Get rid of trivial anonymous functions (part 1)

examples/Reynolds.jl

@@ -241,7 +241,7 @@ function action_on_monomials(R::MPolyRing, d::Int, A::Vector{QQMatrix})
       b = zeros(QQ, length(m))
       y = evaluate(x, h)
       for (c,v) = zip(AbstractAlgebra.coefficients(y), AbstractAlgebra.monomials(y))
-        b[findfirst(l -> l==v, m)] = c
+        b[findfirst(==(v), m)] = c
       end
       push!(bb, b)
     end

experimental/AlgebraicStatistics/src/PhylogeneticAuxiliary.jl

@@ -24,13 +24,13 @@ end
 function interior_nodes(graph::Graph)
   big_graph = Polymake.graph.Graph(ADJACENCY = pm_object(graph))
   degrees = big_graph.NODE_DEGREES
-  return findall(x -> x > 1, degrees)
+  return findall(>(1), degrees)
 end
 
 function leaves(graph::Graph)
   big_graph = Polymake.graph.Graph(ADJACENCY = pm_object(graph))
   degrees = big_graph.NODE_DEGREES
-  return findall(x -> x == 1, degrees)
+  return findall(==(1), degrees)
 end
 
 function vertex_descendants(v::Int, gr::Graph, desc::Vector{Any})

experimental/AlgebraicStatistics/src/PhylogeneticParametrization.jl

@@ -216,7 +216,7 @@ Dict{Tuple{Vararg{Int64}}, QQMPolyRingElem} with 5 entries:
 """
 function compute_equivalent_classes(parametrization::Dict{Tuple{Vararg{Int64}}, QQMPolyRingElem})
   polys = unique(collect(values(parametrization)))
-  polys = polys[findall(x -> x!=0, polys)]
+  polys = polys[findall(!is_zero, polys)]
 
   equivalent_keys = []
   for value in polys

experimental/DoubleAndHyperComplexes/src/Morphisms/ext.jl

@@ -219,7 +219,7 @@ function (fac::InterpretationMorphismFactory)(self::AbsHyperComplexMorphism, I::
     pr = projections_dom[k]
     for (l, L) in enumerate(indices_cod)
       KL = Tuple(vcat(-collect(K), collect(L)))
-      kl = findfirst(x->x==KL, indices_tot)
+      kl = findfirst(==(KL), indices_tot)
       kl === nothing && error("index not found")
       v_loc = (projections_tot[kl])(fac.v)
       phi_loc = element_to_homomorphism(v_loc)

experimental/DoubleAndHyperComplexes/src/Morphisms/linear_strands.jl

@@ -124,7 +124,7 @@ function (fac::LinearStrandComplementChainFactory)(self::AbsHyperComplex, i::Tup
   min_ind = [k for k in 1:rank(F_full) if degree(F_full[k]) == offset]
   comp = [k for k in 1:rank(F_full) if !(k in min_ind)]
   F = graded_free_module(S, elem_type(G)[degree(F_full[k]) for k in comp])
-  map = hom(F_full, F, elem_type(F)[(k in comp ? F[findfirst(i->i==k, comp)] : zero(F)) for k in 1:rank(F_full)])
+  map = hom(F_full, F, elem_type(F)[(k in comp ? F[findfirst(==(k), comp)] : zero(F)) for k in 1:rank(F_full)])
   fac.maps_from_original[i] = map
   return F
 end

experimental/DoubleAndHyperComplexes/src/Morphisms/simplified_complexes.jl

@@ -228,7 +228,7 @@ function (fac::SimplifiedChainFactory)(d::AbsHyperComplex, Ind::Tuple)
       w = Tinv[i]
       new_entries = Vector{Tuple{Int, elem_type(base_ring(w))}}()
       for (real_j, b) in w
-        j = findfirst(k->k==real_j, J)
+        j = findfirst(==(real_j), J)
         j === nothing && continue
         push!(new_entries, (j, b))
       end

experimental/DoubleAndHyperComplexes/src/Objects/Types.jl

@@ -585,7 +585,7 @@ end
     ranges = [(k, u) for (k, u) in v if u isa UnitRange]
     d = length(ranges)
     all_ind = [k for (k, u) in v if u isa UnitRange]
-    @assert all(k->k in all_ind, 1:d) "matching of ranges is not unique"
+    @assert all(in(all_ind), 1:d) "matching of ranges is not unique"
 
