From d2b639670ee90512df447f2569a2d33365de6c69 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Lars=20G=C3=B6ttgens?= <lars.goettgens@rwth-aachen.de>
Date: Wed, 10 Apr 2024 15:41:39 +0200
Subject: [PATCH 01/19] Fix `force_coerce`

---
 src/AbstractAlgebra.jl | 4 ++--
 src/Deprecations.jl    | 3 ++-
 2 files changed, 4 insertions(+), 3 deletions(-)

diff --git a/src/AbstractAlgebra.jl b/src/AbstractAlgebra.jl
index 8c827886dc..2d43c57435 100644
--- a/src/AbstractAlgebra.jl
+++ b/src/AbstractAlgebra.jl
@@ -106,8 +106,8 @@ include("PrintHelper.jl")
 #   parent(b) == a && return a
 #   return force_coerce(a, b)
 #
-function force_coerce(a, b, throw_error::Type{Val{T}} = Val{true}) where {T}
-  if throw_error === Val{true}
+function force_coerce(a, b, throw_error::Val{T} = Val(true)) where {T}
+  if throw_error isa Val{true}
     error("coercion not possible")
   end
   return nothing
diff --git a/src/Deprecations.jl b/src/Deprecations.jl
index aa3046566a..7c73d0c644 100644
--- a/src/Deprecations.jl
+++ b/src/Deprecations.jl
@@ -40,4 +40,5 @@ end
 #
 ###############################################################################
 
-#= currently none =#
+# deprecated during 0.40.*
+@deprecate force_coerce(a, b, throw_error::Type{Val{T}}) where {T} force_coerce(a, b, Val(T))

From 637f63739652e370206b90e4f225bce05ba2ba60 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Lars=20G=C3=B6ttgens?= <lars.goettgens@rwth-aachen.de>
Date: Wed, 10 Apr 2024 15:42:12 +0200
Subject: [PATCH 02/19] Fix `force_op`

---
 src/AbstractAlgebra.jl | 6 +++---
 src/Deprecations.jl    | 1 +
 2 files changed, 4 insertions(+), 3 deletions(-)

diff --git a/src/AbstractAlgebra.jl b/src/AbstractAlgebra.jl
index 2d43c57435..30cfd92d98 100644
--- a/src/AbstractAlgebra.jl
+++ b/src/AbstractAlgebra.jl
@@ -117,15 +117,15 @@ end
 # a common over structure
 # designed(?) to be minimally invasive in AA and Nemo, but filled with
 # content in Hecke/Oscar
-function force_op(op::Function, throw_error::Type{Val{T}}, a...) where {T}
-  if throw_error === Val{true}
+function force_op(op::Function, throw_error::Val{T}, a...) where {T}
+  if throw_error isa Val{true}
     error("no common overstructure for the arguments found")
   end
   return false
 end
 
 function force_op(op::Function, a...)
-  return force_op(op, Val{true}, a...)
+  return force_op(op, Val(true), a...)
 end
 
 ###############################################################################
diff --git a/src/Deprecations.jl b/src/Deprecations.jl
index 7c73d0c644..96ee256e5d 100644
--- a/src/Deprecations.jl
+++ b/src/Deprecations.jl
@@ -42,3 +42,4 @@ end
 
 # deprecated during 0.40.*
 @deprecate force_coerce(a, b, throw_error::Type{Val{T}}) where {T} force_coerce(a, b, Val(T))
+@deprecate force_op(op::Function, throw_error::Type{Val{T}}, a...) where {T} force_op(op, Val(T), a...)

From 7e89d3af09136064bf6094e52d6519b521ace547 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Lars=20G=C3=B6ttgens?= <lars.goettgens@rwth-aachen.de>
Date: Wed, 10 Apr 2024 15:42:56 +0200
Subject: [PATCH 03/19] Fix `_hnf_minors!`

---
 src/Deprecations.jl |  1 +
 src/Matrix.jl       | 26 ++++++++++++--------------
 2 files changed, 13 insertions(+), 14 deletions(-)

diff --git a/src/Deprecations.jl b/src/Deprecations.jl
index 96ee256e5d..2da633c1fc 100644
--- a/src/Deprecations.jl
+++ b/src/Deprecations.jl
@@ -43,3 +43,4 @@ end
 # deprecated during 0.40.*
 @deprecate force_coerce(a, b, throw_error::Type{Val{T}}) where {T} force_coerce(a, b, Val(T))
 @deprecate force_op(op::Function, throw_error::Type{Val{T}}, a...) where {T} force_op(op, Val(T), a...)
+@deprecate _hnf_minors!(H::MatrixElem{T}, U::MatrixElem{T}, with_transform::Type{Val{S}}) where {T <: RingElement, S} _hnf_minors!(H, U, Val(S))
diff --git a/src/Matrix.jl b/src/Matrix.jl
index 0eba74ea38..9ce57835ab 100644
--- a/src/Matrix.jl
+++ b/src/Matrix.jl
@@ -4462,7 +4462,7 @@ Kannan-Bachem. The input must have full column rank.
 """
 function hnf_minors(A::MatrixElem{T}) where {T <: RingElement}
    H = deepcopy(A)
-   _hnf_minors!(H, similar(A, 0, 0), Val{false})
+   _hnf_minors!(H, similar(A, 0, 0), Val(false))
    return H
 end
 
@@ -4476,11 +4476,11 @@ have full column rank.
 function hnf_minors_with_transform(A::MatrixElem{T}) where {T <: RingElement}
    H = deepcopy(A)
    U = similar(A, nrows(A), nrows(A))
-   _hnf_minors!(H, U, Val{true})
+   _hnf_minors!(H, U, Val(true))
    return H, U
 end
 
-function _hnf_minors!(H::MatrixElem{T}, U::MatrixElem{T}, with_transform::Type{Val{S}} = Val{false}) where {T <: RingElement, S}
+function _hnf_minors!(H::MatrixElem{T}, U::MatrixElem{T}, ::Val{with_transform} = Val(false)) where {T <: RingElement, with_transform}
    m = nrows(H)
    n = ncols(H)
 
@@ -4489,9 +4489,7 @@ function _hnf_minors!(H::MatrixElem{T}, U::MatrixElem{T}, with_transform::Type{V
 
    R = base_ring(H)
 
-   with_trafo = with_transform == Val{true} ? true : false
-
-   if with_trafo
+   if with_transform
       for i in 1:m
          for j in 1:m
             if j == i
@@ -4546,7 +4544,7 @@ function _hnf_minors!(H::MatrixElem{T}, U::MatrixElem{T}, with_transform::Type{V
                t = mul!(t, q, H[j, j2])
                H[k, j2] = add!(H[k, j2], H[k, j2], t)
             end
-            if with_trafo
+            if with_transform
                for j2 in 1:m
                   t = mul!(t, q, U[j, j2])
                   U[k, j2] = add!(U[k, j2], U[k, j2], t)
@@ -4572,7 +4570,7 @@ function _hnf_minors!(H::MatrixElem{T}, U::MatrixElem{T}, with_transform::Type{V
             H[k, j2] = reduce!(H[k, j2])
             H[j, j2] = reduce!(H[j, j2])
          end
-         if with_trafo
+         if with_transform
             for j2 in 1:m
                b = mul_red!(b, u, U[j, j2], false)
                t2 = mul_red!(t2, v, U[k, j2], false)
@@ -4588,7 +4586,7 @@ function _hnf_minors!(H::MatrixElem{T}, U::MatrixElem{T}, with_transform::Type{V
 
       if is_zero_entry(H, k, k)
          swap_rows!(H, k, l)
-         if with_trafo
+         if with_transform
             swap_rows!(U, k, l)
          end
          l = l - 1
@@ -4602,7 +4600,7 @@ function _hnf_minors!(H::MatrixElem{T}, U::MatrixElem{T}, with_transform::Type{V
          for j in k:n
             H[k, j] = mul!(H[k, j], H[k, j], u)
          end
-         if with_trafo
+         if with_transform
             for j in 1:m
                U[k, j] = mul!(U[k, j], U[k, j], u)
             end
@@ -4620,7 +4618,7 @@ function _hnf_minors!(H::MatrixElem{T}, U::MatrixElem{T}, with_transform::Type{V
                t = mul!(t, q, H[j, j2])
                H[i, j2] = add!(H[i, j2], H[i, j2], t)
             end
-            if with_trafo
+            if with_transform
                for j2 in 1:m
                   t = mul!(t, q, U[j, j2])
                   U[i, j2] = add!(U[i, j2], U[i, j2], t)
@@ -4658,7 +4656,7 @@ function _hnf_minors!(H::MatrixElem{T}, U::MatrixElem{T}, with_transform::Type{V
                t = mul!(t, q, H[j, j2])
                H[k, j2] = add!(H[k, j2], H[k, j2], t)
             end
-            if with_trafo
+            if with_transform
                for j2 in 1:m
                   t = mul!(t, q, U[j, j2])
                   U[k, j2] = add!(U[k, j2], U[k, j2], t)
@@ -4681,7 +4679,7 @@ function _hnf_minors!(H::MatrixElem{T}, U::MatrixElem{T}, with_transform::Type{V
             H[k, j2] = reduce!(H[k, j2])
             H[j, j2] = reduce!(H[j, j2])
          end
-         if with_trafo
+         if with_transform
             for j2 in 1:m
                b = mul_red!(b, u, U[j, j2], false)
                t2 = mul_red!(t2, v, U[k, j2], false)
@@ -4705,7 +4703,7 @@ function _hnf_minors!(H::MatrixElem{T}, U::MatrixElem{T}, with_transform::Type{V
                t = mul!(t, q, H[j, j2])
                H[i, j2] = add!(H[i, j2], H[i, j2], t)
             end
-            if with_trafo
+            if with_transform
                for j2 in 1:m
                   t = mul!(t, q, U[j, j2])
                   U[i, j2] = add!(U[i, j2], U[i, j2], t)

