More tests and fixes

Author: joschmitt

src/QuadForm.jl

@@ -51,7 +51,7 @@ include("QuadForm/MassQuad.jl")
 # Close vectors
 include("QuadForm/CloseVectors.jl")
 
-# indefinite LLL 
+# indefinite LLL
 include("QuadForm/indefiniteLLL.jl")
 
 # Functionality for IO with Hecke/Magma

src/QuadForm/Morphism.jl

@@ -584,6 +584,7 @@ function init_vector_sums(C::ZLatAutoCtx{S1, S2, S3}, depth::Int) where {S1, S2,
   if depth == -1
     depth = round(Int, C.dim/10)
   end
+  @assert depth >= 0 "`depth` must be non-negative"
   C.depth = depth
 
   small = S1 <: Int
@@ -717,6 +718,7 @@ function bacher_polynomial(C::ZLatAutoCtx{T}, I::Int, S::T) where T
 end
 
 function init_bacher_polynomials(C::ZLatAutoCtx{T}, depth::Int) where T
+  @assert depth >= 0 "`bacher_depth` must be non-negative"
   C.bacher_depth = depth
   C.bacher_polys = Vector{BacherPoly{T}}(undef, depth)
   for i in 1:depth
@@ -1371,7 +1373,7 @@ end
 # allowing overflows via Di/Do and only verify a positive result with ZZRingElem
 # via Ci/Co.
 function cand(candidates::Vector{Int}, I::Int, x::Vector{Int}, Ci::ZLatAutoCtx{ZZRingElem}, Co::ZLatAutoCtx{ZZRingElem}, Di::ZLatAutoCtx{Int}, Do::ZLatAutoCtx{Int})
-  if _cand(candidates, I, x, Di, Do)
+  if _cand(candidates, I, x, Di, Do, true)
     # _cand with Integers returned true, so we have to verify the result with
     # ZZRingElem
     return _cand(candidates, I, x, Ci, Co)
@@ -1382,7 +1384,7 @@ end
 # If the short vectors fit in Int, the last arguments (Di/Do) are ignored.
 cand(candidates::Vector{Int}, I::Int, x::Vector{Int}, Ci::ZLatAutoCtx{Int}, Co::ZLatAutoCtx{Int}, Di::ZLatAutoCtx, Do::ZLatAutoCtx) = _cand(candidates, I, x, Ci, Co)
 
-function _cand(candidates::Vector{Int}, I::Int, x::Vector{Int}, Ci::ZLatAutoCtx{S, T, U}, Co::ZLatAutoCtx{S, T, U}) where {S, T, U}
+function _cand(candidates::Vector{Int}, I::Int, x::Vector{Int}, Ci::ZLatAutoCtx{S, T, U}, Co::ZLatAutoCtx{S, T, U}, overflows::Bool = false) where {S, T, U}
   dep = Ci.depth
   use_vector_sums = (I > 1 && dep > 0)
   dim = Hecke.dim(Ci)
@@ -1509,11 +1511,21 @@ function _cand(candidates::Vector{Int}, I::Int, x::Vector{Int}, Ci::ZLatAutoCtx{
 
     if use_vector_sums
       sign = false
-      if !is_normalized(scpvec)
-        neg!(scpvec)
-        sign = true
+      # If we work with Int's allowing overflows we can't trust the sign anymore
+      if overflows
+        k = get(comb.scpcombs.lookup, scpvec, 0)
+        if k == 0
+          neg!(scpvec)
+          sign = true
+          k = get(comb.scpcombs.lookup, scpvec, 0)
+        end
+      else
+        if !is_normalized(scpvec)
+          neg!(scpvec)
+          sign = true
+        end
+        k = get(comb.scpcombs.lookup, scpvec, 0)
       end
-      k = get(comb.scpcombs.lookup, scpvec, 0)
       is0 = is_zero(scpvec)
       if k > 0
         if !is0
@@ -1933,7 +1945,7 @@ function isometry(Ci::ZLatAutoCtx{SS, T, U}, Co::ZLatAutoCtx{SS, T, U}) where {S
   if found
     ISO = matgen(x, d, Ci.per, Co.V)
     for k in 1:length(Ci.G)
-      ISO * Co.G[k] * ISO' == Ci.G[k]
+      ISO * Co.G[k] * transpose(ISO) == Ci.G[k]
     end
     return true, ISO
   else
@@ -2418,10 +2430,13 @@ function _make_small(C::ZLatAutoCtx{ZZRingElem})
   for i in 1:length(C.v)
     D.v[i] = [ _int_vector_with_overflow(M, tmp) for M in C.v[i] ]
   end
-  D.per = copy(C.per)
-  D.fp = copy(C.fp)
-  D.fp_diagonal = copy(C.fp_diagonal)
-  D.std_basis = copy(C.std_basis)
+
+  if isdefined(C, :per)
+    D.per = copy(C.per)
+    D.fp = copy(C.fp)
+    D.fp_diagonal = copy(C.fp_diagonal)
+    D.std_basis = copy(C.std_basis)
+  end
 
