Random lines in LineEnumCtx (#1271)

src/QuadForm/LineOrbits.jl

@@ -7,7 +7,7 @@
 # We iterate through K by adding 1 in the prime field case and by multiplying
 # with a primitive element in the general case.
 
-function LineEnumCtx(K::T, n) where {T}
+function LineEnumCtx(K::T, n::Int) where {T}
   a = primitive_element(K)
   v = Vector{elem_type(K)}(undef, n)
   for i in 1:n
@@ -16,7 +16,7 @@ function LineEnumCtx(K::T, n) where {T}
   depth = n + 1
   dim = n
   q = order(K)
-  length = divexact(q^n - 1, q - 1)
+  length = divexact(BigInt(q)^n - 1, q - 1)
   return LineEnumCtx{T, elem_type(T)}(K, a, dim, depth, v, length)
 end
 
@@ -29,7 +29,7 @@ function LineEnumCtx(K::T, n::Int) where {T <: Union{fpField, FpField}}
   depth = n + 1
   dim = n
   q = order(K)
-  length = divexact(q^n - 1, q - 1)
+  length = divexact(BigInt(q)^n - 1, q - 1)
   return LineEnumCtx{T, elem_type(T)}(K, a, dim, depth, v, length)
 end
 
@@ -58,12 +58,26 @@ Base.length(P::LineEnumCtx) = P.length
 
 Base.eltype(::Type{LineEnumCtx{T, S}}) where {T, S} = Vector{S}
 
+base_field(P::LineEnumCtx) = P.K
+
 depth(P::LineEnumCtx) = P.depth
 
 dim(P::LineEnumCtx) = P.dim
 
 primitive_element(P::LineEnumCtx) = P.a
 
+function Base.rand(P::LineEnumCtx)
+  K = base_field(P)
+  n = dim(P)
+  v = rand(K, n)
+  while iszero(v)
+    v = rand(K, n)
+  end
+  j = findfirst(!iszero, v)
+  map!(x -> x*inv(v[j]), v, v)
+  return v
+end
+
 ################################################################################
 #
 #  Iteration

test/QuadForm.jl

@@ -15,4 +15,5 @@
   include("QuadForm/indefiniteLLL.jl")
   include("QuadForm/IO.jl")
   include("QuadForm/Database.jl")
+  include("QuadForm/LineOrbits.jl")
 end

test/QuadForm/LineOrbits.jl

@@ -0,0 +1,11 @@
+@testset "Random lines" begin
+  P = Hecke.enumerate_lines(GF(5), 20)
+  io = IOBuffer()
+  show(io, MIME"text/plain"(), P)
+  show(IOContext(io, :supercompact => true), P)
+  show(io, P)
+  for i in 1:100
+    v = rand(P)
+    @test !iszero(v) && isone(v[findfirst(!iszero, v)])
+  end
+end