From abf3bb3ade47e4ccc202c4e98416e4fce212e3aa Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Lars=20G=C3=B6ttgens?= <lars.goettgens@rwth-aachen.de>
Date: Wed, 10 Apr 2024 15:47:54 +0200
Subject: [PATCH 04/19] Fix `_hnf_kb`

---
 src/Deprecations.jl | 1 +
 src/Matrix.jl       | 8 ++++----
 2 files changed, 5 insertions(+), 4 deletions(-)

diff --git a/src/Deprecations.jl b/src/Deprecations.jl
index 2da633c1fc..16ded15543 100644
--- a/src/Deprecations.jl
+++ b/src/Deprecations.jl
@@ -44,3 +44,4 @@ end
 @deprecate force_coerce(a, b, throw_error::Type{Val{T}}) where {T} force_coerce(a, b, Val(T))
 @deprecate force_op(op::Function, throw_error::Type{Val{T}}, a...) where {T} force_op(op, Val(T), a...)
 @deprecate _hnf_minors!(H::MatrixElem{T}, U::MatrixElem{T}, with_transform::Type{Val{S}}) where {T <: RingElement, S} _hnf_minors!(H, U, Val(S))
+@deprecate _hnf_kb(A, trafo::Type{Val{T}} = Val{false}) where T _hnf_kb(A, Val(T))
diff --git a/src/Matrix.jl b/src/Matrix.jl
index 9ce57835ab..b010164996 100644
--- a/src/Matrix.jl
+++ b/src/Matrix.jl
@@ -4725,7 +4725,7 @@ Compute the upper right row Hermite normal form of $A$ using a modification
 of the algorithm of Kannan-Bachem.
 """
 function hnf_kb(A::MatrixElem{T}) where {T <: RingElement}
-   return _hnf_kb(A, Val{false})
+   return _hnf_kb(A, Val(false))
 end
 
 @doc raw"""
@@ -4736,13 +4736,13 @@ matrix $U$ with $UA = H$ using a modification of the algorithm of
 Kannan-Bachem.
 """
 function hnf_kb_with_transform(A::MatrixElem{T}) where {T <: RingElement}
-   return _hnf_kb(A, Val{true})
+   return _hnf_kb(A, Val(true))
 end
 
-function _hnf_kb(A, trafo::Type{Val{T}} = Val{false}) where T
+function _hnf_kb(A, ::Val{with_transform} = Val(false)) where {with_transform}
    H = deepcopy(A)
    m = nrows(H)
-   if trafo == Val{true}
+   if with_transform
       U = identity_matrix(A, m)
       hnf_kb!(H, U, true)
       return H, U

From a4cf07157558de7749423524f0af3d4eb5f33858 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Lars=20G=C3=B6ttgens?= <lars.goettgens@rwth-aachen.de>
Date: Wed, 10 Apr 2024 15:49:58 +0200
Subject: [PATCH 05/19] Fix `_snf_kb`

---
 src/Deprecations.jl | 1 +
 src/Matrix.jl       | 8 ++++----
 2 files changed, 5 insertions(+), 4 deletions(-)

diff --git a/src/Deprecations.jl b/src/Deprecations.jl
index 16ded15543..a32bceb606 100644
--- a/src/Deprecations.jl
+++ b/src/Deprecations.jl
@@ -45,3 +45,4 @@ end
 @deprecate force_op(op::Function, throw_error::Type{Val{T}}, a...) where {T} force_op(op, Val(T), a...)
 @deprecate _hnf_minors!(H::MatrixElem{T}, U::MatrixElem{T}, with_transform::Type{Val{S}}) where {T <: RingElement, S} _hnf_minors!(H, U, Val(S))
 @deprecate _hnf_kb(A, trafo::Type{Val{T}} = Val{false}) where T _hnf_kb(A, Val(T))
+@deprecate _snf_kb(A::MatrixElem{T}, trafo::Type{Val{V}} = Val{false}) where {V, T <: RingElement} _snf_kb(A, Val(V))
diff --git a/src/Matrix.jl b/src/Matrix.jl
index b010164996..1c4f333565 100644
--- a/src/Matrix.jl
+++ b/src/Matrix.jl
@@ -5039,18 +5039,18 @@ function is_snf(A::MatrixElem{T}) where T <: RingElement
 end
 
 function snf_kb(A::MatrixElem{T}) where {T <: RingElement}
-   return _snf_kb(A, Val{false})
+   return _snf_kb(A, Val(false))
 end
 
 function snf_kb_with_transform(A::MatrixElem{T}) where {T <: RingElement}
-   return _snf_kb(A, Val{true})
+   return _snf_kb(A, Val(true))
 end
 
-function _snf_kb(A::MatrixElem{T}, trafo::Type{Val{V}} = Val{false}) where {V, T <: RingElement}
+function _snf_kb(A::MatrixElem{T}, ::Val{with_transform} = Val(false)) where {T <: RingElement, with_transform}
    S = deepcopy(A)
    m = nrows(S)
    n = ncols(S)
-   if trafo == Val{true}
+   if with_transform
       U = identity_matrix(A, m)
       K = identity_matrix(A, n)
       snf_kb!(S, U, K, true)

From 0ff15e8eff5836bcd3f4b7510c56ab4bc8720acc Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Lars=20G=C3=B6ttgens?= <lars.goettgens@rwth-aachen.de>
Date: Wed, 10 Apr 2024 15:51:51 +0200
Subject: [PATCH 06/19] Fix `_weak_popov`

---
 src/Deprecations.jl | 1 +
 src/Matrix.jl       | 8 ++++----
 2 files changed, 5 insertions(+), 4 deletions(-)

diff --git a/src/Deprecations.jl b/src/Deprecations.jl
index a32bceb606..89dcbb89fd 100644
--- a/src/Deprecations.jl
+++ b/src/Deprecations.jl
@@ -46,3 +46,4 @@ end
 @deprecate _hnf_minors!(H::MatrixElem{T}, U::MatrixElem{T}, with_transform::Type{Val{S}}) where {T <: RingElement, S} _hnf_minors!(H, U, Val(S))
 @deprecate _hnf_kb(A, trafo::Type{Val{T}} = Val{false}) where T _hnf_kb(A, Val(T))
 @deprecate _snf_kb(A::MatrixElem{T}, trafo::Type{Val{V}} = Val{false}) where {V, T <: RingElement} _snf_kb(A, Val(V))
+@deprecate _weak_popov(A::MatElem{T}, trafo::Type{Val{S}} = Val{false}) where {T <: PolyRingElem, S} _weak_popov(A, Val(S))
diff --git a/src/Matrix.jl b/src/Matrix.jl
index 1c4f333565..85b28fc83a 100644
--- a/src/Matrix.jl
+++ b/src/Matrix.jl
@@ -5273,7 +5273,7 @@ end
 Return the weak Popov form of $A$.
 """
 function weak_popov(A::MatElem{T}) where {T <: PolyRingElem}
-   return _weak_popov(A, Val{false})
+   return _weak_popov(A, Val(false))
 end
 
 @doc raw"""
@@ -5283,14 +5283,14 @@ Compute a tuple $(P, U)$ where $P$ is the weak Popov form of $A$ and $U$
 is a transformation matrix so that $P = UA$.
 """
 function weak_popov_with_transform(A::MatElem{T}) where {T <: PolyRingElem}
-   return _weak_popov(A, Val{true})
+   return _weak_popov(A, Val(true))
 end
 