   if isdefined(C, :scpcomb)
     D.scpcomb = Vector{SCPComb{Int, Vector{Int}}}(undef, length(C.scpcomb))

test/QuadForm/Lattices.jl

@@ -162,6 +162,15 @@
   R = @inferred fixed_ring(L)
   @test R == ZZ
   @test R != base_ring(base_ring(L))
+
+  # Use ZZRingElem in the automorphism group computation (issue 1054)
+  Qx, x = FlintQQ["x"]
+  K, a = number_field(x^2 + 1, "a")
+  OK = maximal_order(K)
+  G = pseudo_matrix(matrix(K, 6, 6 ,[876708188094148315826780735392810, 798141405233250328867679564294410, -352823337641433300965521329447720, 326768950610851461363580717982402, -690595881941554449465975342845028, 433433545243019702766746394677218, 798141405233250328867679564294410, 867615301468758683549323652197099, -301315621373858240463110267500961, 316796431934778296047626373086339, -725765288914917260527454069649226, 505082964151083450666500945258490, -352823337641433300965521329447720, -301315621373858240463110267500961, 809946152369211852531731702980788, -343784636213856787915462553587466, 84764902049682607076640678540130, -613908853150167850995565570653796, 326768950610851461363580717982402, 316796431934778296047626373086339, -343784636213856787915462553587466, 219957919673551825679009958633894, -226934633316066727073394927118195, 298257387132139131540277459301842, -690595881941554449465975342845028, -725765288914917260527454069649226, 84764902049682607076640678540130, -226934633316066727073394927118195, 671443408734467545153681225010914, -277626128761200144008657217470664, 433433545243019702766746394677218, 505082964151083450666500945258490, -613908853150167850995565570653796, 298257387132139131540277459301842, -277626128761200144008657217470664, 640432299215298238271419741190578]), [ one(K)*OK, one(K)*OK, one(K)*OK, one(K)*OK, one(K)*OK, one(K)*OK ])
+  L = lattice(hermitian_space(K, identity_matrix(K, 6)), G)
+  @test automorphism_group_order(L) == 4
+  @test is_isometric_with_isometry(L, L)[1]
 end
 
 @testset "Misc" begin
@@ -199,7 +208,7 @@ end
   @test ambient_space(Lres) === Vres
   @test all(v -> VrestoV(VrestoV\v) == v, generators(L))
 
-  
+
   Qx, x = polynomial_ring(FlintQQ, "x")
   f = x - 1
   K, a = number_field(f, "a", cached = false)

test/QuadForm/Quad/ZLattices.jl

@@ -273,13 +273,21 @@ end
     @test automorphism_group_order(L) == lattice_automorphism_group_order(D, i)
   end
 
