Add some span utils

src/LinearIndependence.jl

@@ -15,6 +15,11 @@ function is_linearly_independent(V::Vector{T}) where {T}
     return is_linearly_independent_with_relations(V)[1]
 end
 
+"""
+    is_linearly_independent(F::Field, V::Vector{T}) where {T} -> Bool
+
+Checks whether the elements of `V` are linearly independent over `F`.
+"""
 function is_linearly_independent(F::Field, V::Vector{T}) where {T}
     return is_linearly_independent_with_relations(F, V)[1]
 end
@@ -24,11 +29,50 @@ function is_linearly_independent_with_relations(V::Vector{T}) where {T}
     return nrows(M) == 0, M
 end
 
+"""
+    is_linearly_independent_with_relations(F::Field, V::Vector{T}) where {T}
+
+Checks whether the elements of `V` are linearly independent over `F`.
+
+This function returns a tuple `(is_independent, relations)` where `is_independent`
+is a boolean indicating whether the elements are linearly independent and `relations`
+is a matrix whose rows are the coefficients of the linear relations.
+"""
 function is_linearly_independent_with_relations(F::Field, V::Vector{T}) where {T}
     M = kernel(_linear_independence_coeff_matrix(F, V); side=:left)
     return nrows(M) == 0, M
 end
 
+"""
+    is_in_span(F::Field, x::T, V::Vector{T}) where {T} -> Bool
+
+Checks whether `x` is in the `F`-span of `V`.
+"""
+function is_in_span(F::Field, x::T, V::Vector{T}) where {T}
+    cm = _linear_independence_coeff_matrix(F, [x; V])
+    return rank(cm[2:end, :]) == rank(cm)
+end
+
+"""
+    is_span_subset(F::Field, V::Vector{T}, W::Vector{T}) where {T} -> Bool
+
+Checks whether the `F`-span of `V` is a subset of the `F`-span of `W`.
+"""
+function is_span_subset(F::Field, V::Vector{T}, W::Vector{T}) where {T}
+    cm = _linear_independence_coeff_matrix(F, [V; W])
+    return rank(cm[length(V)+1:end, :]) == rank(cm)
+end
+
+"""
+    is_span_equal(F::Field, V::Vector{T}, W::Vector{T}) where {T} -> Bool
+
+Checks whether the `F`-span of `V` is equal to the `F`-span of `W`.
+"""
+function is_span_equal(F::Field, V::Vector{T}, W::Vector{T}) where {T}
+    cm = _linear_independence_coeff_matrix(F, [V; W])
+    return rank(cm[1:length(V), :]) == rank(cm[length(V)+1:end, :]) == rank(cm)
+end
+
 function _linear_independence_coeff_matrix(V::Vector{<:FieldElem})
     @req length(V) > 0 "For empty vectors, the field needs to be specified"
     return _linear_independence_coeff_matrix(parent(V[1]), V)

src/PBWDeformations.jl

@@ -83,9 +83,12 @@ export general_linear_lie_algebra
 export inneighbor
 export inneighbors
 export is_crossing_free
+export is_in_span
 export is_linearly_independent
 export is_linearly_independent_with_relations
 export is_pbwdeformation
+export is_span_equal
+export is_span_subset
 export isomorphic_module_with_simple_structure
 export lookup_data
 export lower_vertex, is_lower_vertex

