From d1866723763b34fcfd355c21b53c74b3c32e284e Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Lars=20G=C3=B6ttgens?= <lars.goettgens@rwth-aachen.de>
Date: Tue, 13 Feb 2024 18:13:46 +0100
Subject: [PATCH] Incorporate linear independence check into ArcDiagBasis
 generation

---
 src/DeformationBases/ArcDiagDeformBasis.jl     | 13 +++++--------
 src/DeformationBases/PseudographDeformBasis.jl | 13 +++++--------
 test/DeformationBases-test.jl                  | 18 ++++++------------
 3 files changed, 16 insertions(+), 28 deletions(-)

diff --git a/src/DeformationBases/ArcDiagDeformBasis.jl b/src/DeformationBases/ArcDiagDeformBasis.jl
index 587eb75..bf1a5a4 100644
--- a/src/DeformationBases/ArcDiagDeformBasis.jl
+++ b/src/DeformationBases/ArcDiagDeformBasis.jl
@@ -101,14 +101,11 @@ struct ArcDiagDeformBasis{C <: RingElem} <: DeformBasis{C}
         iter = Iterators.flatten(iters)
         if !no_normalize
             iter = unique(Iterators.filter(b -> !iszero(b), iter))
-            collected = Vector{eltype(iter)}(collect(iter))
-            if !isempty(collected)
-                _, rels = is_linearly_independent_with_relations(coefficient_ring(sp), reverse(collected))
-                inds = [1 + ncols(rels) - (findfirst(!iszero, vec(rels[i, :]))::Int) for i in nrows(rels):-1:1]
-                deleteat!(collected, inds)
-            end
-            iter = collected
-            len = length(iter)
+            collected = Vector{DeformationMap{C}}(collect(iter))
+            _, rels = is_linearly_independent_with_relations(coefficient_ring(sp), reverse(collected))
+            inds = [1 + ncols(rels) - (findfirst(!iszero, vec(rels[i, :]))::Int) for i in nrows(rels):-1:1]
+            deleteat!(collected, inds)
+            return new{C}(length(collected), collected, extra_data, normalize)
         end
         return new{C}(len, iter, extra_data, normalize)
     end
diff --git a/src/DeformationBases/PseudographDeformBasis.jl b/src/DeformationBases/PseudographDeformBasis.jl
index dd3295b..9d91bef 100644
--- a/src/DeformationBases/PseudographDeformBasis.jl
+++ b/src/DeformationBases/PseudographDeformBasis.jl
@@ -62,14 +62,11 @@ struct PseudographDeformBasis{C <: RingElem} <: DeformBasis{C}
         iter = Iterators.flatten(iters)
         if !no_normalize
             iter = unique(Iterators.filter(b -> !iszero(b), iter))
-            collected = Vector{eltype(iter)}(collect(iter))
-            if !isempty(collected)
-                _, rels = is_linearly_independent_with_relations(coefficient_ring(sp), reverse(collected))
-                inds = [1 + ncols(rels) - (findfirst(!iszero, vec(rels[i, :]))::Int) for i in nrows(rels):-1:1]
-                deleteat!(collected, inds)
-            end
-            iter = collected
-            len = length(iter)
+            collected = Vector{DeformationMap{C}}(collect(iter))
+            _, rels = is_linearly_independent_with_relations(coefficient_ring(sp), reverse(collected))
+            inds = [1 + ncols(rels) - (findfirst(!iszero, vec(rels[i, :]))::Int) for i in nrows(rels):-1:1]
+            deleteat!(collected, inds)
+            return new{C}(length(collected), collected, extra_data, normalize)
         end
         return new{C}(len, iter, extra_data, normalize)
     end
diff --git a/test/DeformationBases-test.jl b/test/DeformationBases-test.jl
index b595ad1..b036489 100644
--- a/test/DeformationBases-test.jl
+++ b/test/DeformationBases-test.jl
@@ -45,15 +45,12 @@
                 @test all_pbwdeformations(sp, b) == collect(b)
 
                 b = ArcDiagDeformBasis{QQFieldElem}(sp, 0:3)
-                @test length(collect(b)) == 4
-                @test all_pbwdeformations(sp, b; special_return=SMat)[1] ==
-                      matrix(QQ, 4, 3, [1, 0, 0, 0, -3 // 2, 1 // 2, 0, 1, 0, 0, 0, 1])
+                @test length(collect(b)) == 3
+                @test all_pbwdeformations(sp, b; special_return=SMat)[1] == matrix(QQ, [1 0; 0 -3//2; 0 1])
                 ms = all_pbwdeformations(sp, b)
-                @test length(ms) == 3
+                @test length(ms) == 2
                 @test ms[1] == collect(b)[1]
                 @test 2 * ms[2] == -3 * collect(b)[2] + 2 * collect(b)[3]
-                @test 2 * ms[3] == 1 * collect(b)[2] + 2 * collect(b)[4]
-                @test iszero(ms[2] + ms[3]) # TODO: Check result for linear independence
             end
 
             @testset "SO_5, ⋀²V" begin
@@ -139,15 +136,12 @@
                 @test all_pbwdeformations(sp, b) == collect(b)
 
                 b = PseudographDeformBasis{QQFieldElem}(sp, 0:3)
-                @test length(collect(b)) == 4
-                @test all_pbwdeformations(sp, b; special_return=SMat)[1] ==
-                      matrix(QQ, 4, 3, [1, 0, 0, 0, -3 // 2, 1 // 2, 0, 1, 0, 0, 0, 1])
+                @test length(collect(b)) == 3
+                @test all_pbwdeformations(sp, b; special_return=SMat)[1] == matrix(QQ, [1 0; 0 -3//2; 0 1])
                 ms = all_pbwdeformations(sp, b)
-                @test length(ms) == 3
+                @test length(ms) == 2
                 @test ms[1] == collect(b)[1]
                 @test 2 * ms[2] == -3 * collect(b)[2] + 2 * collect(b)[3]
-                @test 2 * ms[3] == 1 * collect(b)[2] + 2 * collect(b)[4]
-                @test iszero(ms[2] + ms[3])
             end
 
             @testset "SO_5, ⋀²V" begin