     mapping_matrix = [0 for i in 1:dim(c), j in 1:d]
     new_ranges = Dict(v)

experimental/DoubleAndHyperComplexes/src/Objects/total_complexes.jl

@@ -124,7 +124,7 @@ function (fac::TotalComplexMapFactory)(c::AbsHyperComplex, p::Int, I::Tuple)
     for k in 1:dim(orig)
       target = collect(J) + (direction(orig, k) == :chain ? -1 : 1)*[(l == k ? 1 : 0) for l in 1:dim(orig)]
       T = Tuple(target)
-      index_in_cod = findfirst(t->t == T, index_cache(chain_fac)[next])
+      index_in_cod = findfirst(==(T), index_cache(chain_fac)[next])
       index_in_cod === nothing && continue
       phi = map(orig, k, J)
       @assert codomain(phi) === orig[T]
@@ -228,15 +228,15 @@ end
 function injection(tot::TotalComplex, i::Tuple)
   d = sum(i)
   v = indices_in_summand(tot, d)
-  k = findfirst(k->k==i, v)
+  k = findfirst(==(i), v)
   k === nothing && return nothing
   return injections_for_summand(tot, d)[k]
 end
 
 function projection(tot::TotalComplex, i::Tuple)
   d = sum(i)
   v = indices_in_summand(tot, d)
-  k = findfirst(k->k==i, v)
+  k = findfirst(==(i), v)
   k === nothing && return nothing
   return projections_for_summand(tot, d)[k]
 end

experimental/FTheoryTools/src/AbstractFTheoryModels/methods.jl

@@ -333,7 +333,7 @@ function put_over_concrete_base(m::AbstractFTheoryModel, concrete_data::Dict{Str
     all_appearing_monomials = vcat([collect(monomials(p)) for p in polys]...)
     all_appearing_exponents = hcat([collect(exponents(m))[1] for m in all_appearing_monomials]...)
     for k in 1:nrows(all_appearing_exponents)
-      if any(x -> x != 0, all_appearing_exponents[k,:])
+      if any(!is_zero, all_appearing_exponents[k,:])
         gen_name = string(gens(parent(polys[1]))[k])
         @req haskey(concrete_data, gen_name) "Required base section $gen_name not specified"
         @req parent(concrete_data[gen_name]) == cox_ring(concrete_data["base"]) "Specified sections must reside in Cox ring of given base"
@@ -646,7 +646,7 @@ function set_zero_section_class(m::AbstractFTheoryModel, desired_value::String)
   cohomology_ring(ambient_space(m); check=false)
   cox_gens = string.(gens(cox_ring(ambient_space(m))))
   @req desired_value in cox_gens "Specified zero section is invalid"
-  index = findfirst(x -> x==desired_value, cox_gens)
+  index = findfirst(==(desired_value), cox_gens)
   set_attribute!(m, :zero_section_class => cohomology_class(divs[index]))
 end
 
@@ -840,7 +840,7 @@ function resolve(m::AbstractFTheoryModel, resolution_index::Int)
 
       # Compute strict transform of ideal sheaves appearing in blowup center
       exceptional_center = [c for c in blow_up_center if (c in exceptionals)]
-      positions = [findfirst(x -> x == l, exceptionals) for l in exceptional_center]
+      positions = [findfirst(==(l), exceptionals) for l in exceptional_center]
       exceptional_divisors = [exceptional_divisor(get_attribute(blow_up_chain[l], :blow_down_morphism)) for l in positions]
       exceptional_ideal_sheafs = [ideal_sheaf(d) for d in exceptional_divisors]
       for l in 1:length(positions)

experimental/FTheoryTools/src/HypersurfaceModels/methods.jl

@@ -104,7 +104,7 @@ function tune(h::HypersurfaceModel, input_sections::Dict{String, <:Any}; complet
   isempty(input_sections) && return h
   secs_names = collect(keys(explicit_model_sections(h)))
   tuned_secs_names = collect(keys(input_sections))
-  @req all(x -> x in secs_names, tuned_secs_names) "Provided section name not recognized"
+  @req all(in(secs_names), tuned_secs_names) "Provided section name not recognized"
 