+  # Force using ZZRingElem's
+  L = lattice(D, 75)
+  Hecke.assert_has_automorphisms(L, try_small = false)
+  test_automorphisms(L, L.automorphism_group_generators, true)
+  @test L.automorphism_group_order == lattice_automorphism_group_order(D, 75)
+
   # Call the Bacher polynomials
-  L = integer_lattice(gram = gram_matrix(lattice(D, 100)))
-  Ge = automorphism_group_generators(L, ambient_representation = true, bacher_depth = 1)
-  test_automorphisms(L, Ge, true)
-  Ge = automorphism_group_generators(L, ambient_representation = false, bacher_depth = 1)
-  test_automorphisms(L, Ge, false)
-  @test automorphism_group_order(L) == lattice_automorphism_group_order(D, 100)
+  for i in [ 1, 101, 113 ] # triggering different checks in the Bacher polynomials
+    L = integer_lattice(gram = gram_matrix(lattice(D, i)))
+    Ge = automorphism_group_generators(L, ambient_representation = true, bacher_depth = 1)
+    test_automorphisms(L, Ge, true)
+    Ge = automorphism_group_generators(L, ambient_representation = false, bacher_depth = 1)
+    test_automorphisms(L, Ge, false)
+    @test automorphism_group_order(L) == lattice_automorphism_group_order(D, i)
+  end
 
   # automorphisms for indefinite of rank 2
   U = hyperbolic_plane_lattice()
@@ -334,14 +342,16 @@ end
   end
 
   # Call the Bacher polynomials
-  L = integer_lattice(gram = gram_matrix(lattice(D, 100)))
-  n = rank(L)
-  X = change_base_ring(FlintQQ, _random_invertible_matrix(n, -3:3))
-  @assert abs(det(X)) == 1
-  L2 = integer_lattice(gram = X * gram_matrix(L) * transpose(X))
-  b, T = is_isometric_with_isometry(L, L2, ambient_representation = false, bacher_depth = 1)
-  @test b
-  @test T * gram_matrix(L2) * transpose(T) == gram_matrix(L)
+  for i in [ 1, 101, 113 ] # triggering different checks in the Bacher polynomials
+    L = integer_lattice(gram = gram_matrix(lattice(D, i)))
+    n = rank(L)
+    X = change_base_ring(FlintQQ, _random_invertible_matrix(n, -3:3))
+    @assert abs(det(X)) == 1
+    L2 = integer_lattice(gram = X * gram_matrix(L) * transpose(X))
+    b, T = is_isometric_with_isometry(L, L2, ambient_representation = false, bacher_depth = 1)
+    @test b
+    @test T * gram_matrix(L2) * transpose(T) == gram_matrix(L)
+  end
 
   #discriminant of a lattice
   L = integer_lattice(ZZ[1 0; 0 1], gram = matrix(QQ, 2,2, [2, 1, 1, 2]))
@@ -727,6 +737,7 @@ let
   G = matrix(FlintQQ, 6, 6 ,[876708188094148315826780735392810, 798141405233250328867679564294410, -352823337641433300965521329447720, 326768950610851461363580717982402, -690595881941554449465975342845028, 433433545243019702766746394677218, 798141405233250328867679564294410, 867615301468758683549323652197099, -301315621373858240463110267500961, 316796431934778296047626373086339, -725765288914917260527454069649226, 505082964151083450666500945258490, -352823337641433300965521329447720, -301315621373858240463110267500961, 809946152369211852531731702980788, -343784636213856787915462553587466, 84764902049682607076640678540130, -613908853150167850995565570653796, 326768950610851461363580717982402, 316796431934778296047626373086339, -343784636213856787915462553587466, 219957919673551825679009958633894, -226934633316066727073394927118195, 298257387132139131540277459301842, -690595881941554449465975342845028, -725765288914917260527454069649226, 84764902049682607076640678540130, -226934633316066727073394927118195, 671443408734467545153681225010914, -277626128761200144008657217470664, 433433545243019702766746394677218, 505082964151083450666500945258490, -613908853150167850995565570653796, 298257387132139131540277459301842, -277626128761200144008657217470664, 640432299215298238271419741190578])
   L = integer_lattice(B, gram = G)
   @test automorphism_group_order(L) == 2
+  @test is_isometric_with_isometry(L, L)[1]
   G = [ ZZ[15 0 2 0; 0 30 0 4; 2 0 32 0; 0 4 0 64],
         ZZ[0 15 0 2; 15 0 2 0; 0 2 0 32; 2 0 32 0]];
   C = Hecke.ZLatAutoCtx(G)