-function _weak_popov(A::MatElem{T}, trafo::Type{Val{S}} = Val{false}) where {T <: PolyRingElem, S}
+function _weak_popov(A::MatElem{T}, ::Val{with_transform} = Val(false)) where {T <: PolyRingElem, with_transform}
    P = deepcopy(A)
    m = nrows(P)
    W = similar(A, 0, 0)
-   if trafo == Val{true}
+   if with_transform
       U = identity_matrix(A, m)
       weak_popov!(P, W, U, false, true)
       return P, U

From 332baaf9e99900c01f0bf17a002e8307c56df35c Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Lars=20G=C3=B6ttgens?= <lars.goettgens@rwth-aachen.de>
Date: Wed, 10 Apr 2024 15:54:44 +0200
Subject: [PATCH 07/19] Fix `_extended_weak_popov`

---
 src/Deprecations.jl | 1 +
 src/Matrix.jl       | 8 ++++----
 2 files changed, 5 insertions(+), 4 deletions(-)

diff --git a/src/Deprecations.jl b/src/Deprecations.jl
index 89dcbb89fd..c276bc25ee 100644
--- a/src/Deprecations.jl
+++ b/src/Deprecations.jl
@@ -47,3 +47,4 @@ end
 @deprecate _hnf_kb(A, trafo::Type{Val{T}} = Val{false}) where T _hnf_kb(A, Val(T))
 @deprecate _snf_kb(A::MatrixElem{T}, trafo::Type{Val{V}} = Val{false}) where {V, T <: RingElement} _snf_kb(A, Val(V))
 @deprecate _weak_popov(A::MatElem{T}, trafo::Type{Val{S}} = Val{false}) where {T <: PolyRingElem, S} _weak_popov(A, Val(S))
+@deprecate _extended_weak_popov(A::MatElem{T}, V::MatElem{T}, trafo::Type{Val{S}} = Val{false}) where {T <: PolyRingElem, S} _extended_weak_popov(A, V, Val(S))
diff --git a/src/Matrix.jl b/src/Matrix.jl
index 85b28fc83a..88facfb629 100644
--- a/src/Matrix.jl
+++ b/src/Matrix.jl
@@ -5309,7 +5309,7 @@ on $A$ and a vector $W$ by applying the same transformations on the vector $V$.
 Return the tuple $(P, W)$.
 """
 function extended_weak_popov(A::MatElem{T}, V::MatElem{T}) where {T <: PolyRingElem}
-   return _extended_weak_popov(A, V, Val{false})
+   return _extended_weak_popov(A, V, Val(false))
 end
 
 @doc raw"""
@@ -5321,15 +5321,15 @@ and a transformation matrix $U$ so that $P = UA$.
 Return the tuple $(P, W, U)$.
 """
 function extended_weak_popov_with_transform(A::MatElem{T}, V::MatElem{T}) where {T <: PolyRingElem}
-   return _extended_weak_popov(A, V, Val{true})
+   return _extended_weak_popov(A, V, Val(true))
 end
 
-function _extended_weak_popov(A::MatElem{T}, V::MatElem{T}, trafo::Type{Val{S}} = Val{false}) where {T <: PolyRingElem, S}
+function _extended_weak_popov(A::MatElem{T}, V::MatElem{T}, ::Val{with_transform} = Val(false)) where {T <: PolyRingElem, with_transform}
    @assert nrows(V) == nrows(A) && ncols(V) == 1
    P = deepcopy(A)
    W = deepcopy(V)
    m = nrows(P)
-   if trafo == Val{true}
+   if with_transform
       U = identity_matrix(A)
       weak_popov!(P, W, U, true, true)
       return P, W, U

From 498c7c81245e7f5052fbc418b5334fc18fc01bef Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Lars=20G=C3=B6ttgens?= <lars.goettgens@rwth-aachen.de>
Date: Wed, 10 Apr 2024 16:02:49 +0200
Subject: [PATCH 08/19] Fix `_popov`

---
 src/Deprecations.jl | 9 +++++----
 src/Matrix.jl       | 8 ++++----
 2 files changed, 9 insertions(+), 8 deletions(-)

diff --git a/src/Deprecations.jl b/src/Deprecations.jl
index c276bc25ee..998ec65e7d 100644
--- a/src/Deprecations.jl
+++ b/src/Deprecations.jl
@@ -44,7 +44,8 @@ end
 @deprecate force_coerce(a, b, throw_error::Type{Val{T}}) where {T} force_coerce(a, b, Val(T))
 @deprecate force_op(op::Function, throw_error::Type{Val{T}}, a...) where {T} force_op(op, Val(T), a...)
 @deprecate _hnf_minors!(H::MatrixElem{T}, U::MatrixElem{T}, with_transform::Type{Val{S}}) where {T <: RingElement, S} _hnf_minors!(H, U, Val(S))
-@deprecate _hnf_kb(A, trafo::Type{Val{T}} = Val{false}) where T _hnf_kb(A, Val(T))
-@deprecate _snf_kb(A::MatrixElem{T}, trafo::Type{Val{V}} = Val{false}) where {V, T <: RingElement} _snf_kb(A, Val(V))
-@deprecate _weak_popov(A::MatElem{T}, trafo::Type{Val{S}} = Val{false}) where {T <: PolyRingElem, S} _weak_popov(A, Val(S))
-@deprecate _extended_weak_popov(A::MatElem{T}, V::MatElem{T}, trafo::Type{Val{S}} = Val{false}) where {T <: PolyRingElem, S} _extended_weak_popov(A, V, Val(S))
+@deprecate _hnf_kb(A, trafo::Type{Val{T}}) where T _hnf_kb(A, Val(T))
+@deprecate _snf_kb(A::MatrixElem{T}, trafo::Type{Val{V}}) where {V, T <: RingElement} _snf_kb(A, Val(V))
+@deprecate _weak_popov(A::MatElem{T}, trafo::Type{Val{S}}) where {T <: PolyRingElem, S} _weak_popov(A, Val(S))
+@deprecate _extended_weak_popov(A::MatElem{T}, V::MatElem{T}, trafo::Type{Val{S}}) where {T <: PolyRingElem, S} _extended_weak_popov(A, V, Val(S))
+@deprecate  _popov(A::MatElem{T}, trafo::Type{Val{S}}) where {T <: PolyRingElem, S} _popov(A, Val(S))
diff --git a/src/Matrix.jl b/src/Matrix.jl
index 88facfb629..4fb915aee6 100644
--- a/src/Matrix.jl
+++ b/src/Matrix.jl
@@ -5545,7 +5545,7 @@ end
 Return the Popov form of $A$.
 """
 function popov(A::MatElem{T}) where {T <: PolyRingElem}
-   return _popov(A, Val{false})
+   return _popov(A, Val(false))
 end
 
 @doc raw"""
@@ -5555,13 +5555,13 @@ Compute a tuple $(P, U)$ where $P$ is the Popov form of $A$ and $U$
 is a transformation matrix so that $P = UA$.
 """
 function popov_with_transform(A::MatElem{T}) where {T <: PolyRingElem}
-   return _popov(A, Val{true})
+   return _popov(A, Val(true))
 end
 
-function _popov(A::MatElem{T}, trafo::Type{Val{S}} = Val{false}) where {T <: PolyRingElem, S}
+function _popov(A::MatElem{T}, ::Val{with_transform} = Val(false)) where {T <: PolyRingElem, with_transform}
    P = deepcopy(A)
    m = nrows(P)
-   if trafo == Val{true}
+   if with_transform
       U = identity_matrix(A, m)
       popov!(P, U, true)
       return P, U

From eed3011b4a4b3172d4b804d88914e39d957ed5d2 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Lars=20G=C3=B6ttgens?= <lars.goettgens@rwth-aachen.de>
Date: Wed, 10 Apr 2024 16:05:07 +0200
Subject: [PATCH 09/19] Fix `_hnf_via_popov`