   # 1. Tune model sections
   explicit_secs = deepcopy(explicit_model_sections(h))

experimental/FTheoryTools/src/LiteratureModels/constructors.jl

@@ -297,7 +297,7 @@ end
 #######################################################
 
 function _find_model(doi::String, arxiv_id::String, version::String, equation::String, type::String)
-  @req any(s -> s != "", [doi, arxiv_id, version, equation]) "No information provided; cannot perform look-up"
+  @req any(!isempty, [doi, arxiv_id, version, equation]) "No information provided; cannot perform look-up"
   file_index = JSON.parsefile(joinpath(@__DIR__, "index.json"))
   candidate_files = Vector{String}()
   for k in 1:length(file_index)

experimental/FTheoryTools/src/LiteratureModels/create_index.jl

@@ -23,7 +23,7 @@
 function _create_literature_model_index()
   model_directory = joinpath(@__DIR__, "Models/")
   models = readdir(model_directory)
-  filter!(s -> startswith(s, "model"), models)
+  filter!(startswith("model"), models)
 
   index = Vector{Dict{String,Union{String,Vector{Any}}}}()
   model_indices = JSON.parsefile(joinpath(@__DIR__, "model_indices.json"))

experimental/FTheoryTools/src/TateModels/constructors.jl

@@ -59,7 +59,7 @@ function global_tate_model(base::NormalToricVariety,
   @req haskey(explicit_model_sections, "a4") "Tate section a4 must be specified"
   @req haskey(explicit_model_sections, "a6") "Tate section a6 must be specified"
   vs2 = collect(keys(defining_section_parametrization))
-  @req all(x -> x in ["a1", "a2", "a3", "a4", "a6"], vs2) "Only the Tate sections a1, a2, a3, a4, a6 must be parametrized"
+  @req all(in(["a1", "a2", "a3", "a4", "a6"]), vs2) "Only the Tate sections a1, a2, a3, a4, a6 must be parametrized"
 
   gens_base_names = [string(g) for g in gens(cox_ring(base))]
   if ("x" in gens_base_names) || ("y" in gens_base_names) || ("z" in gens_base_names)

experimental/FTheoryTools/src/TateModels/methods.jl

@@ -29,7 +29,7 @@ function analyze_fibers(model::GlobalTateModel, centers::Vector{<:Vector{<:Integ
 
   # Pick out the singular loci that are more singular than an I_1
   # Then keep only the locus and not the extra info about it
-  interesting_singular_loci = map(tup -> tup[1], filter(locus -> locus[2][3] > 1, sing_loc))
+  interesting_singular_loci = map(first, filter(locus -> locus[2][3] > 1, sing_loc))
 
   # This is a kludge to map polynomials on the base into the ambient space, and should be fixed once the ambient space constructors supply such a map
   base_coords = parent(gens(interesting_singular_loci[1])[1])
@@ -50,7 +50,7 @@ function analyze_fibers(model::GlobalTateModel, centers::Vector{<:Vector{<:Integ
     # Potential components of the fiber over this locus
     # For now, we only consider the associated prime ideal,
     # but we may later want to actually consider the primary ideals
-    potential_components = map(pair -> pair[2], primary_decomposition(strict_transform + res_ring_map(ungraded_locus)))
+    potential_components = map(last, primary_decomposition(strict_transform + res_ring_map(ungraded_locus)))
 
     # Filter out the trivial loci among the potential components
     components = filter(component -> _is_nontrivial(component, res_irr), potential_components)
@@ -59,7 +59,7 @@ function analyze_fibers(model::GlobalTateModel, centers::Vector{<:Vector{<:Integ
     intersections = Tuple{Tuple{Int64, Int64}, Vector{MPolyIdeal{QQMPolyRingElem}}}[]
     for i in 1:length(components) - 1
       for j in i + 1:length(components)
-        intersection = filter(candidate_locus -> _is_nontrivial(candidate_locus, res_irr), map(pair -> pair[2], primary_decomposition(components[i] + components[j])))
+        intersection = filter(candidate_locus -> _is_nontrivial(candidate_locus, res_irr), map(last, primary_decomposition(components[i] + components[j])))
         push!(intersections, ((i, j), intersection))
       end
     end
@@ -163,7 +163,7 @@ function tune(t::GlobalTateModel, input_sections::Dict{String, <:Any}; completen
   isempty(input_sections) && return t
   secs_names = collect(keys(explicit_model_sections(t)))
   tuned_secs_names = collect(keys(input_sections))
-  @req all(x -> x in secs_names, tuned_secs_names) "Provided section name not recognized"
+  @req all(in(secs_names), tuned_secs_names) "Provided section name not recognized"
 
