From 6fd471a03dfe41cc7c2a3d12732968f0ff207c15 Mon Sep 17 00:00:00 2001
From: HechtiDerLachs <zach@mathematik.uni-kl.de>
Date: Thu, 19 Sep 2024 16:45:21 +0200
Subject: [PATCH 01/22] Attempt to speed up mapping of polynomials.

---
 src/Rings/MPolyMap/MPolyAnyMap.jl | 10 +++++++++-
 src/Rings/MPolyMap/MPolyRing.jl   | 31 +++++++++++++++++++++++++++++++
 2 files changed, 40 insertions(+), 1 deletion(-)

diff --git a/src/Rings/MPolyMap/MPolyAnyMap.jl b/src/Rings/MPolyMap/MPolyAnyMap.jl
index 873365b9ad5f..ce09648d1567 100644
--- a/src/Rings/MPolyMap/MPolyAnyMap.jl
+++ b/src/Rings/MPolyMap/MPolyAnyMap.jl
@@ -42,6 +42,10 @@ const _DomainTypes = Union{MPolyRing, MPolyQuoRing}
   coeff_map::U
   img_gens::Vector{V}
   temp_ring           # temporary ring used when evaluating maps
+  variable_indices::Vector{Int} # a table where the i-th entry contains the 
+                                # index of the variable where it's mapped to
+                                # in case the mapping takes such a particularly
+                                # simple form.
 
   function MPolyAnyMap{D, C, U, V}(domain::D,
                                 codomain::C,
@@ -51,7 +55,11 @@ const _DomainTypes = Union{MPolyRing, MPolyQuoRing}
       for g in img_gens
         @assert parent(g) === codomain "elements does not have the correct parent"
       end
-    return new{D, C, U, V}(domain, codomain, coeff_map, img_gens)
+    result = new{D, C, U, V}(domain, codomain, coeff_map, img_gens)
+    if all(x in gens(codomain) for x in img_gens) && length(unique(img_gens)) == ngens(domain)
+      result.variable_indices = [findfirst(x==y for y in gens(codomain)) for x in img_gens]
+    end
+    return result
   end
 end
 
diff --git a/src/Rings/MPolyMap/MPolyRing.jl b/src/Rings/MPolyMap/MPolyRing.jl
index 6040c1c313e4..d8408f5a22f7 100644
--- a/src/Rings/MPolyMap/MPolyRing.jl
+++ b/src/Rings/MPolyMap/MPolyRing.jl
@@ -132,12 +132,43 @@ end
 #
 ################################################################################
 
+function _evaluate_plain(F::MPolyAnyMap{<:MPolyRing, <:MPolyRing}, u)
+  if isdefined(F, :variable_indices)
+    S = codomain(F)::MPolyRing
+    r = ngens(S)
+    ctx = MPolyBuildCtx(S)
+    for (c, e) in zip(coefficients(u), exponents(u))
+      ee = [0 for _ in 1:r]
+      for (i, k) in enumerate(e)
+        ee[F.variable_indices[i]] = k
+      end
+      push_term!(ctx, c, ee)
+    end
+    return finish(ctx)
+  end
+
+  return evaluate(u, F.img_gens)
+end
+
 function _evaluate_plain(F::MPolyAnyMap{<: MPolyRing}, u)
   return evaluate(u, F.img_gens)
 end
 
 # See the comment in MPolyQuo.jl
 function _evaluate_plain(F::MPolyAnyMap{<:MPolyRing, <:MPolyQuoRing}, u)
+  if isdefined(F, :variable_indices)
+    S = base_ring(codomain(F))::MPolyRing
+    r = ngens(S)
+    ctx = MPolyBuildCtx(S)
+    for (c, e) in zip(coefficients(u), exponents(u))
+      ee = [0 for _ in 1:r]
+      for (i, k) in enumerate(e)
+        ee[F.variable_indices[i]] = k
+      end
+      push_term!(ctx, c, ee)
+    end
+    return codomain(F)(finish(ctx))
+  end
   A = codomain(F)
   v = evaluate(lift(u), lift.(_images(F)))
   return simplify(A(v))

From 70279f9cbde57d12c4acb684d71fd11a66e25559 Mon Sep 17 00:00:00 2001
From: HechtiDerLachs <zach@mathematik.uni-kl.de>
Date: Thu, 19 Sep 2024 17:43:20 +0200
Subject: [PATCH 02/22] Some more steps towards making stuff faster.

---
 src/Rings/MPolyMap/MPolyAnyMap.jl | 28 ++++++++++++++++++++--------
 src/Rings/MPolyMap/MPolyRing.jl   |  6 +++++-
 2 files changed, 25 insertions(+), 9 deletions(-)

diff --git a/src/Rings/MPolyMap/MPolyAnyMap.jl b/src/Rings/MPolyMap/MPolyAnyMap.jl
index ce09648d1567..03384f28d7ad 100644
--- a/src/Rings/MPolyMap/MPolyAnyMap.jl
+++ b/src/Rings/MPolyMap/MPolyAnyMap.jl
@@ -48,15 +48,27 @@ const _DomainTypes = Union{MPolyRing, MPolyQuoRing}
                                 # simple form.
 
   function MPolyAnyMap{D, C, U, V}(domain::D,
-                                codomain::C,
-                                coeff_map::U,
-                                img_gens::Vector{V}) where {D, C, U, V}
-      @assert V === elem_type(C)
-      for g in img_gens
-        @assert parent(g) === codomain "elements does not have the correct parent"
-      end
+                                   codomain::C,
+                                   coeff_map::U,
+                                   img_gens::Vector{V}) where {D, C, U, V}
+    @assert V === elem_type(C)
+    for g in img_gens
+      @assert parent(g) === codomain "elements does not have the correct parent"
+    end
+    return new{D, C, U, V}(domain, codomain, coeff_map, img_gens)
+  end
+  function MPolyAnyMap{D, C, U, V}(domain::D,
+                                   codomain::C,
+                                   coeff_map::U,
+                                   img_gens::Vector{V}) where {D <: Union{<:MPolyRing, <:MPolyQuoRing}, 
+                                                               C <: Union{<:MPolyRing, <:MPolyQuoRing}, 
+                                                               U, V}
+    @assert V === elem_type(C)
+    for g in img_gens
+      @assert parent(g) === codomain "elements does not have the correct parent"
+    end
     result = new{D, C, U, V}(domain, codomain, coeff_map, img_gens)
-    if all(x in gens(codomain) for x in img_gens) && length(unique(img_gens)) == ngens(domain)
+    if all(is_gen(x) for x in img_gens) && allunique(img_gens)
       result.variable_indices = [findfirst(x==y for y in gens(codomain)) for x in img_gens]
     end
     return result
diff --git a/src/Rings/MPolyMap/MPolyRing.jl b/src/Rings/MPolyMap/MPolyRing.jl
index d8408f5a22f7..e9df1c4102eb 100644
--- a/src/Rings/MPolyMap/MPolyRing.jl
+++ b/src/Rings/MPolyMap/MPolyRing.jl
@@ -132,12 +132,16 @@ end
 #
 ################################################################################
 
+# Some additional methods needed for the test in the constructor for MPolyAnyMap
+is_gen(x::MPolyQuoRingElem) = is_gen(lift(x))
+is_gen(x::MPolyDecRingElem) = is_gen(forget_grading(x))
+
 function _evaluate_plain(F::MPolyAnyMap{<:MPolyRing, <:MPolyRing}, u)
   if isdefined(F, :variable_indices)
     S = codomain(F)::MPolyRing
     r = ngens(S)
     ctx = MPolyBuildCtx(S)
-    for (c, e) in zip(coefficients(u), exponents(u))
+    for (c, e) in zip(AbstractAlgebra.coefficients(u), AbstractAlgebra.exponent_vectors(u))
       ee = [0 for _ in 1:r]
       for (i, k) in enumerate(e)
         ee[F.variable_indices[i]] = k

From 43048816b2efe96e0e8de4f96dba8eea739750d9 Mon Sep 17 00:00:00 2001
From: HechtiDerLachs <zach@mathematik.uni-kl.de>
Date: Tue, 24 Sep 2024 20:52:21 +0200
Subject: [PATCH 03/22] Try to make general evaluation faster.

---
 src/Rings/MPolyMap/MPolyRing.jl | 51 ++++++++++++++++++++++++++++++++-
 1 file changed, 50 insertions(+), 1 deletion(-)

diff --git a/src/Rings/MPolyMap/MPolyRing.jl b/src/Rings/MPolyMap/MPolyRing.jl
index e9df1c4102eb..4d726ba9d9fe 100644
--- a/src/Rings/MPolyMap/MPolyRing.jl
+++ b/src/Rings/MPolyMap/MPolyRing.jl
@@ -178,6 +178,55 @@ function _evaluate_plain(F::MPolyAnyMap{<:MPolyRing, <:MPolyQuoRing}, u)
   return simplify(A(v))
 end
 