---
 src/Deprecations.jl | 3 ++-
 src/Matrix.jl       | 8 ++++----
 2 files changed, 6 insertions(+), 5 deletions(-)

diff --git a/src/Deprecations.jl b/src/Deprecations.jl
index 998ec65e7d..6d5f6de27e 100644
--- a/src/Deprecations.jl
+++ b/src/Deprecations.jl
@@ -48,4 +48,5 @@ end
 @deprecate _snf_kb(A::MatrixElem{T}, trafo::Type{Val{V}}) where {V, T <: RingElement} _snf_kb(A, Val(V))
 @deprecate _weak_popov(A::MatElem{T}, trafo::Type{Val{S}}) where {T <: PolyRingElem, S} _weak_popov(A, Val(S))
 @deprecate _extended_weak_popov(A::MatElem{T}, V::MatElem{T}, trafo::Type{Val{S}}) where {T <: PolyRingElem, S} _extended_weak_popov(A, V, Val(S))
-@deprecate  _popov(A::MatElem{T}, trafo::Type{Val{S}}) where {T <: PolyRingElem, S} _popov(A, Val(S))
+@deprecate _popov(A::MatElem{T}, trafo::Type{Val{S}}) where {T <: PolyRingElem, S} _popov(A, Val(S))
+@deprecate _hnf_via_popov(A::MatElem{T}, trafo::Type{Val{S}}) where {T <: PolyRingElem, S} _hnf_via_popov(A, Val(S))
diff --git a/src/Matrix.jl b/src/Matrix.jl
index 4fb915aee6..b533554bd6 100644
--- a/src/Matrix.jl
+++ b/src/Matrix.jl
@@ -5686,17 +5686,17 @@ function popov!(P::MatElem{T}, U::MatElem{T}, with_trafo::Bool = false) where {T
 end
 
 function hnf_via_popov(A::MatElem{T}) where {T <: PolyRingElem}
-   return _hnf_via_popov(A, Val{false})
+   return _hnf_via_popov(A, Val(false))
 end
 
 function hnf_via_popov_with_transform(A::MatElem{T}) where {T <: PolyRingElem}
-   return _hnf_via_popov(A, Val{true})
+   return _hnf_via_popov(A, Val(true))
 end
 
-function _hnf_via_popov(A::MatElem{T}, trafo::Type{Val{S}} = Val{false}) where {T <: PolyRingElem, S}
+function _hnf_via_popov(A::MatElem{T}, ::Val{with_transform} = Val(false)) where {T <: PolyRingElem, with_transform}
    H = deepcopy(A)
    m = nrows(H)
-   if trafo == Val{true}
+   if with_transform
       U = identity_matrix(A, m)
       hnf_via_popov!(H, U, true)
       return H, U

From 421423054202da19c1cf2b9946dbed9b78bf3311 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Lars=20G=C3=B6ttgens?= <lars.goettgens@rwth-aachen.de>
Date: Wed, 10 Apr 2024 16:13:08 +0200
Subject: [PATCH 10/19] Add some inference tests to matrix functions

---
 test/generic/MatRing-test.jl | 24 ++++++-------
 test/generic/Matrix-test.jl  | 70 ++++++++++++++++++------------------
 2 files changed, 47 insertions(+), 47 deletions(-)

diff --git a/test/generic/MatRing-test.jl b/test/generic/MatRing-test.jl
index 05dadcaa38..ba95c0243c 100644
--- a/test/generic/MatRing-test.jl
+++ b/test/generic/MatRing-test.jl
@@ -1339,10 +1339,10 @@ if false # see bug 160
 
         A = M(map(R, Any[0 0 0; x^3+1 x^2 0; 0 x^2 x^5]))
 
-        H = hnf_minors(A)
+        H = @inferred hnf_minors(A)
         @test is_upper_triangular(H)
 
-        H, U = hnf_minors_with_transform(A)
+        H, U = @inferred hnf_minors_with_transform(A)
         @test is_upper_triangular(H)
         @test is_unit(det(U))
         @test U*A == H
@@ -1358,10 +1358,10 @@ if false # see bug 160
 
         B = N(map(S, Any[1 0 a 0; a*y^3 0 3*a^2 0; y^4+a 0 y^2+y 5; y 1 y 2]))
 
-        H = hnf_minors(B)
+        H = @inferred hnf_minors(B)
         @test is_upper_triangular(H)
 
-        H, U = hnf_minors_with_transform(B)
+        H, U = @inferred hnf_minors_with_transform(B)
         @test is_upper_triangular(H)
         @test is_unit(det(U))
         @test U*B == H
@@ -1375,10 +1375,10 @@ end
 
    A = M(map(R, Any[0 0 0; x^3+1 x^2 0; 0 x^2 x^5]))
 
-   H = AbstractAlgebra.hnf_kb(A)
+   H = @inferred AbstractAlgebra.hnf_kb(A)
    @test is_upper_triangular(H)
 
-   H, U = AbstractAlgebra.hnf_kb_with_transform(A)
+   H, U = @inferred AbstractAlgebra.hnf_kb_with_transform(A)
    @test is_upper_triangular(H)
    @test is_unit(det(U))
    @test U*A == H
@@ -1394,10 +1394,10 @@ end
 
    B = N(map(S, Any[1 0 a; a*y^3 0 3*a^2; y^4+a 0 y^2+y]))
 
-   H = AbstractAlgebra.hnf_kb(B)
+   H = @inferred AbstractAlgebra.hnf_kb(B)
    @test is_upper_triangular(H)
 
-   H, U = AbstractAlgebra.hnf_kb_with_transform(B)
+   H, U = @inferred AbstractAlgebra.hnf_kb_with_transform(B)
    @test is_upper_triangular(H)
    @test is_unit(det(U))
    @test U*B == H
@@ -1480,10 +1480,10 @@ end
 
    A = M(map(R, Any[0 0 0; x^3+1 x^2 0; 0 x^2 x^5]))
 
-   T = AbstractAlgebra.snf_kb(A)
+   T = @inferred AbstractAlgebra.snf_kb(A)
    @test is_snf(T)
 
-   T, U, K = AbstractAlgebra.snf_kb_with_transform(A)
+   T, U, K = @inferred AbstractAlgebra.snf_kb_with_transform(A)
    @test is_snf(T)
    @test is_unit(det(U))
    @test is_unit(det(K))
@@ -1500,10 +1500,10 @@ end
 
    B = N(map(S, Any[1 0 a; a*y^3 0 3*a^2; y^4+a 0 y^2+y]))
 
-   T = AbstractAlgebra.snf_kb(B)
+   T = @inferred AbstractAlgebra.snf_kb(B)
    @test is_snf(T)
 
-   T, U, K = AbstractAlgebra.snf_kb_with_transform(B)
+   T, U, K = @inferred AbstractAlgebra.snf_kb_with_transform(B)
    @test is_snf(T)
    @test is_unit(det(U))
    @test is_unit(det(K))
diff --git a/test/generic/Matrix-test.jl b/test/generic/Matrix-test.jl
index 81ecda2d73..510a84daa8 100644
--- a/test/generic/Matrix-test.jl
+++ b/test/generic/Matrix-test.jl
@@ -3584,10 +3584,10 @@ end
 
    A = M(map(R, Any[0 0 0; x^3+1 x^2 0; 0 x^2 x^5; x^4+1 x^2 x^5+x^3]))
 
-   H = hnf_minors(A)
+   H = @inferred hnf_minors(A)
    @test is_hnf(H)
 
-   H, U = hnf_minors_with_transform(A)
+   H, U = @inferred hnf_minors_with_transform(A)
    @test is_hnf(H)
    @test is_unit(det(U))
    @test U*A == H
@@ -3603,10 +3603,10 @@ end
 
    B = N(map(S, Any[1 0 a 0; a*y^3 0 3*a^2 0; y^4+a 0 y^2+y 5; y 1 y 2]))
 
-   H = hnf_minors(B)
+   H = @inferred hnf_minors(B)
    @test is_hnf(H)
 
-   H, U = hnf_minors_with_transform(B)
+   H, U = @inferred hnf_minors_with_transform(B)
    @test is_hnf(H)
    @test is_unit(det(U))
    @test U*B == H
@@ -3615,7 +3615,7 @@ end
 @testset "Generic.Mat.hnf_kb" begin
    M = matrix(ZZ, BigInt[4 6 2; 0 0 10; 0 5 3])
 
-   H, U = AbstractAlgebra.hnf_kb_with_transform(M)
+   H, U = @inferred AbstractAlgebra.hnf_kb_with_transform(M)
 
    @test H == matrix(ZZ, BigInt[4 1 9; 0 5 3; 0 0 10])
    @test is_unit(det(U))
@@ -3627,10 +3627,10 @@ end
 
    A = M(map(R, Any[0 0 0; x^3+1 x^2 0; 0 x^2 x^5; x^4+1 x^2 x^5+x^3]))
 
-   H = AbstractAlgebra.hnf_kb(A)
+   H = @inferred AbstractAlgebra.hnf_kb(A)
    @test is_hnf(H)
 
-   H, U = AbstractAlgebra.hnf_kb_with_transform(A)
+   H, U = @inferred AbstractAlgebra.hnf_kb_with_transform(A)
    @test is_hnf(H)
    @test is_unit(det(U))
    @test U*A == H
@@ -3646,10 +3646,10 @@ end
 
    B = N(map(S, Any[1 0 a 0; a*y^3 0 3*a^2 0; y^4+a 0 y^2+y 5]))
 