   # 0. Prepare for computation by setting up some information
   explicit_secs = deepcopy(explicit_model_sections(t))
@@ -220,7 +220,7 @@ function tune(t::GlobalTateModel, input_sections::Dict{String, <:Any}; completen
   # 5. After removing some sections, we must go over the parametrization again and adjust the ring in which the parametrization is given.
   if !isempty(def_secs_param)
     naive_vars = string.(gens(parent(first(values(def_secs_param)))))
-    filtered_vars = filter(x -> x in keys(explicit_secs), naive_vars)
+    filtered_vars = filter(x -> haskey(explicit_secs, x), naive_vars)
     desired_ring, _ = polynomial_ring(QQ, filtered_vars, cached = false)
     for (key, value) in def_secs_param
       def_secs_param[key] = eval_poly(string(value), desired_ring)

experimental/FTheoryTools/src/WeierstrassModels/constructors.jl

@@ -53,7 +53,7 @@ function weierstrass_model(base::NormalToricVariety,
   @req haskey(explicit_model_sections, "f") "Weierstrass section f must be specified"
   @req haskey(explicit_model_sections, "g") "Weierstrass section g must be specified"
   vs2 = collect(keys(defining_section_parametrization))
-  @req all(x -> x in ["f", "g"], vs2) "Only the Weierstrass sections f, g must be parametrized"
+  @req all(in(("f", "g")), vs2) "Only the Weierstrass sections f, g must be parametrized"
 
   gens_base_names = [string(g) for g in gens(cox_ring(base))]
   if ("x" in gens_base_names) || ("y" in gens_base_names) || ("z" in gens_base_names)

experimental/FTheoryTools/src/WeierstrassModels/methods.jl

@@ -86,7 +86,7 @@ function tune(w::WeierstrassModel, input_sections::Dict{String, <:Any}; complete
   isempty(input_sections) && return w
   secs_names = collect(keys(explicit_model_sections(w)))
   tuned_secs_names = collect(keys(input_sections))
-  @req all(x -> x in secs_names, tuned_secs_names) "Provided section name not recognized"
+  @req all(in(secs_names), tuned_secs_names) "Provided section name not recognized"
 
   # 0. Prepare for computation by setting up some information
   explicit_secs = deepcopy(explicit_model_sections(w))
@@ -143,7 +143,7 @@ function tune(w::WeierstrassModel, input_sections::Dict{String, <:Any}; complete
   # 5. After removing some sections, we must go over the parametrization again and adjust the ring in which the parametrization is given.
   if !isempty(def_secs_param)
     naive_vars = string.(gens(parent(first(values(def_secs_param)))))
-    filtered_vars = filter(x -> x in keys(explicit_secs), naive_vars)
+    filtered_vars = filter(x -> haskey(explicit_secs, x), naive_vars)
     desired_ring, _ = polynomial_ring(QQ, filtered_vars, cached = false)
     for (key, value) in def_secs_param
       def_secs_param[key] = eval_poly(string(value), desired_ring)

experimental/FTheoryTools/src/auxiliary.jl

@@ -256,14 +256,14 @@ function _kodaira_type(id::MPolyIdeal{<:MPolyRingElem}, ords::Tuple{Int64, Int64
         push!(quotients, quotient(ideal([9 * g2s[i], gauge2s[i]]), ideal([2 * f2s[i], gauge2s[i]])))
       end
 
-      kod_type = if all(q -> is_radical(q), quotients) "Non-split I_$d_ord" else "Split I_$d_ord" end
+      kod_type = if all(is_radical, quotients) "Non-split I_$d_ord" else "Split I_$d_ord" end
     elseif d_ord == 4 && g_ord == 2 && f_ord >= 2
       quotients = []
       for i in eachindex(gauge2s)
         push!(quotients, quotient(ideal([g2s[i]]), ideal([gauge2s[i]^2])) + ideal([gauge2s[i]]))
       end
 
