@ using Nemo
|
|||
@test GroupRings.augmentation((one(RG)-RG(g))) == 0
|
||||
end
|
||||
|
||||
b = RG(1) + GroupRings.star(a)
|
||||
@test a*b == mul!(a,a,b)
|
||||
|
||||
z = sum((one(RG)-RG(g))*GroupRings.star(one(RG)-RG(g)) for g in elements(G))
|
||||
|
||||
@test GroupRings.augmentation(z) == 0
|
||||
|
|
|
|||
Loading…
Reference in New Issue