-   H = AbstractAlgebra.hnf_kb(B)
+   H = @inferred AbstractAlgebra.hnf_kb(B)
    @test is_hnf(H)
 
-   H, U = AbstractAlgebra.hnf_kb_with_transform(B)
+   H, U = @inferred AbstractAlgebra.hnf_kb_with_transform(B)
    @test is_hnf(H)
    @test is_unit(det(U))
    @test U*B == H
@@ -3755,10 +3755,10 @@ end
 
    A = M(map(R, Any[0 0 0; x^3+1 x^2 0; 0 x^2 x^5; x^4+1 x^2 x^5+x^3]))
 
-   T = AbstractAlgebra.snf_kb(A)
+   T = @inferred AbstractAlgebra.snf_kb(A)
    @test is_snf(T)
 
-   T, U, K = AbstractAlgebra.snf_kb_with_transform(A)
+   T, U, K = @inferred AbstractAlgebra.snf_kb_with_transform(A)
    @test is_snf(T)
    @test is_unit(det(U))
    @test is_unit(det(K))
@@ -3775,10 +3775,10 @@ end
 
    B = N(map(S, Any[1 0 a 0; a*y^3 0 3*a^2 0; y^4+a 0 y^2+y 5]))
 
-   T = AbstractAlgebra.snf_kb(B)
+   T = @inferred AbstractAlgebra.snf_kb(B)
    @test is_snf(T)
 
-   T, U, K = AbstractAlgebra.snf_kb_with_transform(B)
+   T, U, K = @inferred AbstractAlgebra.snf_kb_with_transform(B)
    @test is_snf(T)
    @test is_unit(det(U))
    @test is_unit(det(K))
@@ -3851,10 +3851,10 @@ end
    A = matrix(R, map(R, Any[1 2 3 x; x 2*x 3*x x^2; x x^2+1 x^3+x^2 x^4+x^2+1]))
    r = 2 # == rank(A)
 
-   P = weak_popov(A)
+   P = @inferred weak_popov(A)
    @test is_weak_popov(P, r)
 
-   P, U = weak_popov_with_transform(A)
+   P, U = @inferred weak_popov_with_transform(A)
    @test is_weak_popov(P, r)
    @test U*A == P
    @test is_unit(det(U))
@@ -3866,10 +3866,10 @@ end
    B = matrix(S, map(S, Any[ 4*y^2+3*y+5 4*y^2+3*y+4 6*y^2+1; 3*y+6 3*y+5 y+3; 6*y^2+4*y+2 6*y^2 2*y^2+y]))
    s = 2 # == rank(B)
 
-   P = weak_popov(B)
+   P = @inferred weak_popov(B)
    @test is_weak_popov(P, s)
 
-   P, U = weak_popov_with_transform(B)
+   P, U = @inferred weak_popov_with_transform(B)
    @test is_weak_popov(P, s)
    @test U*B == P
    @test is_unit(det(U))
@@ -3880,10 +3880,10 @@ end
       M = matrix_space(polynomial_ring(QQ, "x")[1], rand(1:5), rand(1:5))
       A = rand(M, -1:5, -5:5)
       r = rank(A)
-      P = weak_popov(A)
+      P = @inferred weak_popov(A)
       @test is_weak_popov(P, r)
 
-      P, U = weak_popov_with_transform(A)
+      P, U = @inferred weak_popov_with_transform(A)
       @test is_weak_popov(P, r)
       @test U*A == P
       @test is_unit(det(U))
@@ -3896,10 +3896,10 @@ end
    for i in 1:2
       A = rand(M, 1:5)
       r = rank(A)
-      P = weak_popov(A)
+      P = @inferred weak_popov(A)
       @test is_weak_popov(P, r)
 
-      P, U = weak_popov_with_transform(A)
+      P, U = @inferred weak_popov_with_transform(A)
       @test is_weak_popov(P, r)
       @test U*A == P
       @test is_unit(det(U))
@@ -3912,10 +3912,10 @@ end
    for i in 1:2
       A = rand(M, -1:5, 0:100)
       r = rank(A)
-      P = weak_popov(A)
+      P = @inferred weak_popov(A)
       @test is_weak_popov(P, r)
 
-      P, U = weak_popov_with_transform(A)
+      P, U = @inferred weak_popov_with_transform(A)
       @test is_weak_popov(P, r)
       @test U*A == P
       @test is_unit(det(U))
@@ -3928,20 +3928,20 @@ end
    A = matrix(R, map(R, Any[1 2 3 x; x 2*x 3*x x^2; x x^2+1 x^3+x^2 x^4+x^2+1]))
    r = 2 # == rank(A)
 
-   P = popov(A)
+   P = @inferred popov(A)
    @test is_popov(P, r)
 
-   P, U = popov_with_transform(A)
+   P, U = @inferred popov_with_transform(A)
    @test is_popov(P, r)
    @test U*A == P
    @test is_unit(det(U))
 
    A = matrix(R, 3, 3, [ x^4, 0, 0, x^3, x^4, x^3, x^3, x^5, x^5 ])
    r = 3 # == rank(A)
-   P = popov(A)
+   P = @inferred popov(A)
    @test is_popov(P, r)
 
-   P, U = popov_with_transform(A)
+   P, U = @inferred popov_with_transform(A)
    @test is_popov(P, r)
    @test U*A == P
    @test is_unit(det(U))
@@ -3953,10 +3953,10 @@ end
    B = matrix(S, map(S, Any[ 4*y^2+3*y+5 4*y^2+3*y+4 6*y^2+1; 3*y+6 3*y+5 y+3; 6*y^2+4*y+2 6*y^2 2*y^2+y]))
    s = 2 # == rank(B)
 
-   P = popov(B)
+   P = @inferred popov(B)
    @test is_popov(P, s)
 
-   P, U = popov_with_transform(B)
+   P, U = @inferred popov_with_transform(B)
    @test is_popov(P, s)
    @test U*B == P
    @test is_unit(det(U))
@@ -3967,10 +3967,10 @@ end
       M = matrix_space(polynomial_ring(QQ, "x")[1], rand(1:5), rand(1:5))
       A = rand(M, -1:5, -5:5)
       r = rank(A)
-      P = popov(A)
+      P = @inferred popov(A)
       @test is_popov(P, r)
 
-      P, U = popov_with_transform(A)
+      P, U = @inferred popov_with_transform(A)
       @test is_popov(P, r)
       @test U*A == P
       @test is_unit(det(U))
@@ -3983,10 +3983,10 @@ end
    for i in 1:2
       A = rand(M, 1:5)
       r = rank(A)
-      P = popov(A)
+      P = @inferred popov(A)
       @test is_popov(P, r)
 
-      P, U = popov_with_transform(A)
+      P, U = @inferred popov_with_transform(A)
       @test is_popov(P, r)
       @test U*A == P
       @test is_unit(det(U))
@@ -3999,10 +3999,10 @@ end
    for i in 1:2
       A = rand(M, -1:5, 0:100)
       r = rank(A)
-      P = popov(A)
+      P = @inferred popov(A)
       @test is_popov(P, r)
 
-      P, U = popov_with_transform(A)
+      P, U = @inferred popov_with_transform(A)
       @test is_popov(P, r)
       @test U*A == P
       @test is_unit(det(U))

From 07e94862936b85e1a3703b0418984531ad5e603a Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Lars=20G=C3=B6ttgens?= <lars.goettgens@rwth-aachen.de>
Date: Wed, 10 Apr 2024 16:17:44 +0200
Subject: [PATCH 11/19] Fix `gen`

---
 src/Deprecations.jl  |  1 +
 src/generic/MPoly.jl | 10 +++++-----
 2 files changed, 6 insertions(+), 5 deletions(-)

diff --git a/src/Deprecations.jl b/src/Deprecations.jl
index 6d5f6de27e..cb6001bc0b 100644
--- a/src/Deprecations.jl
+++ b/src/Deprecations.jl
@@ -50,3 +50,4 @@ end
 @deprecate _extended_weak_popov(A::MatElem{T}, V::MatElem{T}, trafo::Type{Val{S}}) where {T <: PolyRingElem, S} _extended_weak_popov(A, V, Val(S))
 @deprecate _popov(A::MatElem{T}, trafo::Type{Val{S}}) where {T <: PolyRingElem, S} _popov(A, Val(S))
 @deprecate _hnf_via_popov(A::MatElem{T}, trafo::Type{Val{S}}) where {T <: PolyRingElem, S} _hnf_via_popov(A, Val(S))
+@deprecate gen(a::MPolyRing{T}, i::Int, ::Type{Val{ord}}) where {T <: RingElement, ord} gen(a, i, Val(ord))
diff --git a/src/generic/MPoly.jl b/src/generic/MPoly.jl
index ef798643fd..95d8400f02 100644
--- a/src/generic/MPoly.jl
+++ b/src/generic/MPoly.jl
@@ -37,21 +37,21 @@ number_of_variables(a::MPolyRing) = a.num_vars
 
 number_of_generators(a::MPolyRing) = a.num_vars
 
-function gen(a::MPolyRing{T}, i::Int, ::Type{Val{:lex}}) where {T <: RingElement}
+function gen(a::MPolyRing{T}, i::Int, ::Val{:lex}) where {T <: RingElement}
     n = nvars(a)
     @boundscheck 1 <= i <= n || throw(ArgumentError("variable index out of range"))
     return a([one(base_ring(a))], reshape([UInt(j == n - i + 1)
             for j = 1:n], n, 1))
 end
 