+function _evaluate_general(F::MPolyAnyMap{<:MPolyRing, <:MPolyRing}, u)
+  if domain(F) === codomain(F) && coefficient_map(F) === nothing
+    return evaluate(map_coefficients(coefficient_map(F), u,
+                                     parent = domain(F)), F.img_gens)
+  else
+    S = temp_ring(F)
+    if S !== nothing
+      if !isdefined(F, :variable_indices) || coefficient_ring(S) !== codomain(F)
+        return evaluate(map_coefficients(coefficient_map(F), u,
+                                         parent = S), F.img_gens)
+      else
+        tmp_poly = map_coefficients(coefficient_map(F), u, parent = S)
+        cod_ring = codomain(F)::MPolyRing
+        r = ngens(cod_ring)
+        ctx = MPolyBuildCtx(cod_ring)
+        for (p, e) in zip(coefficients(tmp_poly), exponents(tmp_poly))
+          ee = [0 for _ in 1:r]
+          for (i, k) in enumerate(e)
+            ee[F.variable_indices[i]] = k
+          end
+          p::MPolyRingElem
+          @assert parent(p) === cod_ring
+          for (c, d) in zip(coefficients(p), exponents(p))
+            push_term!(ctx, c, ee+d)
+          end
+        end
+        return finish(ctx)
+      end
+    else
+      if !isdefined(F, :variable_indices)
+        return evaluate(map_coefficients(coefficient_map(F), u), F.img_gens)
+      else
+        tmp_poly = map_coefficients(coefficient_map(F), u)
+        cod_ring = codomain(F)::MPolyRing
+        r = ngens(cod_ring)
+        ctx = MPolyBuildCtx(cod_ring)
+        for (c, e) in zip(coefficients(tmp_poly), exponents(tmp_poly))
+          ee = [0 for _ in 1:r]
+          for (i, k) in enumerate(e)
+            ee[F.variable_indices[i]] = k
+          end
+          push_term!(ctx, c, ee)
+        end
+        return finish(ctx)
+      end
+    end
+  end
+end
+
 function _evaluate_general(F::MPolyAnyMap{<: MPolyRing}, u)
   if domain(F) === codomain(F) && coefficient_map(F) === nothing
     return evaluate(map_coefficients(coefficient_map(F), u,
@@ -186,7 +235,7 @@ function _evaluate_general(F::MPolyAnyMap{<: MPolyRing}, u)
     S = temp_ring(F)
     if S !== nothing
       return evaluate(map_coefficients(coefficient_map(F), u,
-                                parent = S), F.img_gens)
+                                       parent = S), F.img_gens)
     else
       return evaluate(map_coefficients(coefficient_map(F), u), F.img_gens)
     end

From a96cf364a948d9853925f8111bf64c78b2c769c6 Mon Sep 17 00:00:00 2001
From: HechtiDerLachs <zach@mathematik.uni-kl.de>
Date: Wed, 25 Sep 2024 08:26:02 +0200
Subject: [PATCH 04/22] Clean up general evaluation.

---
 src/Rings/MPolyMap/MPolyAnyMap.jl |  6 ++--
 src/Rings/MPolyMap/MPolyRing.jl   | 52 ++++++++++++++-----------------
 2 files changed, 27 insertions(+), 31 deletions(-)

diff --git a/src/Rings/MPolyMap/MPolyAnyMap.jl b/src/Rings/MPolyMap/MPolyAnyMap.jl
index 03384f28d7ad..1fbb44a86bb7 100644
--- a/src/Rings/MPolyMap/MPolyAnyMap.jl
+++ b/src/Rings/MPolyMap/MPolyAnyMap.jl
@@ -43,7 +43,7 @@ const _DomainTypes = Union{MPolyRing, MPolyQuoRing}
   img_gens::Vector{V}
   temp_ring           # temporary ring used when evaluating maps
   variable_indices::Vector{Int} # a table where the i-th entry contains the 
-                                # index of the variable where it's mapped to
+                                # index of the variable where it is mapped to
                                 # in case the mapping takes such a particularly
                                 # simple form.
 
@@ -68,8 +68,8 @@ const _DomainTypes = Union{MPolyRing, MPolyQuoRing}
       @assert parent(g) === codomain "elements does not have the correct parent"
     end
     result = new{D, C, U, V}(domain, codomain, coeff_map, img_gens)
-    if all(is_gen(x) for x in img_gens) && allunique(img_gens)
-      result.variable_indices = [findfirst(x==y for y in gens(codomain)) for x in img_gens]
+    if all(_is_gen, img_gens) && allunique(img_gens)
+      result.variable_indices = [findfirst(==(x), gens(codomain)) for x in img_gens]
     end
     return result
   end
diff --git a/src/Rings/MPolyMap/MPolyRing.jl b/src/Rings/MPolyMap/MPolyRing.jl
index 4d726ba9d9fe..4736a125b656 100644
--- a/src/Rings/MPolyMap/MPolyRing.jl
+++ b/src/Rings/MPolyMap/MPolyRing.jl
@@ -133,8 +133,9 @@ end
 ################################################################################
 
 # Some additional methods needed for the test in the constructor for MPolyAnyMap
-is_gen(x::MPolyQuoRingElem) = is_gen(lift(x))
-is_gen(x::MPolyDecRingElem) = is_gen(forget_grading(x))
+_is_gen(x::MPolyQuoRingElem) = _is_gen(lift(x))
+_is_gen(x::MPolyDecRingElem) = is_gen(forget_grading(x))
+_is_gen(x::MPolyRingElem) = is_gen(x)
 
 function _evaluate_plain(F::MPolyAnyMap{<:MPolyRing, <:MPolyRing}, u)
   if isdefined(F, :variable_indices)
@@ -178,6 +179,24 @@ function _evaluate_plain(F::MPolyAnyMap{<:MPolyRing, <:MPolyQuoRing}, u)
   return simplify(A(v))
 end
 
+# The following assumes `p` to be in `S[x₁,…,xₙ]` where `S` is the 
+# actual codomain of the map.
+function _evaluate_with_build_ctx(p::MPolyRingElem, ind::Vector{Int})
+  cod_ring = coefficient_ring(parent(p))
+  r = ngens(cod_ring)
+  ctx = MPolyBuildCtx(cod_ring)
+  for (q, e) in zip(coefficients(p), exponents(p))
+    ee = [0 for _ in 1:r]
+    for (i, k) in enumerate(e)
+      ee[ind[i]] = k
+    end
+    for (c, d) in zip(coefficients(q), exponents(q))
+      push_term!(ctx, c, ee+d)
+    end
+  end
+  return finish(ctx)
+end
+
 function _evaluate_general(F::MPolyAnyMap{<:MPolyRing, <:MPolyRing}, u)
   if domain(F) === codomain(F) && coefficient_map(F) === nothing
     return evaluate(map_coefficients(coefficient_map(F), u,
@@ -190,38 +209,15 @@ function _evaluate_general(F::MPolyAnyMap{<:MPolyRing, <:MPolyRing}, u)
                                          parent = S), F.img_gens)
       else
         tmp_poly = map_coefficients(coefficient_map(F), u, parent = S)
-        cod_ring = codomain(F)::MPolyRing
-        r = ngens(cod_ring)
-        ctx = MPolyBuildCtx(cod_ring)
-        for (p, e) in zip(coefficients(tmp_poly), exponents(tmp_poly))
-          ee = [0 for _ in 1:r]
-          for (i, k) in enumerate(e)
-            ee[F.variable_indices[i]] = k
-          end
-          p::MPolyRingElem
-          @assert parent(p) === cod_ring
-          for (c, d) in zip(coefficients(p), exponents(p))
-            push_term!(ctx, c, ee+d)
-          end
-        end
-        return finish(ctx)
+        return _evaluate_with_build_ctx(tmp_poly, F.variable_indices)
       end
     else
       if !isdefined(F, :variable_indices)
         return evaluate(map_coefficients(coefficient_map(F), u), F.img_gens)
       else
         tmp_poly = map_coefficients(coefficient_map(F), u)
-        cod_ring = codomain(F)::MPolyRing
-        r = ngens(cod_ring)
-        ctx = MPolyBuildCtx(cod_ring)
-        for (c, e) in zip(coefficients(tmp_poly), exponents(tmp_poly))
-          ee = [0 for _ in 1:r]
-          for (i, k) in enumerate(e)
-            ee[F.variable_indices[i]] = k
-          end
-          push_term!(ctx, c, ee)
-        end
-        return finish(ctx)
+        coefficient_ring(parent(tmp_poly)) === codomain(F) && return _evaluate_with_build_ctx(tmp_poly, F.variable_indices)
+        return evaluate(tmp_poly, F.variable_indices)
       end
     end
   end

From b6a3c405bb2856024f1e564a6e850fda774b75fa Mon Sep 17 00:00:00 2001
From: HechtiDerLachs <zach@mathematik.uni-kl.de>
Date: Mon, 30 Sep 2024 13:48:29 +0200
Subject: [PATCH 05/22] Fix tests.

---
 src/Rings/MPolyMap/MPolyAnyMap.jl |  6 ++++--
 src/Rings/MPolyMap/MPolyRing.jl   | 26 +++++++++++++++++++++-----
 2 files changed, 25 insertions(+), 7 deletions(-)

diff --git a/src/Rings/MPolyMap/MPolyAnyMap.jl b/src/Rings/MPolyMap/MPolyAnyMap.jl
index 1fbb44a86bb7..e7fef2ecd0a1 100644
--- a/src/Rings/MPolyMap/MPolyAnyMap.jl
+++ b/src/Rings/MPolyMap/MPolyAnyMap.jl
@@ -60,7 +60,9 @@ const _DomainTypes = Union{MPolyRing, MPolyQuoRing}
   function MPolyAnyMap{D, C, U, V}(domain::D,
                                    codomain::C,
                                    coeff_map::U,
-                                   img_gens::Vector{V}) where {D <: Union{<:MPolyRing, <:MPolyQuoRing}, 
+                                   img_gens::Vector{V};
+                                   check_for_mapping_of_vars::Bool=true
+                                  ) where {D <: Union{<:MPolyRing, <:MPolyQuoRing}, 
                                                                C <: Union{<:MPolyRing, <:MPolyQuoRing}, 
                                                                U, V}
     @assert V === elem_type(C)
@@ -68,7 +70,7 @@ const _DomainTypes = Union{MPolyRing, MPolyQuoRing}
       @assert parent(g) === codomain "elements does not have the correct parent"
     end
     result = new{D, C, U, V}(domain, codomain, coeff_map, img_gens)
-    if all(_is_gen, img_gens) && allunique(img_gens)
+    if check_for_mapping_of_vars && all(_is_gen, img_gens) && _allunique(img_gens)
       result.variable_indices = [findfirst(==(x), gens(codomain)) for x in img_gens]
     end
     return result
diff --git a/src/Rings/MPolyMap/MPolyRing.jl b/src/Rings/MPolyMap/MPolyRing.jl
index 4736a125b656..fb58a4eae962 100644
--- a/src/Rings/MPolyMap/MPolyRing.jl
+++ b/src/Rings/MPolyMap/MPolyRing.jl
@@ -137,9 +137,17 @@ _is_gen(x::MPolyQuoRingElem) = _is_gen(lift(x))
 _is_gen(x::MPolyDecRingElem) = is_gen(forget_grading(x))
 _is_gen(x::MPolyRingElem) = is_gen(x)
 
