Move eigenspaces etc to new matrix.jl file

Nemocas · Feb 23, 2024 · fc0ea6d · fc0ea6d
1 parent 42fd431
commit fc0ea6d
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Showing 3 changed files with 112 additions and 97 deletions.
diff --git a/src/HeckeMiscMatrix.jl b/src/HeckeMiscMatrix.jl
@@ -614,98 +614,3 @@ function map_entries(R::ZZModRing, M::ZZMatrix)
     end
     return N
 end
-
-################################################################################
-#
-#  Eigenvalues and eigenspaces
-#
-################################################################################
-
-@doc raw"""
-    eigenvalues(M::MatElem{T}) where T <: FieldElem
-
-Return the eigenvalues of `M`.
-"""
-function eigenvalues(M::MatElem{T}) where T <: FieldElem
-  @assert is_square(M)
-  K = base_ring(M)
-  f = charpoly(M)
-  return roots(f)
-end
-
-@doc raw"""
-    eigenvalues_with_multiplicities(M::MatElem{T}) where T <: FieldElem
-
-Return the eigenvalues of `M` together with their algebraic multiplicities as a
-vector of tuples.
-"""
-function eigenvalues_with_multiplicities(M::MatElem{T}) where T <: FieldElem
-  @assert is_square(M)
-  K = base_ring(M)
-  Kx, x = polynomial_ring(K, "x", cached = false)
-  f = charpoly(Kx, M)
-  r = roots(f)
-  return [ (a, valuation(f, x - a)) for a in r ]
-end
-
-@doc raw"""
-    eigenvalues(L::Field, M::MatElem{T}) where T <: RingElem
-
-Return the eigenvalues of `M` over the field `L`.
-"""
-function eigenvalues(L::Field, M::MatElem{T}) where T <: RingElem
-  @assert is_square(M)
-  M1 = change_base_ring(L, M)
-  return eigenvalues(M1)
-end
-
-@doc raw"""
-    eigenvalues_with_multiplicities(L::Field, M::MatElem{T}) where T <: RingElem
-
-Return the eigenvalues of `M` over the field `L` together with their algebraic
-multiplicities as a vector of tuples.
-"""
-function eigenvalues_with_multiplicities(L::Field, M::MatElem{T}) where T <: RingElem
-  @assert is_square(M)
-  M1 = change_base_ring(L, M)
-  return eigenvalues_with_multiplicities(M1)
-end
-
-@doc raw"""
-    eigenspace(M::MatElem{T}, lambda::T; side::Symbol = :left)
-      where T <: FieldElem -> Vector{MatElem{T}}
-
-Return a basis of the eigenspace of $M$ with respect to the eigenvalue $\lambda$.
-If side is `:right`, the right eigenspace is computed, i.e. vectors $v$ such that
-$Mv = \lambda v$. If side is `:left`, the left eigenspace is computed, i.e. vectors
-$v$ such that $vM = \lambda v$.
-"""
-function eigenspace(M::MatElem{T}, lambda::T; side::Symbol = :left) where T <: FieldElem
-  @assert is_square(M)
-  N = deepcopy(M)
-  for i = 1:ncols(N)
-    N[i, i] -= lambda
-  end
-  return kernel(N, side = side)
-end
-
-@doc raw"""
-    eigenspaces(M::MatElem{T}; side::Symbol = :left)
-      where T <: FieldElem -> Dict{T, MatElem{T}}
-
-Return a dictionary containing the eigenvalues of $M$ as keys and bases for the
-corresponding eigenspaces as values.
-If side is `:right`, the right eigenspaces are computed, if it is `:left` then the
-left eigenspaces are computed.
-
-See also `eigenspace`.
-"""
-function eigenspaces(M::MatElem{T}; side::Symbol = :left) where T<:FieldElem
-
-  S = eigenvalues(M)
-  L = Dict{elem_type(base_ring(M)), typeof(M)}()
-  for k in S
-    push!(L, k => vcat(eigenspace(M, k, side = side)))
-  end
-  return L
-end
diff --git a/src/matrix.jl b/src/matrix.jl
@@ -1,4 +1,8 @@
-# Support for view(A, :, i) and view(A, i, :)
+################################################################################
+#
+#  Support for view(A, :, i) and view(A, i, :)
+#
+################################################################################
 
 struct MatrixView{S, T} <: AbstractVector{T}
   A::S
@@ -26,7 +30,12 @@ function Base.view(x::_MatTypes, r::UnitRange{Int}, c::Int)
 	return MatrixView{typeof(x), typeof(base_ring(x))}(A)
 end
 