-function gen(a::MPolyRing{T}, i::Int, ::Type{Val{:deglex}}) where {T <: RingElement}
+function gen(a::MPolyRing{T}, i::Int, ::Val{:deglex}) where {T <: RingElement}
     n = nvars(a)
     @boundscheck 1 <= i <= n || throw(ArgumentError("variable index out of range"))
     return a([one(base_ring(a))], reshape([[UInt(j == n - i + 1)
             for j in 1:n]..., UInt(1)], n + 1, 1))
 end
 
-function gen(a::MPolyRing{T}, i::Int, ::Type{Val{:degrevlex}}) where {T <: RingElement}
+function gen(a::MPolyRing{T}, i::Int, ::Val{:degrevlex}) where {T <: RingElement}
     n = nvars(a)
     @boundscheck 1 <= i <= n || throw(ArgumentError("variable index out of range"))
     return a([one(base_ring(a))], reshape([[UInt(j == i)
@@ -66,7 +66,7 @@ ring.
 """
 function gens(a::MPolyRing{T}) where {T <: RingElement}
    n = a.num_vars
-   return elem_type(a)[gen(a, i, Val{a.ord})::elem_type(a) for i in 1:n]
+   return elem_type(a)[gen(a, i, Val(internal_ordering(a))) for i in 1:n]
 end
 
 @doc raw"""
@@ -76,7 +76,7 @@ Return the $i$-th generator (variable) of the given polynomial
 ring.
 """
 function gen(a::MPolyRing{T}, i::Int) where {T <: RingElement}
-   return gen(a, i, Val{a.ord})
+   return gen(a, i, Val(a.ord))
 end
 
 function vars(p::MPoly{T}) where {T <: RingElement}

From 65fefcaa6e2766491e91a586136bc9847d785ee5 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Lars=20G=C3=B6ttgens?= <lars.goettgens@rwth-aachen.de>
Date: Wed, 10 Apr 2024 16:34:11 +0200
Subject: [PATCH 12/19] Fix `exponent_vector`

---
 src/Deprecations.jl  | 1 +
 src/generic/MPoly.jl | 8 ++++----
 2 files changed, 5 insertions(+), 4 deletions(-)

diff --git a/src/Deprecations.jl b/src/Deprecations.jl
index cb6001bc0b..6e3b6fadd5 100644
--- a/src/Deprecations.jl
+++ b/src/Deprecations.jl
@@ -51,3 +51,4 @@ end
 @deprecate _popov(A::MatElem{T}, trafo::Type{Val{S}}) where {T <: PolyRingElem, S} _popov(A, Val(S))
 @deprecate _hnf_via_popov(A::MatElem{T}, trafo::Type{Val{S}}) where {T <: PolyRingElem, S} _hnf_via_popov(A, Val(S))
 @deprecate gen(a::MPolyRing{T}, i::Int, ::Type{Val{ord}}) where {T <: RingElement, ord} gen(a, i, Val(ord))
+import .Generic: exponent_vector; @deprecate exponent_vector(a::Generic.MPoly{T}, i::Int, ::Type{Val{ord}}) where {T <: RingElement, ord} exponent_vector(a, i, Val(ord))
diff --git a/src/generic/MPoly.jl b/src/generic/MPoly.jl
index 95d8400f02..ca55835c4b 100644
--- a/src/generic/MPoly.jl
+++ b/src/generic/MPoly.jl
@@ -125,7 +125,7 @@ end
 #
 ###############################################################################
 
-function exponent_vector(a::MPoly{T}, i::Int, ::Type{Val{:lex}}) where T <: RingElement
+function exponent_vector(a::MPoly{T}, i::Int, ::Val{:lex}) where T <: RingElement
    A = a.exps
    N = size(A, 1)
    return [Int(A[j, i]) for j in N:-1:1]
@@ -135,7 +135,7 @@ function exponent(a::MPoly{T}, i::Int, j::Int, ::Type{Val{:lex}}) where T <: Rin
    return Int(a.exps[size(a.exps, 1) + 1 - j, i])
 end
 
-function exponent_vector(a::MPoly{T}, i::Int, ::Type{Val{:deglex}}) where T <: RingElement
+function exponent_vector(a::MPoly{T}, i::Int, ::Val{:deglex}) where T <: RingElement
    A = a.exps
    N = size(A, 1)
    return [Int(A[j, i]) for j in N - 1:-1:1]
@@ -145,7 +145,7 @@ function exponent(a::MPoly{T}, i::Int, j::Int, ::Type{Val{:deglex}}) where T <:
    return Int(a.exps[size(a.exps, 1) - j, i])
 end
 
-function exponent_vector(a::MPoly{T}, i::Int, ::Type{Val{:degrevlex}}) where T <: RingElement
+function exponent_vector(a::MPoly{T}, i::Int, ::Val{:degrevlex}) where T <: RingElement
    A = a.exps
    N = size(A, 1)
    return [Int(A[j, i]) for j in 1:N - 1]
@@ -164,7 +164,7 @@ are given in the order of the variables for the ring, as supplied when the
 ring was created.
 """
 function exponent_vector(a::MPoly{T}, i::Int) where T <: RingElement
-   return exponent_vector(a, i, Val{parent(a).ord})
+   return exponent_vector(a, i, Val(internal_ordering(parent(a))))
 end
 
 @doc raw"""

From b4083dc0248c1ac02ae7aaf673fbce98e051bcde Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Lars=20G=C3=B6ttgens?= <lars.goettgens@rwth-aachen.de>
Date: Wed, 10 Apr 2024 16:34:21 +0200
Subject: [PATCH 13/19] Fix `exponent`

---
 src/Deprecations.jl  | 1 +
 src/generic/MPoly.jl | 8 ++++----
 2 files changed, 5 insertions(+), 4 deletions(-)

diff --git a/src/Deprecations.jl b/src/Deprecations.jl
index 6e3b6fadd5..359224ec5e 100644
--- a/src/Deprecations.jl
+++ b/src/Deprecations.jl
@@ -52,3 +52,4 @@ end
 @deprecate _hnf_via_popov(A::MatElem{T}, trafo::Type{Val{S}}) where {T <: PolyRingElem, S} _hnf_via_popov(A, Val(S))
 @deprecate gen(a::MPolyRing{T}, i::Int, ::Type{Val{ord}}) where {T <: RingElement, ord} gen(a, i, Val(ord))
 import .Generic: exponent_vector; @deprecate exponent_vector(a::Generic.MPoly{T}, i::Int, ::Type{Val{ord}}) where {T <: RingElement, ord} exponent_vector(a, i, Val(ord))
+import .Generic: exponent; @deprecate exponent(a::Generic.MPoly{T}, i::Int, j::Int, ::Type{Val{ord}}) where {T <: RingElement, ord} exponent(a, i, j, Val(ord))
diff --git a/src/generic/MPoly.jl b/src/generic/MPoly.jl
index ca55835c4b..d9d423cb9c 100644
--- a/src/generic/MPoly.jl
+++ b/src/generic/MPoly.jl
@@ -131,7 +131,7 @@ function exponent_vector(a::MPoly{T}, i::Int, ::Val{:lex}) where T <: RingElemen
    return [Int(A[j, i]) for j in N:-1:1]
 end
 
-function exponent(a::MPoly{T}, i::Int, j::Int, ::Type{Val{:lex}}) where T <: RingElement
+function exponent(a::MPoly{T}, i::Int, j::Int, ::Val{:lex}) where T <: RingElement
    return Int(a.exps[size(a.exps, 1) + 1 - j, i])
 end
 
@@ -141,7 +141,7 @@ function exponent_vector(a::MPoly{T}, i::Int, ::Val{:deglex}) where T <: RingEle
    return [Int(A[j, i]) for j in N - 1:-1:1]
 end
 