+# In case there is a type of polynomials for which hashing is not implemented 
+# and throws an error, this gives the opportunity to overwrite the `allunique`
+# to be used within the constructor for maps. 
+function _allunique(lst::Vector{T}) where {T<:RingElem}
+  return allunique(lst)
+end
+
 function _evaluate_plain(F::MPolyAnyMap{<:MPolyRing, <:MPolyRing}, u)
   if isdefined(F, :variable_indices)
     S = codomain(F)::MPolyRing
+    kk = coefficient_ring(S)
     r = ngens(S)
     ctx = MPolyBuildCtx(S)
     for (c, e) in zip(AbstractAlgebra.coefficients(u), AbstractAlgebra.exponent_vectors(u))
@@ -147,7 +155,7 @@ function _evaluate_plain(F::MPolyAnyMap{<:MPolyRing, <:MPolyRing}, u)
       for (i, k) in enumerate(e)
         ee[F.variable_indices[i]] = k
       end
-      push_term!(ctx, c, ee)
+      push_term!(ctx, kk(c), ee)
     end
     return finish(ctx)
   end
@@ -181,9 +189,12 @@ end
 
 # The following assumes `p` to be in `S[x₁,…,xₙ]` where `S` is the 
 # actual codomain of the map.
-function _evaluate_with_build_ctx(p::MPolyRingElem, ind::Vector{Int})
+function _evaluate_with_build_ctx(
+    p::MPolyRingElem, ind::Vector{Int}
+  )
   cod_ring = coefficient_ring(parent(p))
   r = ngens(cod_ring)
+  kk = coefficient_ring(cod_ring)
   ctx = MPolyBuildCtx(cod_ring)
   for (q, e) in zip(coefficients(p), exponents(p))
     ee = [0 for _ in 1:r]
@@ -191,7 +202,7 @@ function _evaluate_with_build_ctx(p::MPolyRingElem, ind::Vector{Int})
       ee[ind[i]] = k
     end
     for (c, d) in zip(coefficients(q), exponents(q))
-      push_term!(ctx, c, ee+d)
+      push_term!(ctx, kk(c), ee+d)
     end
   end
   return finish(ctx)
@@ -215,9 +226,14 @@ function _evaluate_general(F::MPolyAnyMap{<:MPolyRing, <:MPolyRing}, u)
       if !isdefined(F, :variable_indices)
         return evaluate(map_coefficients(coefficient_map(F), u), F.img_gens)
       else
+        # For the case where we can recycle the method above, do so.
         tmp_poly = map_coefficients(coefficient_map(F), u)
-        coefficient_ring(parent(tmp_poly)) === codomain(F) && return _evaluate_with_build_ctx(tmp_poly, F.variable_indices)
-        return evaluate(tmp_poly, F.variable_indices)
+        coefficient_ring(parent(tmp_poly)) === codomain(F) && return _evaluate_with_build_ctx(
+                   tmp_poly,
+                   F.variable_indices
+                 )
+        # Otherwise default to the standard evaluation for the time being.
+        return evaluate(tmp_poly, F.img_gens)
       end
     end
   end

From d1f90e3de26f3ec8c0d1f3080ae96d72b4096835 Mon Sep 17 00:00:00 2001
From: HechtiDerLachs <zach@mathematik.uni-kl.de>
Date: Mon, 30 Sep 2024 14:46:29 +0200
Subject: [PATCH 06/22] Widen type signature so that more rings benefit from
 variable-map.

---
 src/Rings/MPolyMap/MPolyAnyMap.jl | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/src/Rings/MPolyMap/MPolyAnyMap.jl b/src/Rings/MPolyMap/MPolyAnyMap.jl
index e7fef2ecd0a1..1e7c0879f72f 100644
--- a/src/Rings/MPolyMap/MPolyAnyMap.jl
+++ b/src/Rings/MPolyMap/MPolyAnyMap.jl
@@ -63,8 +63,7 @@ const _DomainTypes = Union{MPolyRing, MPolyQuoRing}
                                    img_gens::Vector{V};
                                    check_for_mapping_of_vars::Bool=true
                                   ) where {D <: Union{<:MPolyRing, <:MPolyQuoRing}, 
-                                                               C <: Union{<:MPolyRing, <:MPolyQuoRing}, 
-                                                               U, V}
+                                           C, U, V}
     @assert V === elem_type(C)
     for g in img_gens
       @assert parent(g) === codomain "elements does not have the correct parent"

From f98f1983aecaa3598d23863086eae8698961956b Mon Sep 17 00:00:00 2001
From: HechtiDerLachs <zach@mathematik.uni-kl.de>
Date: Mon, 30 Sep 2024 14:46:45 +0200
Subject: [PATCH 07/22] Fix call.

---
 src/Rings/MPolyMap/MPolyRing.jl | 11 +++++++----
 1 file changed, 7 insertions(+), 4 deletions(-)

diff --git a/src/Rings/MPolyMap/MPolyRing.jl b/src/Rings/MPolyMap/MPolyRing.jl
index fb58a4eae962..a2e07c0b3e1b 100644
--- a/src/Rings/MPolyMap/MPolyRing.jl
+++ b/src/Rings/MPolyMap/MPolyRing.jl
@@ -136,6 +136,8 @@ end
 _is_gen(x::MPolyQuoRingElem) = _is_gen(lift(x))
 _is_gen(x::MPolyDecRingElem) = is_gen(forget_grading(x))
 _is_gen(x::MPolyRingElem) = is_gen(x)
+# default method; overwrite if you want this to work for your rings.
+_is_gen(x::NCRingElem) = false
 
 # In case there is a type of polynomials for which hashing is not implemented 
 # and throws an error, this gives the opportunity to overwrite the `allunique`
@@ -190,9 +192,9 @@ end
 # The following assumes `p` to be in `S[x₁,…,xₙ]` where `S` is the 
 # actual codomain of the map.
 function _evaluate_with_build_ctx(
-    p::MPolyRingElem, ind::Vector{Int}
+    p::MPolyRingElem, ind::Vector{Int}, cod_ring::MPolyRing
   )
-  cod_ring = coefficient_ring(parent(p))
+  @assert cod_ring === coefficient_ring(parent(p))
   r = ngens(cod_ring)
   kk = coefficient_ring(cod_ring)
   ctx = MPolyBuildCtx(cod_ring)
@@ -220,7 +222,7 @@ function _evaluate_general(F::MPolyAnyMap{<:MPolyRing, <:MPolyRing}, u)
                                          parent = S), F.img_gens)
       else
         tmp_poly = map_coefficients(coefficient_map(F), u, parent = S)
-        return _evaluate_with_build_ctx(tmp_poly, F.variable_indices)
+        return _evaluate_with_build_ctx(tmp_poly, F.variable_indices, codomain(F))
       end
     else
       if !isdefined(F, :variable_indices)
@@ -230,7 +232,8 @@ function _evaluate_general(F::MPolyAnyMap{<:MPolyRing, <:MPolyRing}, u)
         tmp_poly = map_coefficients(coefficient_map(F), u)
         coefficient_ring(parent(tmp_poly)) === codomain(F) && return _evaluate_with_build_ctx(
                    tmp_poly,
-                   F.variable_indices
+                   F.variable_indices,
+                   codomain(F)
                  )
         # Otherwise default to the standard evaluation for the time being.
         return evaluate(tmp_poly, F.img_gens)

From 570e769e84b351e13ca73b3ad0d207a7577aac72 Mon Sep 17 00:00:00 2001
From: HechtiDerLachs <zach@mathematik.uni-kl.de>
Date: Mon, 30 Sep 2024 14:47:41 +0200
Subject: [PATCH 08/22] Implement extension for localizations and quotients.

---
 src/Rings/mpolyquo-localizations.jl | 102 ++++++++++++++++++++++++++++
 1 file changed, 102 insertions(+)

diff --git a/src/Rings/mpolyquo-localizations.jl b/src/Rings/mpolyquo-localizations.jl
index 551d7a82cbfa..76475bef5f29 100644
--- a/src/Rings/mpolyquo-localizations.jl
+++ b/src/Rings/mpolyquo-localizations.jl
@@ -2717,3 +2717,105 @@ function dim(R::MPolyQuoLocRing)
   return dim(modulus(R))
 end
 