test/LinearIndependence-test.jl

@@ -0,0 +1,105 @@
+@testset "LinearIndependence.jl tests" begin
+    @testset "is_linearly_independent(_with_relations)" begin
+        #TODO
+
+    end
+
+    @testset" is_in_span" begin
+        @test is_in_span(QQ, matrix(QQ, 2, 2, [1, 2, 3, 4]), [matrix(QQ, 2, 2, [1, 2, 3, 4])])
+
+        @test !is_in_span(QQ, matrix(QQ, 2, 2, [1, 2, 3, 4]), [matrix(QQ, 2, 2, [1, 1, 1, 1])])
+
+        @test is_in_span(
+            QQ,
+            matrix(QQ, 2, 2, [1, 2, 3, 4]),
+            [matrix(QQ, 2, 2, [1, 2, 3, 4]), matrix(QQ, 2, 2, [0, 0, 0, 1])],
+        )
+
+        @test !is_in_span(
+            QQ,
+            matrix(QQ, 2, 2, [1, 2, 3, 4]),
+            [matrix(QQ, 2, 2, [1, 2, 3, 6]), matrix(QQ, 2, 2, [1, 1, 1, 1])],
+        )
+
+        @test is_in_span(
+            QQ,
+            matrix(QQ, 2, 2, [1, 2, 3, 4]),
+            [matrix(QQ, 2, 2, [1, 2, 3, 6]), matrix(QQ, 2, 2, [0, 0, 0, 1])],
+        )
+
+    end
+
+    @testset "is_span_subset" begin
+        @test is_span_subset(
+            QQ,
+            [matrix(QQ, 2, 2, [1, 2, 3, 4])],
+            [matrix(QQ, 2, 2, [1, 2, 3, 6]), matrix(QQ, 2, 2, [0, 0, 0, 1])],
+        )
+
+        @test is_span_subset(
+            QQ,
+            [matrix(QQ, 2, 2, [1, 2, 3, 4]), matrix(QQ, 2, 2, [1, 2, 3, 5])],
+            [matrix(QQ, 2, 2, [1, 2, 3, 6]), matrix(QQ, 2, 2, [0, 0, 0, 1])],
+        )
+
+        @test is_span_subset(
+            QQ,
+            [matrix(QQ, 2, 2, [1, 2, 3, 6]), matrix(QQ, 2, 2, [0, 0, 0, 1])],
+            [matrix(QQ, 2, 2, [1, 2, 3, 4]), matrix(QQ, 2, 2, [1, 2, 3, 5])],
+        )
+
+        @test !is_span_subset(
+            QQ,
+            [matrix(QQ, 2, 2, [1, 2, 3, 6]), matrix(QQ, 2, 2, [0, 0, 0, 1])],
+            [matrix(QQ, 2, 2, [1, 2, 3, 4]), matrix(QQ, 2, 2, [1, 1, 1, 1])],
+        )
+
+        @test !is_span_subset(
+            QQ,
+            [matrix(QQ, 2, 2, [1, 2, 3, 4]), matrix(QQ, 2, 2, [1, 1, 1, 1])],
+            [matrix(QQ, 2, 2, [1, 2, 3, 6]), matrix(QQ, 2, 2, [0, 0, 0, 1])],
+        )
+
+        @test is_span_subset(
+            QQ,
+            [matrix(QQ, 2, 2, [1, 2, 3, 4]), matrix(QQ, 2, 2, [2, 4, 6, 8])],
+            [matrix(QQ, 2, 2, [1, 2, 3, 4]), matrix(QQ, 2, 2, [1, 1, 1, 1])],
+        )
+
+        @test !is_span_subset(
+            QQ,
+            [matrix(QQ, 2, 2, [1, 2, 3, 4]), matrix(QQ, 2, 2, [1, 1, 1, 1])],
+            [matrix(QQ, 2, 2, [1, 2, 3, 4]), matrix(QQ, 2, 2, [2, 4, 6, 8])],
+        )
+
+    end
+
+    @testset "is_span_equal" begin
+        @test !is_span_equal(
+            QQ,
+            [matrix(QQ, 2, 2, [1, 2, 3, 4]), matrix(QQ, 2, 2, [1, 1, 1, 1])],
+            [matrix(QQ, 2, 2, [1, 2, 3, 6]), matrix(QQ, 2, 2, [0, 0, 0, 1])],
+        )
+
+        @test !is_span_equal(
+            QQ,
+            [matrix(QQ, 2, 2, [1, 2, 3, 4]), matrix(QQ, 2, 2, [1, 1, 1, 1])],
+            [matrix(QQ, 2, 2, [1, 2, 3, 4]), matrix(QQ, 2, 2, [2, 4, 6, 8])],
+        )
+
+        @test is_span_equal(
+            QQ,
+            [matrix(QQ, 2, 2, [1, 2, 3, 4]), matrix(QQ, 2, 2, [1, 2, 3, 5])],
+            [matrix(QQ, 2, 2, [1, 2, 3, 6]), matrix(QQ, 2, 2, [0, 0, 0, 1])],
+        )
+
+        @test is_span_equal(
+            QQ,
+            [matrix(QQ, 2, 2, [1, 2, 3, 4]), matrix(QQ, 2, 2, [1, 2, 3, 5]), matrix(QQ, 2, 2, [1, 2, 3, 6])],
+            [matrix(QQ, 2, 2, [1, 2, 3, 6]), matrix(QQ, 2, 2, [0, 0, 0, 1])],
+        )
+
+    end
+
+
+end

test/runtests.jl

@@ -4,6 +4,7 @@ Oscar.with_unicode(true) do
     # short
     include("ArcDiagram-test.jl")
     include("DeformationBases-test.jl")
+    include("LinearIndependence-test.jl")
     include("Pseudograph-test.jl")
     include("SmashProductLie-test.jl")
     include("SmashProductLieDeform-test.jl")