-function exponent(a::MPoly{T}, i::Int, j::Int, ::Type{Val{:deglex}}) where T <: RingElement
+function exponent(a::MPoly{T}, i::Int, j::Int, ::Val{:deglex}) where T <: RingElement
    return Int(a.exps[size(a.exps, 1) - j, i])
 end
 
@@ -151,7 +151,7 @@ function exponent_vector(a::MPoly{T}, i::Int, ::Val{:degrevlex}) where T <: Ring
    return [Int(A[j, i]) for j in 1:N - 1]
 end
 
-function exponent(a::MPoly{T}, i::Int, j::Int, ::Type{Val{:degrevlex}}) where T <: RingElement
+function exponent(a::MPoly{T}, i::Int, j::Int, ::Val{:degrevlex}) where T <: RingElement
    return Int(a.exps[j, i])
 end
 
@@ -175,7 +175,7 @@ Term and variable numbering begins at $1$ and variables are ordered as
 during the creation of the ring.
 """
 function exponent(a::MPoly{T}, i::Int, j::Int) where T <: RingElement
-   return exponent(a, i, j, Val{parent(a).ord})
+   return exponent(a, i, j, Val(internal_ordering(parent(a))))
 end
 
 function set_exponent_vector!(a::MPoly{T}, i::Int, exps::Vector{Int}, ::Type{Val{:lex}}) where T <: RingElement

From 53f695cfa3aaba54792de5ae106b2040820a8ca8 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Lars=20G=C3=B6ttgens?= <lars.goettgens@rwth-aachen.de>
Date: Wed, 10 Apr 2024 16:42:57 +0200
Subject: [PATCH 14/19] Fix `set_exponent_vector!`

---
 src/Deprecations.jl  | 1 +
 src/generic/MPoly.jl | 8 ++++----
 2 files changed, 5 insertions(+), 4 deletions(-)

diff --git a/src/Deprecations.jl b/src/Deprecations.jl
index 359224ec5e..87b6957c9c 100644
--- a/src/Deprecations.jl
+++ b/src/Deprecations.jl
@@ -53,3 +53,4 @@ end
 @deprecate gen(a::MPolyRing{T}, i::Int, ::Type{Val{ord}}) where {T <: RingElement, ord} gen(a, i, Val(ord))
 import .Generic: exponent_vector; @deprecate exponent_vector(a::Generic.MPoly{T}, i::Int, ::Type{Val{ord}}) where {T <: RingElement, ord} exponent_vector(a, i, Val(ord))
 import .Generic: exponent; @deprecate exponent(a::Generic.MPoly{T}, i::Int, j::Int, ::Type{Val{ord}}) where {T <: RingElement, ord} exponent(a, i, j, Val(ord))
+import .Generic: set_exponent_vector!; @deprecate set_exponent_vector!(a::Generic.MPoly{T}, i::Int, exps::Vector{Int}, ::Type{Val{ord}}) where {T <: RingElement, ord} set_exponent_vector!(a, i, exps, Val(ord))
diff --git a/src/generic/MPoly.jl b/src/generic/MPoly.jl
index d9d423cb9c..70ca9645f6 100644
--- a/src/generic/MPoly.jl
+++ b/src/generic/MPoly.jl
@@ -178,7 +178,7 @@ function exponent(a::MPoly{T}, i::Int, j::Int) where T <: RingElement
    return exponent(a, i, j, Val(internal_ordering(parent(a))))
 end
 
-function set_exponent_vector!(a::MPoly{T}, i::Int, exps::Vector{Int}, ::Type{Val{:lex}}) where T <: RingElement
+function set_exponent_vector!(a::MPoly{T}, i::Int, exps::Vector{Int}, ::Val{:lex}) where T <: RingElement
    fit!(a, i)
    A = a.exps
    A[:, i] = exps[end:-1:1]
@@ -188,7 +188,7 @@ function set_exponent_vector!(a::MPoly{T}, i::Int, exps::Vector{Int}, ::Type{Val
    return a
 end
 
-function set_exponent_vector!(a::MPoly{T}, i::Int, exps::Vector{Int}, ::Type{Val{:deglex}}) where T <: RingElement
+function set_exponent_vector!(a::MPoly{T}, i::Int, exps::Vector{Int}, ::Val{:deglex}) where T <: RingElement
    fit!(a, i)
    A = a.exps
    A[1:end - 1, i] = exps[end:-1:1]
@@ -199,7 +199,7 @@ function set_exponent_vector!(a::MPoly{T}, i::Int, exps::Vector{Int}, ::Type{Val
    return a
 end
 
-function set_exponent_vector!(a::MPoly{T}, i::Int, exps::Vector{Int}, ::Type{Val{:degrevlex}}) where T <: RingElement
+function set_exponent_vector!(a::MPoly{T}, i::Int, exps::Vector{Int}, ::Val{:degrevlex}) where T <: RingElement
    fit!(a, i)
    A = a.exps
    A[1:end - 1, i] = exps
@@ -218,7 +218,7 @@ correspond to the exponents of the variables in the order supplied when
 the ring was created. The modified polynomial is returned.
 """
 function set_exponent_vector!(a::MPoly{T}, i::Int, exps::Vector{Int}) where T <: RingElement
-   return set_exponent_vector!(a, i, exps, Val{parent(a).ord})
+   return set_exponent_vector!(a, i, exps, Val(internal_ordering(parent(a))))
 end
 
 @doc raw"""

From a3f14f85d91a72f077ffad0c9d1200727aa352a7 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Lars=20G=C3=B6ttgens?= <lars.goettgens@rwth-aachen.de>
Date: Wed, 10 Apr 2024 16:46:31 +0200
Subject: [PATCH 15/19] Fix `is_gen`

---
 src/Deprecations.jl  | 1 +
 src/generic/MPoly.jl | 8 ++++----
 2 files changed, 5 insertions(+), 4 deletions(-)

diff --git a/src/Deprecations.jl b/src/Deprecations.jl
index 87b6957c9c..19bd261208 100644
--- a/src/Deprecations.jl
+++ b/src/Deprecations.jl
@@ -54,3 +54,4 @@ end
 import .Generic: exponent_vector; @deprecate exponent_vector(a::Generic.MPoly{T}, i::Int, ::Type{Val{ord}}) where {T <: RingElement, ord} exponent_vector(a, i, Val(ord))
 import .Generic: exponent; @deprecate exponent(a::Generic.MPoly{T}, i::Int, j::Int, ::Type{Val{ord}}) where {T <: RingElement, ord} exponent(a, i, j, Val(ord))
 import .Generic: set_exponent_vector!; @deprecate set_exponent_vector!(a::Generic.MPoly{T}, i::Int, exps::Vector{Int}, ::Type{Val{ord}}) where {T <: RingElement, ord} set_exponent_vector!(a, i, exps, Val(ord))
+import .Generic: is_gen; @deprecate is_gen(x::Generic.MPoly{T}, ::Type{Val{ord}}) where {T <: RingElement, ord} is_gen(x, Val(ord))
diff --git a/src/generic/MPoly.jl b/src/generic/MPoly.jl
index 70ca9645f6..aceb32f958 100644
--- a/src/generic/MPoly.jl
+++ b/src/generic/MPoly.jl
@@ -596,7 +596,7 @@ function Base.hash(x::MPoly{T}, h::UInt) where {T <: RingElement}
    return b
 end
 
-function is_gen(x::MPoly{T}, ::Type{Val{:lex}}) where {T <: RingElement}
+function is_gen(x::MPoly{T}, ::Val{:lex}) where {T <: RingElement}
    exps = x.exps
    N = size(exps, 1)
    for k = 1:N
@@ -616,12 +616,12 @@ function is_gen(x::MPoly{T}, ::Type{Val{:lex}}) where {T <: RingElement}
    return false
 end
 
-function is_gen(x::MPoly{T}, ::Type{Val{:deglex}}) where {T <: RingElement}
+function is_gen(x::MPoly{T}, ::Val{:deglex}) where {T <: RingElement}
    N = size(x.exps, 1)
    return x.exps[N, 1] == UInt(1)
 end
 
-function is_gen(x::MPoly{T}, ::Type{Val{:degrevlex}}) where {T <: RingElement}
+function is_gen(x::MPoly{T}, ::Val{:degrevlex}) where {T <: RingElement}
     N = size(x.exps, 1)
     return x.exps[N, 1] == UInt(1)
 end
@@ -639,7 +639,7 @@ function is_gen(x::MPoly{T}) where {T <: RingElement}
    if !isone(coeff(x, 1))
       return false
    end
-   return is_gen(x, Val{parent(x).ord})
+   return is_gen(x, Val(internal_ordering(parent(x))))
 end
 
 @doc raw"""

