Use more FLINT methods for fmpz_mod_mat (#1966)

Co-authored-by: Tommy Hofmann <thofma@gmail.com>

src/flint/fmpz_mod_mat.jl

@@ -376,35 +376,27 @@ end
 #
 ################################################################################
 
-#= Not implemented in Flint yet
-
 function det(a::ZZModMatrix)
-!is_square(a) && error("Matrix must be a square matrix")
-if is_prime(a.n)
-r = @ccall libflint.fmpz_mod_mat_det(a::Ref{ZZModMatrix})::UInt
-return base_ring(a)(r)
-else
-try
-return AbstractAlgebra.det_fflu(a)
-catch
-return AbstractAlgebra.det_df(a)
-end
-end
+  !is_square(a) && error("Matrix must be a square matrix")
+  z = ZZRingElem()
+  r = @ccall libflint.fmpz_mod_mat_det(z::Ref{ZZRingElem}, a::Ref{ZZModMatrix}, base_ring(a).ninv::Ref{fmpz_mod_ctx_struct})::Nothing
+  return base_ring(a)(z)
 end
 
-=#
-
 ################################################################################
 #
 #  Rank
 #
 ################################################################################
 
-#= Not implemented in Flint yet
+#= There are some doubts whether fmpz_mod_mat_rank is what we want: there are
+several non-equivalent ways to define the rank of a matrix over a ring with
+zero divisors. FLINT does not seem to document what exactly fmpz_mod_mat_rank
+computes...
 
 function rank(a::T) where T <: Zmod_fmpz_mat
-r = @ccall libflint.fmpz_mod_mat_rank(a::Ref{T})::Int
-return r
+  r = @ccall libflint.fmpz_mod_mat_rank(a::Ref{T}, base_ring(a).ninv::Ref{fmpz_mod_ctx_struct})::Int
+  return r
 end
 
 =#
@@ -434,18 +426,14 @@ function inv(a::ZZModMatrix)
   end
 end
 
-#= Not implemented in Flint yet
-
 function inv(a::T) where T <: Zmod_fmpz_mat
-!is_square(a) && error("Matrix must be a square matrix")
-z = similar(a)
-r = @ccall libflint.fmpz_mod_mat_inv(z::Ref{T}, a::Ref{T})::Int
-!Bool(r) && error("Matrix not invertible")
-return z
+  !is_square(a) && error("Matrix must be a square matrix")
+  z = similar(a)
+  r = @ccall libflint.fmpz_mod_mat_inv(z::Ref{T}, a::Ref{T}, base_ring(a).ninv::Ref{fmpz_mod_ctx_struct})::Int
+  !Bool(r) && error("Matrix not invertible")
+  return z
 end
 
-=#
-
 ################################################################################
 #
 #  Linear solving
@@ -599,45 +587,20 @@ end
 #
 ################################################################################
 
-#= Not implemented in Flint yet
-
-@doc raw"""
-    lift(a::T) where {T <: Zmod_fmpz_mat}
-
-Return a lift of the matrix $a$ to a matrix over $\mathbb{Z}$, i.e. where the
-entries of the returned matrix are those of $a$ lifted to $\mathbb{Z}$.
-"""
-function lift(a::T) where {T <: Zmod_fmpz_mat}
-z = ZZMatrix(nrows(a), ncols(a))
-@ccall libflint.fmpz_mat_set_fmpz_mod_mat(z::Ref{ZZMatrix}, a::Ref{T})::Nothing
-return z
-end
-
 function lift!(z::ZZMatrix, a::T) where T <: Zmod_fmpz_mat
-@ccall libflint.fmpz_mat_set_fmpz_mod_mat(z::Ref{ZZMatrix}, a::Ref{T})::Nothing
-return z
+  @ccall libflint.fmpz_mod_mat_get_fmpz_mat(z::Ref{ZZMatrix}, a::Ref{T})::Nothing
+  return z
 end
 
-=#
-
 @doc raw"""
     lift(a::T) where {T <: Zmod_fmpz_mat}
 
 Return a lift of the matrix $a$ to a matrix over $\mathbb{Z}$, i.e. where the
 entries of the returned matrix are those of $a$ lifted to $\mathbb{Z}$.
 """
 function lift(a::Zmod_fmpz_mat)
-  z = zero_matrix(ZZ, nrows(a), ncols(a))
-  GC.@preserve a z begin
-    for i in 1:nrows(a)
-      for j in 1:ncols(a)
-        m = mat_entry_ptr(z, i, j)
-        n = mat_entry_ptr(a, i, j)
-        set!(m, n)
-      end
-    end
-  end
-  return z
+  z = ZZMatrix(nrows(a), ncols(a))
+  return lift!(z, a)
 end
 
 ################################################################################
@@ -646,33 +609,26 @@ end
 #
 ################################################################################
 
-#= Not implemented in Flint yet
-
 function charpoly(R::ZZModPolyRing, a::ZZModMatrix)
-m = deepcopy(a)
-p = R()
-@ccall libflint.fmpz_mod_mat_charpoly(p::Ref{ZZModPolyRingElem}, m::Ref{ZZModMatrix})::Nothing
-return p
+  @req base_ring(R) == base_ring(a) "base rings don't match'"
+  m = deepcopy(a)
+  p = R()
+  @ccall libflint.fmpz_mod_mat_charpoly(p::Ref{ZZModPolyRingElem}, m::Ref{ZZModMatrix}, base_ring(a).ninv::Ref{fmpz_mod_ctx_struct})::Nothing
+  return p
 end
 
-=#
-
 ################################################################################
 #
 #  Minimal polynomial
 #
 ################################################################################
 
-#= Not implemented in Flint yet
-
 function minpoly(R::ZZModPolyRing, a::ZZModMatrix)
-p = R()
-@ccall libflint.fmpz_mod_mat_minpoly(p::Ref{ZZModPolyRingElem}, a::Ref{ZZModMatrix})::Nothing
-return p
+  p = R()
+  @ccall libflint.fmpz_mod_mat_minpoly(p::Ref{ZZModPolyRingElem}, a::Ref{ZZModMatrix}, base_ring(a).ninv::Ref{fmpz_mod_ctx_struct})::Nothing
+  return p
 end
 
-=#
-
 ###############################################################################
 #
 #   Promotion rules

src/flint/gfp_fmpz_mat.jl

@@ -406,6 +406,17 @@ function lu(x::FpMatrix, P = SymmetricGroup(nrows(x)))
   return rank, p, L, U
 end
 
+################################################################################
+#
+#  Rank
+#
+################################################################################
+
+function rank(a::FpMatrix)
+  r = @ccall libflint.fmpz_mod_mat_rank(a::Ref{FpMatrix}, base_ring(a).ninv::Ref{fmpz_mod_ctx_struct})::Int
+  return r
+end
+
 ################################################################################
 #
 #  Entry pointers

test/flint/fmpz_mod_mat-test.jl

@@ -520,6 +520,13 @@ end
   R, = residue_ring(ZZ, 3^5)
   a = R[1;]
   @test @inferred isone(det(a))
+
+  for n in 2:12
+    R, = residue_ring(ZZ, ZZ(n))
+    a = matrix(R, [ 1 2 3 ; 4 5 6; 0 42 9])
+    @test det(a) == det(lift(a)) % modulus(R)
+    @test tr(a) == tr(lift(a)) % modulus(R)
+  end
 end
 
 @testset "ZZModMatrix.rank" begin