-      kod_type = if all(q -> is_radical(q), quotients) "Non-split IV" else "Split IV" end
+      kod_type = if all(is_radical, quotients) "Non-split IV" else "Split IV" end
     elseif f_ord == 2 && g_ord == 3 && d_ord >= 7
       quotients = []
       if d_ord % 2 == 0
@@ -276,14 +276,14 @@ function _kodaira_type(id::MPolyIdeal{<:MPolyRingElem}, ords::Tuple{Int64, Int64
         end
       end
 
-      kod_type = if all(q -> is_radical(q), quotients) "Non-split I^*_$(d_ord - 6)" else "Split I^*_$(d_ord - 6)" end
+      kod_type = if all(is_radical, quotients) "Non-split I^*_$(d_ord - 6)" else "Split I^*_$(d_ord - 6)" end
     elseif d_ord == 8 && g_ord == 4 && f_ord >= 3
       quotients = []
       for i in eachindex(gauge2s)
         push!(quotients, quotient(ideal([g2s[i]]), ideal([gauge2s[i]^4])) + ideal([gauge2s[i]]))
       end
 
-      kod_type = if all(q -> is_radical(q), quotients) "Non-split IV^*" else "Split IV^*" end
+      kod_type = if all(is_radical, quotients) "Non-split IV^*" else "Split IV^*" end
     else
       kod_type = "Unrecognized"
     end
@@ -464,7 +464,7 @@ _strict_transform(bd::AbsCoveredSchemeMorphism, II::AbsIdealSheaf; coordinate_na
 
 function _strict_transform(bd::ToricBlowdownMorphism, II::ToricIdealSheafFromCoxRingIdeal; coordinate_name = "e")
   center_ideal = ideal_in_cox_ring(center_unnormalized(bd))
-  if (ngens(ideal_in_cox_ring(II)) != 1) || (all(x -> x in gens(base_ring(center_ideal)), gens(center_ideal)) == false)
+  if (ngens(ideal_in_cox_ring(II)) != 1) || (all(in(gens(base_ring(center_ideal))), gens(center_ideal)) == false)
     return strict_transform(bd, II)
   end
   S = cox_ring(domain(bd))

experimental/GITFans/src/GITFans.jl

@@ -132,8 +132,7 @@ function orbit_cones(I::MPolyIdeal, Q::Matrix{Int}, G::PermGroup = symmetric_gro
                 # computing rays and facets.
                 facets(cone)
                 rays(cone)
-                if ! any(j -> j == cone,
-                      collector_cones)
+                if !any(==(cone), collector_cones)
                     push!(collector_cones, cone)
                 end
             end
@@ -333,7 +332,7 @@ function orbit_cone_orbits(cones::Vector{Cone{T}}, ghom::GAPGroupHomomorphism) w
         # the heavy lifting of computing rays and facets.
         rays(c)
         facets(c)
-        if all(o -> all(x -> c != x, o), result)
+        if all(o -> all(!=(c), o), result)
             push!(result, orbit(c, matgens, act, Base.:(==)))
         end
     end
@@ -472,7 +471,7 @@ function fan_traversal(orbit_list::Vector{Vector{Cone{T}}}, q_cone::Cone{T}, per
         for i in neighbor_hashes
             if i in hash_list
                 # perhaps we have found a new incidence
-                push!(edges, sort!([findfirst(x->x == i, hash_list), current_pos]))
+                push!(edges, sort!([findfirst(==(i), hash_list), current_pos]))
             else
                 # new representative found
                 push!(hash_list, i)
@@ -511,12 +510,12 @@ function hashes_to_polyhedral_fan(orbit_list::Vector{Vector{Cone{T}}}, hash_list
     allrays = sort!(unique(vcat(rays_maxcones...)))
 
     # the indices of rays that belong to each maximal cone (0-based)
-    index_maxcones = [sort([findfirst(x -> x == v, allrays)-1
+    index_maxcones = [sort([findfirst(==(v), allrays)-1
                             for v in rays])
                       for rays in rays_maxcones]
 