From bf08607ee97138100c604dc480cade5148fb2009 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Lars=20G=C3=B6ttgens?= <lars.goettgens@rwth-aachen.de>
Date: Wed, 10 Apr 2024 16:49:47 +0200
Subject: [PATCH 16/19] Fix `degree`

---
 src/Deprecations.jl  | 1 +
 src/generic/MPoly.jl | 8 ++++----
 2 files changed, 5 insertions(+), 4 deletions(-)

diff --git a/src/Deprecations.jl b/src/Deprecations.jl
index 19bd261208..2b9ffeec3d 100644
--- a/src/Deprecations.jl
+++ b/src/Deprecations.jl
@@ -55,3 +55,4 @@ import .Generic: exponent_vector; @deprecate exponent_vector(a::Generic.MPoly{T}
 import .Generic: exponent; @deprecate exponent(a::Generic.MPoly{T}, i::Int, j::Int, ::Type{Val{ord}}) where {T <: RingElement, ord} exponent(a, i, j, Val(ord))
 import .Generic: set_exponent_vector!; @deprecate set_exponent_vector!(a::Generic.MPoly{T}, i::Int, exps::Vector{Int}, ::Type{Val{ord}}) where {T <: RingElement, ord} set_exponent_vector!(a, i, exps, Val(ord))
 import .Generic: is_gen; @deprecate is_gen(x::Generic.MPoly{T}, ::Type{Val{ord}}) where {T <: RingElement, ord} is_gen(x, Val(ord))
+import .Generic: degree; @deprecate degree(f::Generic.MPoly{T}, i::Int, ::Type{Val{ord}}) where {T <: RingElement, ord} degree(f, i, Val(ord))
diff --git a/src/generic/MPoly.jl b/src/generic/MPoly.jl
index aceb32f958..71f68ac472 100644
--- a/src/generic/MPoly.jl
+++ b/src/generic/MPoly.jl
@@ -760,7 +760,7 @@ function max_fields(f::MPoly{T}) where {T <: RingElement}
    return biggest, b
 end
 
-function degree(f::MPoly{T}, i::Int, ::Type{Val{:lex}}) where T <: RingElement
+function degree(f::MPoly{T}, i::Int, ::Val{:lex}) where T <: RingElement
    A = f.exps
    N = size(A, 1)
    if i == 1
@@ -777,7 +777,7 @@ function degree(f::MPoly{T}, i::Int, ::Type{Val{:lex}}) where T <: RingElement
    end
 end
 
-function degree(f::MPoly{T}, i::Int, ::Type{Val{:deglex}}) where T <: RingElement
+function degree(f::MPoly{T}, i::Int, ::Val{:deglex}) where T <: RingElement
    A = f.exps
    N = size(A, 1)
    biggest = -1
@@ -790,7 +790,7 @@ function degree(f::MPoly{T}, i::Int, ::Type{Val{:deglex}}) where T <: RingElemen
    return biggest
 end
 
-function degree(f::MPoly{T}, i::Int, ::Type{Val{:degrevlex}}) where T <: RingElement
+function degree(f::MPoly{T}, i::Int, ::Val{:degrevlex}) where T <: RingElement
    A = f.exps
    N = size(A, 1)
    biggest = -1
@@ -804,7 +804,7 @@ function degree(f::MPoly{T}, i::Int, ::Type{Val{:degrevlex}}) where T <: RingEle
 end
 
 function degree(f::MPoly{T}, i::Int) where T <: RingElement
-   return degree(f, i, Val{parent(f).ord})
+   return degree(f, i, Val(internal_ordering(parent(f))))
 end
 
 @doc raw"""

From 907b92d805b39e3a7e8874ff7db496ed6b17cc8e Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Lars=20G=C3=B6ttgens?= <lars.goettgens@rwth-aachen.de>
Date: Wed, 10 Apr 2024 16:54:56 +0200
Subject: [PATCH 17/19] Fix `main_variable_coefficient`

---
 src/generic/MPoly.jl | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/src/generic/MPoly.jl b/src/generic/MPoly.jl
index 71f68ac472..787b4c08a1 100644
--- a/src/generic/MPoly.jl
+++ b/src/generic/MPoly.jl
@@ -3670,7 +3670,7 @@ function main_variable_coefficient_lex(a::MPoly{T}, k0::Int, n::Int) where {T <:
    return parent(a)(Ac, Ae)
 end
 
-function main_variable_coefficient(a::MPoly{T}, k::Int, n::Int, ::Type{Val{:lex}}) where {T <: RingElement}
+function main_variable_coefficient(a::MPoly{T}, k::Int, n::Int, ::Val{:lex}) where {T <: RingElement}
    return main_variable_coefficient_lex(a, k, n)
 end
 
@@ -3707,11 +3707,11 @@ function main_variable_coefficient_deglex(a::MPoly{T}, k0::Int, n::Int) where {T
    return parent(a)(Ac, Ae)
 end
 
-function main_variable_coefficient(a::MPoly{T}, k::Int, n::Int, ::Type{Val{:deglex}}) where {T <: RingElement}
+function main_variable_coefficient(a::MPoly{T}, k::Int, n::Int, ::Val{:deglex}) where {T <: RingElement}
    return main_variable_coefficient_deglex(a, k, n)
 end
 
-function main_variable_coefficient(a::MPoly{T}, k::Int, n::Int, ::Type{Val{:degrevlex}}) where {T <: RingElement}
+function main_variable_coefficient(a::MPoly{T}, k::Int, n::Int, ::Val{:degrevlex}) where {T <: RingElement}
    return main_variable_coefficient_deglex(a, k, n)
 end
 
@@ -3737,10 +3737,10 @@ function main_variable_extract(R::SparsePolyRing, a::MPoly{T}, k::Int) where {T
    A = main_variable_terms(a2, k)
    Pe = zeros(UInt, length(A))
    Pc = Vector{MPoly{T}}(undef, length(A))
-   ord = parent(a).ord
+   ord = internal_ordering(parent(a))
    for i = 1:length(A)
       Pe[i] = a2.exps[k, A[i]]
-      Pc[i] = main_variable_coefficient(a2, k, A[i], Val{ord})
+      Pc[i] = main_variable_coefficient(a2, k, A[i], Val(ord))
    end
    return R(Pc, Pe)
 end

From 9e82859fef1b02d155865be045973eb3821f872b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Lars=20G=C3=B6ttgens?= <lars.goettgens@rwth-aachen.de>
Date: Thu, 11 Apr 2024 18:00:30 +0200
Subject: [PATCH 18/19] Add transition hack

---
 src/AbstractAlgebra.jl | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/src/AbstractAlgebra.jl b/src/AbstractAlgebra.jl
index 30cfd92d98..62eb9e6b88 100644
--- a/src/AbstractAlgebra.jl
+++ b/src/AbstractAlgebra.jl
@@ -125,6 +125,11 @@ function force_op(op::Function, throw_error::Val{T}, a...) where {T}
 end
 
 function force_op(op::Function, a...)
+  ### TODO: remove in the next breaking release, and fix downstream packages instead
+  if applicable(force_op, op, Val{true}, a...) && !endswith(functionloc(force_op, (typeof(op), Type{Val{true}}, typeof.(a)...))[1], joinpath("base", "deprecated.jl"))
+    return force_op(op, Val{true}, a...)
+  end
+  ###
   return force_op(op, Val(true), a...)
 end
 

From 6b2e0b75b086a6562c9b7a844ab5868316fca5aa Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Lars=20G=C3=B6ttgens?= <lars.goettgens@rwth-aachen.de>
Date: Thu, 11 Apr 2024 18:50:11 +0200
Subject: [PATCH 19/19] Small enhancement

---
 src/AbstractAlgebra.jl | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/src/AbstractAlgebra.jl b/src/AbstractAlgebra.jl
index 62eb9e6b88..defb6f51b9 100644
--- a/src/AbstractAlgebra.jl
+++ b/src/AbstractAlgebra.jl
@@ -106,8 +106,8 @@ include("PrintHelper.jl")
 #   parent(b) == a && return a
 #   return force_coerce(a, b)
 #
-function force_coerce(a, b, throw_error::Val{T} = Val(true)) where {T}
-  if throw_error isa Val{true}
+function force_coerce(a, b, ::Val{throw_error} = Val(true)) where {throw_error}
+  if throw_error
     error("coercion not possible")
   end
   return nothing
@@ -117,8 +117,8 @@ end
 # a common over structure
 # designed(?) to be minimally invasive in AA and Nemo, but filled with
 # content in Hecke/Oscar
-function force_op(op::Function, throw_error::Val{T}, a...) where {T}
-  if throw_error isa Val{true}
+function force_op(op::Function, ::Val{throw_error}, a...) where {throw_error}
+  if throw_error
     error("no common overstructure for the arguments found")
   end
   return false