+### extra methods for speedup of mappings
+# See `src/Rings/MPolyMap/MPolyRing.jl` for the original implementation and 
+# the rationale. These methods make speedup available for quotient rings 
+# and localizations of polynomial rings.
+function _allunique(lst::Vector{T}) where {T<:MPolyLocRingElem}
+  return _allunique(numerator.(lst))
+end
+
+function _allunique(lst::Vector{T}) where {T<:MPolyQuoLocRingElem}
+  return _allunique(lifted_numerator.(lst))
+end
+
+_is_gen(x::MPolyLocRingElem) = is_one(denominator(x)) && _is_gen(numerator(x))
+_is_gen(x::MPolyQuoLocRingElem) = is_one(lifted_denominator(x)) && _is_gen(lifted_numerator(x))
+
+function _evaluate_plain(
+    F::MPolyAnyMap{<:MPolyRing, CT}, u
+  ) where {CT <: Union{<:MPolyLocRing, <:MPolyQuoLocRing}}
+  if isdefined(F, :variable_indices)
+    W = codomain(F)::MPolyLocRing
+    S = base_ring(W)
+    kk = coefficient_ring(S)
+    r = ngens(S)
+    ctx = MPolyBuildCtx(S)
+    for (c, e) in zip(AbstractAlgebra.coefficients(u), AbstractAlgebra.exponent_vectors(u))
+      ee = [0 for _ in 1:r]
+      for (i, k) in enumerate(e)
+        ee[F.variable_indices[i]] = k
+      end
+      push_term!(ctx, kk(c), ee)
+    end
+    return W(finish(ctx))
+  end
+
+  return evaluate(u, F.img_gens)
+end
+
+function _evaluate_general(
+    F::MPolyAnyMap{<:MPolyRing, CT}, u
+  ) where {CT <: Union{<:MPolyQuoRing, <:MPolyLocRing, <:MPolyQuoLocRing}}
+  if domain(F) === codomain(F) && coefficient_map(F) === nothing
+    return evaluate(map_coefficients(coefficient_map(F), u,
+                                     parent = domain(F)), F.img_gens)
+  else
+    S = temp_ring(F)
+    if S !== nothing
+      if !isdefined(F, :variable_indices) || coefficient_ring(S) !== codomain(F)
+        return evaluate(map_coefficients(coefficient_map(F), u,
+                                         parent = S), F.img_gens)
+      else
+        tmp_poly = map_coefficients(coefficient_map(F), u, parent = S)
+        return _evaluate_with_build_ctx(tmp_poly, F.variable_indices, codomain(F))
+      end
+    else
+      if !isdefined(F, :variable_indices)
+        return evaluate(map_coefficients(coefficient_map(F), u), F.img_gens)
+      else
+        # For the case where we can recycle the method above, do so.
+        tmp_poly = map_coefficients(coefficient_map(F), u)
+        coefficient_ring(parent(tmp_poly)) === codomain(F) && return _evaluate_with_build_ctx(
+                   tmp_poly,
+                   F.variable_indices,
+                   codomain(F)
+                 )
+        # Otherwise default to the standard evaluation for the time being.
+        return evaluate(tmp_poly, F.img_gens)
+      end
+    end
+  end
+end
+
+function _evaluate_with_build_ctx(
+    p::MPolyRingElem, ind::Vector{Int}, 
+    Q::Union{<:MPolyQuoRing, <:MPolyLocRing, <:MPolyQuoLocRing}
+  )
+  @assert Q === coefficient_ring(parent(p))
+  cod_ring = base_ring(Q)
+  r = ngens(cod_ring)
+  kk = coefficient_ring(cod_ring)
+  ctx = MPolyBuildCtx(cod_ring)
+  for (q, e) in zip(coefficients(p), exponents(p))
+    ee = [0 for _ in 1:r]
+    for (i, k) in enumerate(e)
+      ee[ind[i]] = k
+    end
+    for (c, d) in zip(_coefficients(q), _exponents(q))
+      push_term!(ctx, kk(c), ee+d)
+    end
+  end
+  return Q(finish(ctx))
+end
+
+_coefficients(x::MPolyRingElem) = coefficients(x)
+_coefficients(x::MPolyQuoRingElem) = coefficients(lift(x))
+_coefficients(x::MPolyLocRingElem) = coefficients(numerator(x))
+_coefficients(x::MPolyQuoLocRingElem) = coefficients(lifted_numerator(x))
+
+_exponents(x::MPolyRingElem) = exponents(x)
+_exponents(x::MPolyQuoRingElem) = exponents(lift(x))
+_exponents(x::MPolyLocRingElem) = exponents(numerator(x))
+_exponents(x::MPolyQuoLocRingElem) = exponents(lifted_numerator(x))
+

From 2d83dd6d80c71afe9387dc4675653ad38a3d9320 Mon Sep 17 00:00:00 2001
From: HechtiDerLachs <zach@mathematik.uni-kl.de>
Date: Mon, 30 Sep 2024 14:53:14 +0200
Subject: [PATCH 09/22] Switch default for _allunique.

---
 src/Rings/MPolyMap/MPolyRing.jl | 12 +++++++++---
 1 file changed, 9 insertions(+), 3 deletions(-)

diff --git a/src/Rings/MPolyMap/MPolyRing.jl b/src/Rings/MPolyMap/MPolyRing.jl
index a2e07c0b3e1b..5be25f43ea5e 100644
--- a/src/Rings/MPolyMap/MPolyRing.jl
+++ b/src/Rings/MPolyMap/MPolyRing.jl
@@ -139,13 +139,19 @@ _is_gen(x::MPolyRingElem) = is_gen(x)
 # default method; overwrite if you want this to work for your rings.
 _is_gen(x::NCRingElem) = false
 
-# In case there is a type of polynomials for which hashing is not implemented 
-# and throws an error, this gives the opportunity to overwrite the `allunique`
+# In case there is a type of ring elements for which hashing is correctly implemented 
+# and does not throw an error, this gives the opportunity to overwrite the `allunique`
 # to be used within the constructor for maps. 
-function _allunique(lst::Vector{T}) where {T<:RingElem}
+function _allunique(lst::Vector{T}) where {T<:MPolyRingElem}
   return allunique(lst)
 end
 
+# We have a lot of rings which do/can not implement correct hashing. 
+# So we make the following the default.
+function _allunique(lst::Vector{T}) where {T<:RingElem}
+  return all(!(x in lst[i+1:end]) for (i, x) in enumerate(lst))
+end
+
 function _evaluate_plain(F::MPolyAnyMap{<:MPolyRing, <:MPolyRing}, u)
   if isdefined(F, :variable_indices)
     S = codomain(F)::MPolyRing

From 9a5961338c135456ce21489ede1a910f0d5a4036 Mon Sep 17 00:00:00 2001
From: HechtiDerLachs <zach@mathematik.uni-kl.de>
Date: Mon, 30 Sep 2024 15:15:23 +0200
Subject: [PATCH 10/22] Fix tests.

---
 .../Schemes/AffineSchemeOpenSubscheme/Rings/Methods.jl        | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/src/AlgebraicGeometry/Schemes/AffineSchemeOpenSubscheme/Rings/Methods.jl b/src/AlgebraicGeometry/Schemes/AffineSchemeOpenSubscheme/Rings/Methods.jl
index e54bba5722a9..1419c4e2f157 100644
--- a/src/AlgebraicGeometry/Schemes/AffineSchemeOpenSubscheme/Rings/Methods.jl
+++ b/src/AlgebraicGeometry/Schemes/AffineSchemeOpenSubscheme/Rings/Methods.jl
@@ -506,3 +506,7 @@ function Base.show(io::IO, ::MIME"text/plain", a::AffineSchemeOpenSubschemeRingE
   end
 end
 
+# overwrite a method for mapping of rings which would throw otherwise
+function _allunique(lst::Vector{T}) where {T<:MPolyQuoRingElem{<:MPolyRingElem{<:AffineSchemeOpenSubschemeRingElem}}}
+  return false
+end

From 4e5b8e7be11eb53c2c131b98e5a9b72415149c0d Mon Sep 17 00:00:00 2001
From: HechtiDerLachs <zach@mathematik.uni-kl.de>
Date: Mon, 30 Sep 2024 15:27:18 +0200
Subject: [PATCH 11/22] Remove superfluous if-clause and add some comments.

---
 src/Rings/mpolyquo-localizations.jl | 48 ++++++++++++++---------------
 1 file changed, 23 insertions(+), 25 deletions(-)

diff --git a/src/Rings/mpolyquo-localizations.jl b/src/Rings/mpolyquo-localizations.jl
index 76475bef5f29..4e32732adc08 100644
--- a/src/Rings/mpolyquo-localizations.jl
+++ b/src/Rings/mpolyquo-localizations.jl
@@ -2757,33 +2757,28 @@ end
 function _evaluate_general(
     F::MPolyAnyMap{<:MPolyRing, CT}, u
   ) where {CT <: Union{<:MPolyQuoRing, <:MPolyLocRing, <:MPolyQuoLocRing}}
-  if domain(F) === codomain(F) && coefficient_map(F) === nothing
-    return evaluate(map_coefficients(coefficient_map(F), u,
-                                     parent = domain(F)), F.img_gens)
+  S = temp_ring(F)
+  if S !== nothing
+    if !isdefined(F, :variable_indices) || coefficient_ring(S) !== codomain(F)
+      return evaluate(map_coefficients(coefficient_map(F), u,
+                                       parent = S), F.img_gens)
+    else
+      tmp_poly = map_coefficients(coefficient_map(F), u, parent = S)
+      return _evaluate_with_build_ctx(tmp_poly, F.variable_indices, codomain(F))
+    end
   else
-    S = temp_ring(F)
-    if S !== nothing
-      if !isdefined(F, :variable_indices) || coefficient_ring(S) !== codomain(F)
-        return evaluate(map_coefficients(coefficient_map(F), u,
-                                         parent = S), F.img_gens)
-      else
-        tmp_poly = map_coefficients(coefficient_map(F), u, parent = S)
-        return _evaluate_with_build_ctx(tmp_poly, F.variable_indices, codomain(F))
-      end
+    if !isdefined(F, :variable_indices)
+      return evaluate(map_coefficients(coefficient_map(F), u), F.img_gens)
     else
-      if !isdefined(F, :variable_indices)
-        return evaluate(map_coefficients(coefficient_map(F), u), F.img_gens)
-      else
-        # For the case where we can recycle the method above, do so.
-        tmp_poly = map_coefficients(coefficient_map(F), u)
-        coefficient_ring(parent(tmp_poly)) === codomain(F) && return _evaluate_with_build_ctx(
-                   tmp_poly,
-                   F.variable_indices,
-                   codomain(F)
-                 )
-        # Otherwise default to the standard evaluation for the time being.
-        return evaluate(tmp_poly, F.img_gens)
-      end
+      # For the case where we can recycle the method above, do so.
+      tmp_poly = map_coefficients(coefficient_map(F), u)
+      coefficient_ring(parent(tmp_poly)) === codomain(F) && return _evaluate_with_build_ctx(
+                                                                                            tmp_poly,
+                                                                                            F.variable_indices,
+                                                                                            codomain(F)
+                                                                                           )
+      # Otherwise default to the standard evaluation for the time being.
+      return evaluate(tmp_poly, F.img_gens)
     end
   end
 end
@@ -2809,6 +2804,9 @@ function _evaluate_with_build_ctx(
   return Q(finish(ctx))
 end
 
+# The following methods are only safe, because they are called 
+# exclusively in a setup where variables map to variables 
+# and no denominators are introduced. 
 _coefficients(x::MPolyRingElem) = coefficients(x)
 _coefficients(x::MPolyQuoRingElem) = coefficients(lift(x))
 _coefficients(x::MPolyLocRingElem) = coefficients(numerator(x))

From f005ce1e58f96598933a3e0ed1e82afe6efd3f07 Mon Sep 17 00:00:00 2001
From: HechtiDerLachs <zach@mathematik.uni-kl.de>
Date: Mon, 30 Sep 2024 18:22:13 +0200
Subject: [PATCH 12/22] Fix doctests in Algebraic statistics.