     # the indices of rays that belong to each repres. cone
-    index_result_cones = [sort([findfirst(x -> x == v, allrays)
+    index_result_cones = [sort([findfirst(==(v), allrays)
                             for v in rays])
                       for rays in rays_result_cones]
 

experimental/GModule/src/Brueckner.jl

@@ -69,7 +69,7 @@ function reps(K, G::Oscar.PcGroup)
           X = l[1]
           Xp = X^p
           #Brueckner: C*Xp == Y for some scalar C
-          ii = findfirst(x->!iszero(x), Xp)
+          ii = findfirst(!is_zero, Xp)
           @assert !iszero(Y[ii])
           C = divexact(Y[ii], Xp[ii])
           @assert C*Xp == Y

experimental/GModule/src/Cohomology.jl

@@ -348,7 +348,7 @@ function induce(C::GModule{<:Oscar.GAPGroup}, h::Map, D = nothing, mDC = nothing
   for s = gens(G)
     sigma = ra(s)
     u = [ g[i]*s*g[i^sigma]^-1 for i=1:length(g)]
-    @assert all(x->x in iU, u)
+    @assert all(in(iU), u)
     im_q = []
     for q = gens(indC)
       push!(im_q, sum(inj[i^sigma](action(C, preimage(h, u[i]), pro[i](q))) for i=1:length(g)))
@@ -358,7 +358,7 @@ function induce(C::GModule{<:Oscar.GAPGroup}, h::Map, D = nothing, mDC = nothing
     s = inv(s)
     sigma = ra(s)
     u = [ g[i]*s*g[i^sigma]^-1 for i=1:length(g)]
-    @assert all(x->x in iU, u)
+    @assert all(in(iU), u)
     im_q = []
     for q = gens(indC)
       push!(im_q, sum(inj[i^sigma](action(C, preimage(h, u[i]), pro[i](q))) for i=1:length(g)))

experimental/GModule/src/GModule.jl

@@ -1177,7 +1177,7 @@ function _two_cocycle(mA::Map, C::GModule{<:Any, <:AbstractAlgebra.FPModule{AbsS
       elseif isone(h)
         sigma[(g, h)] = (one(K))
       else
-        lf = findfirst(x->!iszero(x), X[g*h])
+        lf = findfirst(!is_zero, X[g*h])
         sigma[(g, h)] = (X[g*h][lf]//(map_entries(mA(h), X[g])*X[h])[lf])
 #        sigma[(g, h)] = MK(X[g*h][lf]//(X[h]*map_entries(mA(h), X[g]))[lf])
       end

experimental/GModule/src/GaloisCohomology.jl

@@ -868,7 +868,7 @@ function idele_class_gmodule(k::AbsSimpleNumField, s::Vector{Int} = Int[]; redo:
   @vprint :GaloisCohomology 2 " .. S-units (for all) ..\n"
   U, mU = sunit_group_fac_elem(S)
   I.mU = mU
-  z = MapFromFunc(codomain(mU), k, x->evaluate(x), y->FacElem(y))
+  z = MapFromFunc(codomain(mU), k, evaluate, FacElem)
   E = gmodule(G, mU, mG)
   Hecke.assure_has_hnf(E.M)
   @hassert :GaloisCohomology -1 is_consistent(E)
@@ -1641,7 +1641,7 @@ function relative_brauer_group(K::AbsSimpleNumField, k::Union{QQField, AbsSimple
     G = s
     mG = ms*mG
   else
-    mp = MapFromFunc(QQ, K, x -> K(x), y-> QQ(y))
+    mp = MapFromFunc(QQ, K, K, QQ)
   end
   B = RelativeBrauerGroup(mp)
   B.mG = mG
@@ -1673,7 +1673,7 @@ function relative_brauer_group(K::AbsSimpleNumField, k::Union{QQField, AbsSimple
     S, mS = sunit_group(lP)
 
     MC = Oscar.GrpCoh.MultGrp(K)
-    mMC = MapFromFunc(K, MC, x->MC(x), y->y.data)
+    mMC = MapFromFunc(K, MC, MC, y->y.data)
 
     mG = B.mG
     G = domain(mG)
@@ -1724,8 +1724,8 @@ function relative_brauer_group(K::AbsSimpleNumField, k::Union{QQField, AbsSimple
   end
 
   B.map =  MapFromFunc(B, Oscar.GrpCoh.AllCoChains{2, PermGroupElem, Oscar.GrpCoh.MultGrpElem{AbsSimpleNumFieldElem}}(),
-                       x->elem_to_cocycle(x), 
-                       y->cocycle_to_elem(y))
+                       elem_to_cocycle, 
+                       cocycle_to_elem)
   return B, B.map
 end