Add linear independence check function

src/DeformationBases/ArcDiagDeformBasis.jl

@@ -101,6 +101,13 @@ 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)
         end
         return new{C}(len, iter, extra_data, normalize)

src/DeformationBases/PseudographDeformBasis.jl

@@ -62,6 +62,13 @@ 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)
         end
         return new{C}(len, iter, extra_data, normalize)

src/LinearIndependence.jl

@@ -0,0 +1,71 @@
+function is_linearly_independent(F::Field, V::Vector{T}) where {T}
+    return is_linearly_independent_with_relations(F, V)[1]
+end
+
+function is_linearly_independent(V::Vector{T}) where {T}
+    return is_linearly_independent_with_relations(V)[1]
+end
+
+function is_linearly_independent_with_relations(F::Field, V::Vector{<:FieldElem})
+    n, M = kernel(matrix(F, length(V), 1, V); side=:left)
+    return n == 0, M
+end
+
+function is_linearly_independent_with_relations(F::Field, V::Vector{<:PolyRingElem})
+    n = length(V)
+    if n == 0
+        return false, zero_matrix(F, 0, 0)
+    end
+    rels = identity_matrix(F, n)
+    maxdeg = maximum(degree, V)
+    for i in 1:maxdeg
+        rels = basis_intersection(rels, is_linearly_independent_with_relations(F, [coeff(v, i) for v in V])[2])
+        iszero(rels) && return true, rels
+    end
+    return false, rels
+end
+
+function is_linearly_independent_with_relations(F::Field, V::Vector{<:MatElem})
+    n = length(V)
+    if n == 0
+        return false, zero_matrix(F, 0, 0)
+    end
+    @req all(size(v) == size(V[1]) for v in V) "Size mismatch"
+    rels = identity_matrix(F, n)
+    for i in eachindex(V[1])
+        rels = basis_intersection(rels, is_linearly_independent_with_relations(F, [v[i] for v in V])[2])
+        iszero(rels) && return true, rels
+    end
+    return false, rels
+end
+
+function is_linearly_independent_with_relations(F::Field, V::Vector{<:FreeAssAlgElem})
+    coeff_maps = [Dict{Vector{Int}, elem_type(F)}(zip(exponent_words(v), coefficients(v))) for v in V]
+    words = reduce(union, keys.(coeff_maps))
+    n = length(V)
+    rels = identity_matrix(F, n)
+    for word in words
+        rels = basis_intersection(
+            rels,
+            is_linearly_independent_with_relations(F, [get(coeff_map, word, zero(F)) for coeff_map in coeff_maps])[2],
+        )
+        iszero(rels) && return true, rels
+    end
+    return false, rels
+end
+
+function basis_intersection(V::MatElem{T}, W::MatElem{T}) where {T <: FieldElem}
+    # using Zassenhaus
+    @req base_ring(V) == base_ring(W) "Incompatible base rings"
+    @req ncols(V) == ncols(W) "Size mismatch"
+    if nrows(V) == 0 || nrows(W) == 0
+        return zero(V, 0, ncols(V))
+    end
+    if V == W
+        return V
+    end
+    block_mat = vcat(hcat(V, V), hcat(W, zero(W)))
+    s = rref!(block_mat)
+    r = rank(block_mat[:, 1:ncols(V)])
+    return block_mat[r+1:s, ncols(V)+1:end]
+end

src/PBWDeformations.jl

@@ -81,6 +81,8 @@ export general_linear_lie_algebra
 export inneighbor
 export inneighbors
 export is_crossing_free
+export is_linearly_independent
+export is_linearly_independent_with_relations
 export is_pbwdeformation
 export isomorphic_module_with_simple_structure
 export lookup_data
@@ -117,6 +119,7 @@ end
 
 include("OscarPatches.jl")
 
+include("LinearIndependence.jl")
 include("ModuleSimpleStructure.jl")
 
 include("DeformationBases/DeformBasis.jl")