---
 experimental/AlgebraicStatistics/src/CI.jl    |   6 +-
 .../AlgebraicStatistics/src/Markov.jl         |   6 +-
 .../src/PhylogeneticParametrization.jl        | 112 +++++++++++++++---
 3 files changed, 108 insertions(+), 16 deletions(-)

diff --git a/experimental/AlgebraicStatistics/src/CI.jl b/experimental/AlgebraicStatistics/src/CI.jl
index 0e4d096eeeff..a1f6dcea65ff 100644
--- a/experimental/AlgebraicStatistics/src/CI.jl
+++ b/experimental/AlgebraicStatistics/src/CI.jl
@@ -137,7 +137,11 @@ julia> ci_statements(["A", "B", "X", "Y"])
  [B _||_ Y | {A, X}]
  [X _||_ Y | {}]
  [X _||_ Y | A]
- ⋮
+ [X _||_ Y | B]
+ [X _||_ Y | {A, B}]
+ [A _||_ X | {}]
+ [A _||_ X | B]
+ [A _||_ X | Y]
  [A _||_ X | {B, Y}]
  [B _||_ X | {}]
  [B _||_ X | A]
diff --git a/experimental/AlgebraicStatistics/src/Markov.jl b/experimental/AlgebraicStatistics/src/Markov.jl
index 3fb204f42e1e..d5a2c50a4ce4 100644
--- a/experimental/AlgebraicStatistics/src/Markov.jl
+++ b/experimental/AlgebraicStatistics/src/Markov.jl
@@ -124,7 +124,11 @@ julia> ci_statements(R)
  [B _||_ Y | {A, X}]
  [X _||_ Y | {}]
  [X _||_ Y | A]
- ⋮
+ [X _||_ Y | B]
+ [X _||_ Y | {A, B}]
+ [A _||_ X | {}]
+ [A _||_ X | B]
+ [A _||_ X | Y]
  [A _||_ X | {B, Y}]
  [B _||_ X | {}]
  [B _||_ X | A]
diff --git a/experimental/AlgebraicStatistics/src/PhylogeneticParametrization.jl b/experimental/AlgebraicStatistics/src/PhylogeneticParametrization.jl
index 3bd020933569..0788cd641b77 100644
--- a/experimental/AlgebraicStatistics/src/PhylogeneticParametrization.jl
+++ b/experimental/AlgebraicStatistics/src/PhylogeneticParametrization.jl
@@ -62,22 +62,64 @@ Dict{Tuple{Vararg{Int64}}, QQMPolyRingElem} with 64 entries:
   (1, 2, 1) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
   (3, 1, 1) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
   (4, 4, 2) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
-  (1, 2, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] …
+  (1, 2, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
   (3, 1, 3) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
-  (3, 2, 4) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] …
-  (3, 2, 1) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] …
-  (2, 1, 4) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] …
+  (3, 2, 4) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (3, 2, 1) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (2, 1, 4) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
   (3, 2, 3) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
   (2, 1, 1) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
-  (1, 3, 2) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] …
-  (1, 4, 2) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] …
-  (2, 1, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] …
+  (1, 3, 2) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (1, 4, 2) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (2, 1, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
   (2, 2, 4) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
   (4, 3, 4) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
   (2, 2, 1) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
   (4, 4, 4) => 1//4*a[1]*a[2]*a[3] + 3//4*b[1]*b[2]*b[3]
-  (4, 3, 1) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] …
+  (4, 3, 1) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
   (3, 3, 2) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
+  (4, 1, 2) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (4, 4, 1) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
+  (2, 2, 3) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
+  (3, 4, 2) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (4, 3, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
+  (4, 4, 3) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
+  (4, 2, 2) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
+  (1, 3, 4) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (2, 3, 2) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
+  (1, 4, 4) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
+  (1, 3, 1) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
+  (2, 4, 2) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
+  (1, 1, 2) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
+  (1, 4, 1) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
+  (1, 3, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
+  (3, 3, 4) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
+  (1, 4, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (4, 1, 4) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
+  (3, 4, 4) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
+  (3, 3, 1) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
+  (4, 1, 1) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
+  (1, 2, 2) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
+  (3, 1, 2) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (3, 4, 1) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (3, 3, 3) => 1//4*a[1]*a[2]*a[3] + 3//4*b[1]*b[2]*b[3]
+  (4, 1, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (4, 2, 4) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
+  (3, 4, 3) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
+  (4, 2, 1) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (3, 2, 2) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
+  (2, 3, 4) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (4, 2, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (2, 3, 1) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (2, 4, 4) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
+  (1, 1, 4) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
+  (2, 1, 2) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
+  (2, 4, 1) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (1, 1, 1) => 1//4*a[1]*a[2]*a[3] + 3//4*b[1]*b[2]*b[3]
+  (2, 3, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
+  (2, 4, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (1, 1, 3) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
+  (1, 2, 4) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
   ⋮         => ⋮
 ```
 """
@@ -155,6 +197,48 @@ Dict{Tuple{Vararg{Int64}}, QQMPolyRingElem} with 64 entries:
   (4, 4, 4) => 0
   (4, 3, 1) => 0
   (3, 3, 2) => 0
+  (4, 1, 2) => 0
+  (4, 4, 1) => x[3, 1]*x[1, 2]*x[2, 2]
+  (2, 2, 3) => 0
+  (3, 4, 2) => x[1, 2]*x[2, 2]*x[3, 2]
+  (4, 3, 3) => 0
+  (4, 4, 3) => 0
+  (4, 2, 2) => 0
+  (1, 3, 4) => 0
+  (2, 3, 2) => 0
+  (1, 4, 4) => x[1, 1]*x[2, 2]*x[3, 2]
+  (1, 3, 1) => 0
+  (2, 4, 2) => 0
+  (1, 1, 2) => 0
+  (1, 4, 1) => 0
+  (1, 3, 3) => x[1, 1]*x[2, 2]*x[3, 2]
+  (3, 3, 4) => 0
+  (1, 4, 3) => 0
+  (4, 1, 4) => x[2, 1]*x[1, 2]*x[3, 2]
+  (3, 4, 4) => 0
+  (3, 3, 1) => x[3, 1]*x[1, 2]*x[2, 2]
+  (4, 1, 1) => 0
+  (1, 2, 2) => x[1, 1]*x[2, 2]*x[3, 2]
+  (3, 1, 2) => 0
+  (3, 4, 1) => 0
+  (3, 3, 3) => 0
+  (4, 1, 3) => 0
+  (4, 2, 4) => 0
+  (3, 4, 3) => 0
+  (4, 2, 1) => 0
+  (3, 2, 2) => 0
+  (2, 3, 4) => x[1, 2]*x[2, 2]*x[3, 2]
+  (4, 2, 3) => x[1, 2]*x[2, 2]*x[3, 2]
+  (2, 3, 1) => 0
+  (2, 4, 4) => 0
+  (1, 1, 4) => 0
+  (2, 1, 2) => x[2, 1]*x[1, 2]*x[3, 2]
+  (2, 4, 1) => 0
+  (1, 1, 1) => x[1, 1]*x[2, 1]*x[3, 1]
+  (2, 3, 3) => 0
+  (2, 4, 3) => x[1, 2]*x[2, 2]*x[3, 2]
+  (1, 1, 3) => 0
+  (1, 2, 4) => 0
   ⋮         => ⋮
 ```
 """
@@ -192,16 +276,16 @@ Dict{Tuple{Vararg{Int64}}, QQMPolyRingElem} with 5 entries:
   (1, 2, 1) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
   (1, 1, 1) => 1//4*a[1]*a[2]*a[3] + 3//4*b[1]*b[2]*b[3]
   (1, 2, 2) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
-  (1, 2, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] …
+  (1, 2, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
   (1, 1, 2) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
 
 julia> p_equivclasses.classes
 Dict{Tuple{Vararg{Int64}}, Vector{Tuple{Vararg{Int64}}}} with 5 entries:
-  (1, 2, 1) => [(1, 2, 1), (1, 3, 1), (1, 4, 1), (2, 1, 2), (2, 3, 2), (2, 4, 2…
+  (1, 2, 1) => [(1, 2, 1), (1, 3, 1), (1, 4, 1), (2, 1, 2), (2, 3, 2), (2, 4, 2), (3, 1, 3), (3, 2, 3), (3, 4, 3), (4, 1, 4), (4, 2, 4), (4, 3, 4)]
   (1, 1, 1) => [(1, 1, 1), (2, 2, 2), (3, 3, 3), (4, 4, 4)]
-  (1, 2, 2) => [(1, 2, 2), (1, 3, 3), (1, 4, 4), (2, 1, 1), (2, 3, 3), (2, 4, 4…
-  (1, 2, 3) => [(1, 2, 3), (1, 2, 4), (1, 3, 2), (1, 3, 4), (1, 4, 2), (1, 4, 3…
-  (1, 1, 2) => [(1, 1, 2), (1, 1, 3), (1, 1, 4), (2, 2, 1), (2, 2, 3), (2, 2, 4…
+  (1, 2, 2) => [(1, 2, 2), (1, 3, 3), (1, 4, 4), (2, 1, 1), (2, 3, 3), (2, 4, 4), (3, 1, 1), (3, 2, 2), (3, 4, 4), (4, 1, 1), (4, 2, 2), (4, 3, 3)]
+  (1, 2, 3) => [(1, 2, 3), (1, 2, 4), (1, 3, 2), (1, 3, 4), (1, 4, 2), (1, 4, 3), (2, 1, 3), (2, 1, 4), (2, 3, 1), (2, 3, 4)  …  (3, 2, 1), (3, 2, 4), (3, 4, 1), (3, 4, 2), (4, 1, 2), (4, 1, 3), (4, 2, 1), (4, …
+  (1, 1, 2) => [(1, 1, 2), (1, 1, 3), (1, 1, 4), (2, 2, 1), (2, 2, 3), (2, 2, 4), (3, 3, 1), (3, 3, 2), (3, 3, 4), (4, 4, 1), (4, 4, 2), (4, 4, 3)]
 
 julia> q_equivclasses = compute_equivalent_classes(q);
 