-# Generic kernel (calling nullspace in flint)
+################################################################################
+#
+#  Generic kernel (calling nullspace in flint)
+#
+################################################################################
+
 const _FieldMatTypes = Union{QQMatrix, fpMatrix, FpMatrix, FqMatrix, fqPolyRepMatrix, FqPolyRepMatrix}
 
 function kernel(A::_FieldMatTypes; side::Symbol = :left)
@@ -40,6 +49,12 @@ function kernel(A::_FieldMatTypes; side::Symbol = :left)
   return nullspace(A)[2]
 end
 
+################################################################################
+#
+#  Solve context functionality
+#
+################################################################################
+
 # Overwrite some solve context functionality so that it uses `transpose` and not
 # `lazy_transpose`
 
@@ -83,3 +98,98 @@ function Solve.kernel(C::Solve.SolveCtx{S, T}; side::Symbol = :left) where {S <:
     return transpose(X)
   end
 end
+
+################################################################################
+#
+#  Eigenvalues and eigenspaces
+#
+################################################################################
+
+@doc raw"""
+    eigenvalues(M::MatElem{T}) where T <: FieldElem
+
+Return the eigenvalues of `M`.
+"""
+function eigenvalues(M::MatElem{T}) where T <: FieldElem
+  @assert is_square(M)
+  K = base_ring(M)
+  f = charpoly(M)
+  return roots(f)
+end
+
+@doc raw"""
+    eigenvalues_with_multiplicities(M::MatElem{T}) where T <: FieldElem
+
+Return the eigenvalues of `M` together with their algebraic multiplicities as a
+vector of tuples.
+"""
+function eigenvalues_with_multiplicities(M::MatElem{T}) where T <: FieldElem
+  @assert is_square(M)
+  K = base_ring(M)
+  Kx, x = polynomial_ring(K, "x", cached = false)
+  f = charpoly(Kx, M)
+  r = roots(f)
+  return [ (a, valuation(f, x - a)) for a in r ]
+end
+
+@doc raw"""
+    eigenvalues(L::Field, M::MatElem{T}) where T <: RingElem
+
+Return the eigenvalues of `M` over the field `L`.
+"""
+function eigenvalues(L::Field, M::MatElem{T}) where T <: RingElem
+  @assert is_square(M)
+  M1 = change_base_ring(L, M)
+  return eigenvalues(M1)
+end
+
+@doc raw"""
+    eigenvalues_with_multiplicities(L::Field, M::MatElem{T}) where T <: RingElem
+
+Return the eigenvalues of `M` over the field `L` together with their algebraic
+multiplicities as a vector of tuples.
+"""
+function eigenvalues_with_multiplicities(L::Field, M::MatElem{T}) where T <: RingElem
+  @assert is_square(M)
+  M1 = change_base_ring(L, M)
+  return eigenvalues_with_multiplicities(M1)
+end
+
+@doc raw"""
+    eigenspace(M::MatElem{T}, lambda::T; side::Symbol = :left)
+      where T <: FieldElem -> Vector{MatElem{T}}
+
+Return a basis of the eigenspace of $M$ with respect to the eigenvalue $\lambda$.
+If side is `:right`, the right eigenspace is computed, i.e. vectors $v$ such that
+$Mv = \lambda v$. If side is `:left`, the left eigenspace is computed, i.e. vectors
+$v$ such that $vM = \lambda v$.
+"""
+function eigenspace(M::MatElem{T}, lambda::T; side::Symbol = :left) where T <: FieldElem
+  @assert is_square(M)
+  N = deepcopy(M)
+  for i = 1:ncols(N)
+    N[i, i] -= lambda
+  end
+  return kernel(N, side = side)
+end
+
+@doc raw"""
+    eigenspaces(M::MatElem{T}; side::Symbol = :left)
+      where T <: FieldElem -> Dict{T, MatElem{T}}
+
+Return a dictionary containing the eigenvalues of $M$ as keys and bases for the
+corresponding eigenspaces as values.
+If side is `:right`, the right eigenspaces are computed, if it is `:left` then the
+left eigenspaces are computed.
+
+See also `eigenspace`.
+"""
+function eigenspaces(M::MatElem{T}; side::Symbol = :left) where T<:FieldElem
+
+  S = eigenvalues(M)
+  L = Dict{elem_type(base_ring(M)), typeof(M)}()
+  for k in S
+    push!(L, k => vcat(eigenspace(M, k, side = side)))
+  end
+  return L
+end
diff --git a/test/HeckeMiscMatrix-test.jl → test/matrix-test.jl b/test/HeckeMiscMatrix-test.jl → test/matrix-test.jl