@@ -251,7 +335,7 @@ Dict{Tuple{Int64, Int64, Int64}, QQMPolyRingElem} with 5 entries:
   (1, 2, 1) => 3*a[1]*a[3]*b[2] + 3*a[2]*b[1]*b[3] + 6*b[1]*b[2]*b[3]
   (1, 1, 1) => a[1]*a[2]*a[3] + 3*b[1]*b[2]*b[3]
   (1, 2, 2) => 3*a[1]*b[2]*b[3] + 3*a[2]*a[3]*b[1] + 6*b[1]*b[2]*b[3]
-  (1, 2, 3) => 6*a[1]*b[2]*b[3] + 6*a[2]*b[1]*b[3] + 6*a[3]*b[1]*b[2] + 6*b[1]*…
+  (1, 2, 3) => 6*a[1]*b[2]*b[3] + 6*a[2]*b[1]*b[3] + 6*a[3]*b[1]*b[2] + 6*b[1]*b[2]*b[3]
   (1, 1, 2) => 3*a[1]*a[2]*b[3] + 3*a[3]*b[1]*b[2] + 6*b[1]*b[2]*b[3]
 ```
 """

From 0c65e56d996201f535647cb7d578c2742d38426a Mon Sep 17 00:00:00 2001
From: HechtiDerLachs <zach@mathematik.uni-kl.de>
Date: Mon, 30 Sep 2024 18:22:38 +0200
Subject: [PATCH 13/22] Fix doctests in FTheoryTools.

---
 .../FTheoryTools/src/AbstractFTheoryModels/attributes.jl       | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/experimental/FTheoryTools/src/AbstractFTheoryModels/attributes.jl b/experimental/FTheoryTools/src/AbstractFTheoryModels/attributes.jl
index 5161ab59517b..374abd08a795 100644
--- a/experimental/FTheoryTools/src/AbstractFTheoryModels/attributes.jl
+++ b/experimental/FTheoryTools/src/AbstractFTheoryModels/attributes.jl
@@ -1677,7 +1677,8 @@ julia> components_of_dual_graph(qsm_model)
  "C7"
  "C8"
  "C9"
- ⋮
+ "C13"
+ "C14"
  "C16"
  "C17"
  "C21"

From 8944bb2e448545e6707c91ed95be09cb6841c82b Mon Sep 17 00:00:00 2001
From: HechtiDerLachs <zach@mathematik.uni-kl.de>
Date: Mon, 30 Sep 2024 18:23:15 +0200
Subject: [PATCH 14/22] Fix doctests in AffineSchemes.

---
 .../Schemes/AffineSchemes/Morphisms/Attributes.jl         | 8 ++++----
 .../Schemes/AffineSchemes/Morphisms/Constructors.jl       | 4 ++--
 .../Schemes/AffineSchemes/Objects/Attributes.jl           | 2 +-
 3 files changed, 7 insertions(+), 7 deletions(-)

diff --git a/src/AlgebraicGeometry/Schemes/AffineSchemes/Morphisms/Attributes.jl b/src/AlgebraicGeometry/Schemes/AffineSchemes/Morphisms/Attributes.jl
index 5e00d1ebc382..5bc7f57aea79 100644
--- a/src/AlgebraicGeometry/Schemes/AffineSchemes/Morphisms/Attributes.jl
+++ b/src/AlgebraicGeometry/Schemes/AffineSchemes/Morphisms/Attributes.jl
@@ -46,7 +46,7 @@ Affine scheme morphism
   from [x1, x2, x3]  scheme(x1)
   to   [x1, x2, x3]  affine 3-space over QQ
 given by the pullback function
-  x1 -> 0
+  x1 -> x1
   x2 -> x2
   x3 -> x3
 
@@ -95,7 +95,7 @@ Affine scheme morphism
   from [x1, x2, x3]  scheme(x1)
   to   [x1, x2, x3]  affine 3-space over QQ
 given by the pullback function
-  x1 -> 0
+  x1 -> x1
   x2 -> x2
   x3 -> x3
 
@@ -143,7 +143,7 @@ Ring homomorphism
   from multivariate polynomial ring in 3 variables over QQ
   to quotient of multivariate polynomial ring by ideal (x1)
 defined by
-  x1 -> 0
+  x1 -> x1
   x2 -> x2
   x3 -> x3
 ```
@@ -254,7 +254,7 @@ Affine scheme morphism
   from [x1, x2, x3]  scheme(x1)
   to   [x1, x2, x3]  affine 3-space over QQ
 given by the pullback function
-  x1 -> 0
+  x1 -> x1
   x2 -> x2
   x3 -> x3
 
diff --git a/src/AlgebraicGeometry/Schemes/AffineSchemes/Morphisms/Constructors.jl b/src/AlgebraicGeometry/Schemes/AffineSchemes/Morphisms/Constructors.jl
index 2b5e02d949ff..56f8667ba51a 100644
--- a/src/AlgebraicGeometry/Schemes/AffineSchemes/Morphisms/Constructors.jl
+++ b/src/AlgebraicGeometry/Schemes/AffineSchemes/Morphisms/Constructors.jl
@@ -132,7 +132,7 @@ Affine scheme morphism
   from [x1, x2, x3]  scheme(x1)
   to   [x1, x2, x3]  affine 3-space over QQ
 given by the pullback function
-  x1 -> 0
+  x1 -> x1
   x2 -> x2
   x3 -> x3
 
@@ -181,7 +181,7 @@ Affine scheme morphism
   from [x1, x2, x3]  scheme(x1)
   to   [x1, x2, x3]  affine 3-space over QQ
 given by the pullback function
-  x1 -> 0
+  x1 -> x1
   x2 -> x2
   x3 -> x3
 
diff --git a/src/AlgebraicGeometry/Schemes/AffineSchemes/Objects/Attributes.jl b/src/AlgebraicGeometry/Schemes/AffineSchemes/Objects/Attributes.jl
index 8b9d9f96e7e1..2ad15abb7fac 100644
--- a/src/AlgebraicGeometry/Schemes/AffineSchemes/Objects/Attributes.jl
+++ b/src/AlgebraicGeometry/Schemes/AffineSchemes/Objects/Attributes.jl
@@ -234,7 +234,7 @@ Affine scheme morphism
   from [x, y]  scheme(x)
   to   [x, y]  affine 2-space over QQ
 given by the pullback function
-  x -> 0
+  x -> x
   y -> y
 
 julia> inc == inclusion_morphism(Y, X)

From 90dc0955498255f64846902cb637148671357899 Mon Sep 17 00:00:00 2001
From: HechtiDerLachs <zach@mathematik.uni-kl.de>
Date: Mon, 30 Sep 2024 19:00:15 +0200
Subject: [PATCH 15/22] Revert "Fix doctests in FTheoryTools."

This reverts commit 0c65e56d996201f535647cb7d578c2742d38426a.
---
 .../FTheoryTools/src/AbstractFTheoryModels/attributes.jl       | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/experimental/FTheoryTools/src/AbstractFTheoryModels/attributes.jl b/experimental/FTheoryTools/src/AbstractFTheoryModels/attributes.jl
index 374abd08a795..5161ab59517b 100644
--- a/experimental/FTheoryTools/src/AbstractFTheoryModels/attributes.jl
+++ b/experimental/FTheoryTools/src/AbstractFTheoryModels/attributes.jl
@@ -1677,8 +1677,7 @@ julia> components_of_dual_graph(qsm_model)
  "C7"
  "C8"
  "C9"
- "C13"
- "C14"
+ ⋮
  "C16"
  "C17"
  "C21"

From 5d61dda13ba0b2445bfc2f96111509b7de76e844 Mon Sep 17 00:00:00 2001
From: HechtiDerLachs <zach@mathematik.uni-kl.de>
Date: Mon, 30 Sep 2024 19:00:21 +0200
Subject: [PATCH 16/22] Revert "Fix doctests in Algebraic statistics."

This reverts commit f005ce1e58f96598933a3e0ed1e82afe6efd3f07.
---
 experimental/AlgebraicStatistics/src/CI.jl    |   6 +-
 .../AlgebraicStatistics/src/Markov.jl         |   6 +-
 .../src/PhylogeneticParametrization.jl        | 112 +++---------------
 3 files changed, 16 insertions(+), 108 deletions(-)

diff --git a/experimental/AlgebraicStatistics/src/CI.jl b/experimental/AlgebraicStatistics/src/CI.jl
index a1f6dcea65ff..0e4d096eeeff 100644
--- a/experimental/AlgebraicStatistics/src/CI.jl
+++ b/experimental/AlgebraicStatistics/src/CI.jl
@@ -137,11 +137,7 @@ julia> ci_statements(["A", "B", "X", "Y"])
  [B _||_ Y | {A, X}]
  [X _||_ Y | {}]
  [X _||_ Y | A]
- [X _||_ Y | B]
- [X _||_ Y | {A, B}]
- [A _||_ X | {}]
- [A _||_ X | B]
- [A _||_ X | Y]
+ ⋮
  [A _||_ X | {B, Y}]
  [B _||_ X | {}]
  [B _||_ X | A]
diff --git a/experimental/AlgebraicStatistics/src/Markov.jl b/experimental/AlgebraicStatistics/src/Markov.jl
index d5a2c50a4ce4..3fb204f42e1e 100644
--- a/experimental/AlgebraicStatistics/src/Markov.jl
+++ b/experimental/AlgebraicStatistics/src/Markov.jl
@@ -124,11 +124,7 @@ julia> ci_statements(R)
  [B _||_ Y | {A, X}]
  [X _||_ Y | {}]
  [X _||_ Y | A]
- [X _||_ Y | B]
- [X _||_ Y | {A, B}]
- [A _||_ X | {}]
- [A _||_ X | B]
- [A _||_ X | Y]
+ ⋮
  [A _||_ X | {B, Y}]
  [B _||_ X | {}]
  [B _||_ X | A]
diff --git a/experimental/AlgebraicStatistics/src/PhylogeneticParametrization.jl b/experimental/AlgebraicStatistics/src/PhylogeneticParametrization.jl
index 0788cd641b77..3bd020933569 100644
--- a/experimental/AlgebraicStatistics/src/PhylogeneticParametrization.jl
+++ b/experimental/AlgebraicStatistics/src/PhylogeneticParametrization.jl
@@ -62,64 +62,22 @@ Dict{Tuple{Vararg{Int64}}, QQMPolyRingElem} with 64 entries:
   (1, 2, 1) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
   (3, 1, 1) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
   (4, 4, 2) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
-  (1, 2, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (1, 2, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] …
   (3, 1, 3) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
-  (3, 2, 4) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
-  (3, 2, 1) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
-  (2, 1, 4) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (3, 2, 4) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] …
+  (3, 2, 1) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] …
+  (2, 1, 4) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] …
   (3, 2, 3) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
   (2, 1, 1) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
-  (1, 3, 2) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
-  (1, 4, 2) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
-  (2, 1, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (1, 3, 2) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] …
+  (1, 4, 2) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] …
+  (2, 1, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] …
   (2, 2, 4) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
   (4, 3, 4) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
   (2, 2, 1) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
   (4, 4, 4) => 1//4*a[1]*a[2]*a[3] + 3//4*b[1]*b[2]*b[3]
-  (4, 3, 1) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (4, 3, 1) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] …
   (3, 3, 2) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
-  (4, 1, 2) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
-  (4, 4, 1) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
-  (2, 2, 3) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
-  (3, 4, 2) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
-  (4, 3, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
-  (4, 4, 3) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
-  (4, 2, 2) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
-  (1, 3, 4) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
-  (2, 3, 2) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
-  (1, 4, 4) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
-  (1, 3, 1) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
-  (2, 4, 2) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
-  (1, 1, 2) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
-  (1, 4, 1) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
-  (1, 3, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
-  (3, 3, 4) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
-  (1, 4, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
-  (4, 1, 4) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
-  (3, 4, 4) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
-  (3, 3, 1) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
-  (4, 1, 1) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
-  (1, 2, 2) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
-  (3, 1, 2) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
-  (3, 4, 1) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
-  (3, 3, 3) => 1//4*a[1]*a[2]*a[3] + 3//4*b[1]*b[2]*b[3]
-  (4, 1, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
-  (4, 2, 4) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
-  (3, 4, 3) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
-  (4, 2, 1) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
-  (3, 2, 2) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
-  (2, 3, 4) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
-  (4, 2, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
-  (2, 3, 1) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
-  (2, 4, 4) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
-  (1, 1, 4) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
-  (2, 1, 2) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
-  (2, 4, 1) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
-  (1, 1, 1) => 1//4*a[1]*a[2]*a[3] + 3//4*b[1]*b[2]*b[3]
-  (2, 3, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
-  (2, 4, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
-  (1, 1, 3) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
-  (1, 2, 4) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
   ⋮         => ⋮
 ```
 """
@@ -197,48 +155,6 @@ Dict{Tuple{Vararg{Int64}}, QQMPolyRingElem} with 64 entries:
   (4, 4, 4) => 0
   (4, 3, 1) => 0
   (3, 3, 2) => 0
-  (4, 1, 2) => 0
-  (4, 4, 1) => x[3, 1]*x[1, 2]*x[2, 2]
-  (2, 2, 3) => 0
-  (3, 4, 2) => x[1, 2]*x[2, 2]*x[3, 2]
-  (4, 3, 3) => 0
-  (4, 4, 3) => 0
-  (4, 2, 2) => 0
-  (1, 3, 4) => 0
-  (2, 3, 2) => 0
-  (1, 4, 4) => x[1, 1]*x[2, 2]*x[3, 2]
-  (1, 3, 1) => 0
-  (2, 4, 2) => 0
-  (1, 1, 2) => 0
-  (1, 4, 1) => 0
-  (1, 3, 3) => x[1, 1]*x[2, 2]*x[3, 2]
-  (3, 3, 4) => 0
-  (1, 4, 3) => 0
-  (4, 1, 4) => x[2, 1]*x[1, 2]*x[3, 2]
-  (3, 4, 4) => 0
-  (3, 3, 1) => x[3, 1]*x[1, 2]*x[2, 2]
-  (4, 1, 1) => 0
-  (1, 2, 2) => x[1, 1]*x[2, 2]*x[3, 2]
-  (3, 1, 2) => 0
-  (3, 4, 1) => 0
-  (3, 3, 3) => 0
-  (4, 1, 3) => 0
-  (4, 2, 4) => 0
-  (3, 4, 3) => 0
-  (4, 2, 1) => 0
-  (3, 2, 2) => 0
-  (2, 3, 4) => x[1, 2]*x[2, 2]*x[3, 2]
-  (4, 2, 3) => x[1, 2]*x[2, 2]*x[3, 2]
-  (2, 3, 1) => 0
-  (2, 4, 4) => 0
-  (1, 1, 4) => 0
-  (2, 1, 2) => x[2, 1]*x[1, 2]*x[3, 2]
-  (2, 4, 1) => 0
-  (1, 1, 1) => x[1, 1]*x[2, 1]*x[3, 1]
-  (2, 3, 3) => 0
-  (2, 4, 3) => x[1, 2]*x[2, 2]*x[3, 2]
-  (1, 1, 3) => 0
-  (1, 2, 4) => 0
   ⋮         => ⋮
 ```
 """
@@ -276,16 +192,16 @@ Dict{Tuple{Vararg{Int64}}, QQMPolyRingElem} with 5 entries:
   (1, 2, 1) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
   (1, 1, 1) => 1//4*a[1]*a[2]*a[3] + 3//4*b[1]*b[2]*b[3]
   (1, 2, 2) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
-  (1, 2, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (1, 2, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] …
   (1, 1, 2) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
 
 julia> p_equivclasses.classes
 Dict{Tuple{Vararg{Int64}}, Vector{Tuple{Vararg{Int64}}}} with 5 entries:
-  (1, 2, 1) => [(1, 2, 1), (1, 3, 1), (1, 4, 1), (2, 1, 2), (2, 3, 2), (2, 4, 2), (3, 1, 3), (3, 2, 3), (3, 4, 3), (4, 1, 4), (4, 2, 4), (4, 3, 4)]
+  (1, 2, 1) => [(1, 2, 1), (1, 3, 1), (1, 4, 1), (2, 1, 2), (2, 3, 2), (2, 4, 2…
   (1, 1, 1) => [(1, 1, 1), (2, 2, 2), (3, 3, 3), (4, 4, 4)]
-  (1, 2, 2) => [(1, 2, 2), (1, 3, 3), (1, 4, 4), (2, 1, 1), (2, 3, 3), (2, 4, 4), (3, 1, 1), (3, 2, 2), (3, 4, 4), (4, 1, 1), (4, 2, 2), (4, 3, 3)]
-  (1, 2, 3) => [(1, 2, 3), (1, 2, 4), (1, 3, 2), (1, 3, 4), (1, 4, 2), (1, 4, 3), (2, 1, 3), (2, 1, 4), (2, 3, 1), (2, 3, 4)  …  (3, 2, 1), (3, 2, 4), (3, 4, 1), (3, 4, 2), (4, 1, 2), (4, 1, 3), (4, 2, 1), (4, …
-  (1, 1, 2) => [(1, 1, 2), (1, 1, 3), (1, 1, 4), (2, 2, 1), (2, 2, 3), (2, 2, 4), (3, 3, 1), (3, 3, 2), (3, 3, 4), (4, 4, 1), (4, 4, 2), (4, 4, 3)]
+  (1, 2, 2) => [(1, 2, 2), (1, 3, 3), (1, 4, 4), (2, 1, 1), (2, 3, 3), (2, 4, 4…
+  (1, 2, 3) => [(1, 2, 3), (1, 2, 4), (1, 3, 2), (1, 3, 4), (1, 4, 2), (1, 4, 3…
+  (1, 1, 2) => [(1, 1, 2), (1, 1, 3), (1, 1, 4), (2, 2, 1), (2, 2, 3), (2, 2, 4…
 
 julia> q_equivclasses = compute_equivalent_classes(q);
 
@@ -335,7 +251,7 @@ Dict{Tuple{Int64, Int64, Int64}, QQMPolyRingElem} with 5 entries:
   (1, 2, 1) => 3*a[1]*a[3]*b[2] + 3*a[2]*b[1]*b[3] + 6*b[1]*b[2]*b[3]
   (1, 1, 1) => a[1]*a[2]*a[3] + 3*b[1]*b[2]*b[3]
   (1, 2, 2) => 3*a[1]*b[2]*b[3] + 3*a[2]*a[3]*b[1] + 6*b[1]*b[2]*b[3]
-  (1, 2, 3) => 6*a[1]*b[2]*b[3] + 6*a[2]*b[1]*b[3] + 6*a[3]*b[1]*b[2] + 6*b[1]*b[2]*b[3]
+  (1, 2, 3) => 6*a[1]*b[2]*b[3] + 6*a[2]*b[1]*b[3] + 6*a[3]*b[1]*b[2] + 6*b[1]*…
   (1, 1, 2) => 3*a[1]*a[2]*b[3] + 3*a[3]*b[1]*b[2] + 6*b[1]*b[2]*b[3]
 ```
 """

From 7ad7f39b4bcfff07fbaeab49984dc20ef0c2f90b Mon Sep 17 00:00:00 2001
From: HechtiDerLachs <zach@mathematik.uni-kl.de>
Date: Mon, 30 Sep 2024 22:30:02 +0200
Subject: [PATCH 17/22] Remove duplicated code.

---
 src/Rings/MPolyMap/MPolyRing.jl | 42 +++++++++++++--------------------
 1 file changed, 16 insertions(+), 26 deletions(-)

diff --git a/src/Rings/MPolyMap/MPolyRing.jl b/src/Rings/MPolyMap/MPolyRing.jl
index 5be25f43ea5e..4d43595aec67 100644
--- a/src/Rings/MPolyMap/MPolyRing.jl
+++ b/src/Rings/MPolyMap/MPolyRing.jl
@@ -152,22 +152,23 @@ function _allunique(lst::Vector{T}) where {T<:RingElem}
   return all(!(x in lst[i+1:end]) for (i, x) in enumerate(lst))
 end
 
-function _evaluate_plain(F::MPolyAnyMap{<:MPolyRing, <:MPolyRing}, u)
-  if isdefined(F, :variable_indices)
-    S = codomain(F)::MPolyRing
-    kk = coefficient_ring(S)
-    r = ngens(S)
-    ctx = MPolyBuildCtx(S)
-    for (c, e) in zip(AbstractAlgebra.coefficients(u), AbstractAlgebra.exponent_vectors(u))
-      ee = [0 for _ in 1:r]
-      for (i, k) in enumerate(e)
-        ee[F.variable_indices[i]] = k
-      end
-      push_term!(ctx, kk(c), ee)
+function _build_poly(u::MPolyRingElem, indices::Vector{Int}, S::MPolyRing)
+  S = codomain(F)::MPolyRing
+  kk = coefficient_ring(S)
+  r = ngens(S)
+  ctx = MPolyBuildCtx(S)
+  for (c, e) in zip(AbstractAlgebra.coefficients(u), AbstractAlgebra.exponent_vectors(u))
+    ee = [0 for _ in 1:r]
+    for (i, k) in enumerate(e)
+      ee[indices[i]] = k
     end
-    return finish(ctx)
+    push_term!(ctx, kk(c), ee)
   end
+  return finish(ctx)
+end
 
+function _evaluate_plain(F::MPolyAnyMap{<:MPolyRing, <:MPolyRing}, u)
+  isdefined(F, :variable_indices) && return _build_poly(u, F.variable_indices, codomain(F))
   return evaluate(u, F.img_gens)
 end
 
@@ -177,20 +178,9 @@ end
 
 # See the comment in MPolyQuo.jl
 function _evaluate_plain(F::MPolyAnyMap{<:MPolyRing, <:MPolyQuoRing}, u)
-  if isdefined(F, :variable_indices)
-    S = base_ring(codomain(F))::MPolyRing
-    r = ngens(S)
-    ctx = MPolyBuildCtx(S)
-    for (c, e) in zip(coefficients(u), exponents(u))
-      ee = [0 for _ in 1:r]
-      for (i, k) in enumerate(e)
-        ee[F.variable_indices[i]] = k
-      end
-      push_term!(ctx, c, ee)
-    end
-    return codomain(F)(finish(ctx))
-  end
   A = codomain(F)
+  R = base_ring(A)
+  isdefined(F, :variable_indices) && return A(_build_poly(u, F.variable_indices, R))
   v = evaluate(lift(u), lift.(_images(F)))
   return simplify(A(v))
 end

From 4d17d351fa66e8c06291be3b18174a8caf58e584 Mon Sep 17 00:00:00 2001
From: HechtiDerLachs <zach@mathematik.uni-kl.de>
Date: Mon, 30 Sep 2024 22:35:29 +0200
Subject: [PATCH 18/22] Revert to a single internal constructor.

---
 src/Rings/MPolyMap/MPolyAnyMap.jl | 18 ++++++------------
 1 file changed, 6 insertions(+), 12 deletions(-)

diff --git a/src/Rings/MPolyMap/MPolyAnyMap.jl b/src/Rings/MPolyMap/MPolyAnyMap.jl
index 1e7c0879f72f..009cebd8380f 100644
--- a/src/Rings/MPolyMap/MPolyAnyMap.jl
+++ b/src/Rings/MPolyMap/MPolyAnyMap.jl
@@ -47,28 +47,22 @@ const _DomainTypes = Union{MPolyRing, MPolyQuoRing}
                                 # in case the mapping takes such a particularly
                                 # simple form.
 
-  function MPolyAnyMap{D, C, U, V}(domain::D,
-                                   codomain::C,
-                                   coeff_map::U,
-                                   img_gens::Vector{V}) where {D, C, U, V}
-    @assert V === elem_type(C)
-    for g in img_gens
-      @assert parent(g) === codomain "elements does not have the correct parent"
-    end
-    return new{D, C, U, V}(domain, codomain, coeff_map, img_gens)
-  end
   function MPolyAnyMap{D, C, U, V}(domain::D,
                                    codomain::C,
                                    coeff_map::U,
                                    img_gens::Vector{V};
                                    check_for_mapping_of_vars::Bool=true
-                                  ) where {D <: Union{<:MPolyRing, <:MPolyQuoRing}, 
-                                           C, U, V}
+                                  ) where {D, C, U, V}
     @assert V === elem_type(C)
     for g in img_gens
       @assert parent(g) === codomain "elements does not have the correct parent"
     end
     result = new{D, C, U, V}(domain, codomain, coeff_map, img_gens)
+    # If it ever turned out that doing the checks within the following if-block
+    # is a bottleneck, consider passing on the `check_for_mapping_of_vars` kw 
+    # argument to the outer constructors or make the outer constructors 
+    # call the inner one with this argument set to `false`. This way the check 
+    # can safely be disabled.
     if check_for_mapping_of_vars && all(_is_gen, img_gens) && _allunique(img_gens)
       result.variable_indices = [findfirst(==(x), gens(codomain)) for x in img_gens]
     end

From f7289e832d5210ef4145a0c7f056239a699426a5 Mon Sep 17 00:00:00 2001
From: HechtiDerLachs <zach@mathematik.uni-kl.de>
Date: Mon, 30 Sep 2024 22:36:42 +0200
Subject: [PATCH 19/22] Fix internal method.

---
 src/Rings/MPolyMap/MPolyRing.jl | 1 -
 1 file changed, 1 deletion(-)

diff --git a/src/Rings/MPolyMap/MPolyRing.jl b/src/Rings/MPolyMap/MPolyRing.jl
index 4d43595aec67..ca21f18226ff 100644
--- a/src/Rings/MPolyMap/MPolyRing.jl
+++ b/src/Rings/MPolyMap/MPolyRing.jl
@@ -153,7 +153,6 @@ function _allunique(lst::Vector{T}) where {T<:RingElem}
 end
 
 function _build_poly(u::MPolyRingElem, indices::Vector{Int}, S::MPolyRing)
-  S = codomain(F)::MPolyRing
   kk = coefficient_ring(S)
   r = ngens(S)
   ctx = MPolyBuildCtx(S)

From 9092a8a4acaa6d754237f18e000cdc23015f7757 Mon Sep 17 00:00:00 2001
From: HechtiDerLachs <zach@mathematik.uni-kl.de>
Date: Mon, 30 Sep 2024 22:53:56 +0200
Subject: [PATCH 20/22] Remove some more code duplication.

---
 src/Rings/mpolyquo-localizations.jl | 19 +++----------------
 1 file changed, 3 insertions(+), 16 deletions(-)

diff --git a/src/Rings/mpolyquo-localizations.jl b/src/Rings/mpolyquo-localizations.jl
index 4e32732adc08..5294ea50c6ad 100644
--- a/src/Rings/mpolyquo-localizations.jl
+++ b/src/Rings/mpolyquo-localizations.jl
@@ -2735,22 +2735,9 @@ _is_gen(x::MPolyQuoLocRingElem) = is_one(lifted_denominator(x)) && _is_gen(lifte
 function _evaluate_plain(
     F::MPolyAnyMap{<:MPolyRing, CT}, u
   ) where {CT <: Union{<:MPolyLocRing, <:MPolyQuoLocRing}}
-  if isdefined(F, :variable_indices)
-    W = codomain(F)::MPolyLocRing
-    S = base_ring(W)
-    kk = coefficient_ring(S)
-    r = ngens(S)
-    ctx = MPolyBuildCtx(S)
-    for (c, e) in zip(AbstractAlgebra.coefficients(u), AbstractAlgebra.exponent_vectors(u))
-      ee = [0 for _ in 1:r]
-      for (i, k) in enumerate(e)
-        ee[F.variable_indices[i]] = k
-      end
-      push_term!(ctx, kk(c), ee)
-    end
-    return W(finish(ctx))
-  end
-
+  W = codomain(F)::MPolyLocRing
+  S = base_ring(W)
+  isdefined(F, :variable_indices) && return W(_build_poly(u, F.variable_indices, S))
   return evaluate(u, F.img_gens)
 end
 

From 733b8f1f096b1b02addb1b41b70afdce5954964e Mon Sep 17 00:00:00 2001
From: HechtiDerLachs <zach@mathematik.uni-kl.de>
Date: Tue, 1 Oct 2024 09:56:43 +0200
Subject: [PATCH 21/22] Switch to the AA methods.

---
 src/Rings/MPolyMap/MPolyRing.jl     |  4 ++--
 src/Rings/mpolyquo-localizations.jl | 24 ++++++++++++------------
 2 files changed, 14 insertions(+), 14 deletions(-)

diff --git a/src/Rings/MPolyMap/MPolyRing.jl b/src/Rings/MPolyMap/MPolyRing.jl
index ca21f18226ff..0b3b9b6044ea 100644
--- a/src/Rings/MPolyMap/MPolyRing.jl
+++ b/src/Rings/MPolyMap/MPolyRing.jl
@@ -193,12 +193,12 @@ function _evaluate_with_build_ctx(
   r = ngens(cod_ring)
   kk = coefficient_ring(cod_ring)
   ctx = MPolyBuildCtx(cod_ring)
-  for (q, e) in zip(coefficients(p), exponents(p))
+  for (q, e) in zip(AbstractAlgebra.coefficients(p), AbstractAlgebra.exponent_vectors(p))
     ee = [0 for _ in 1:r]
     for (i, k) in enumerate(e)
       ee[ind[i]] = k
     end
-    for (c, d) in zip(coefficients(q), exponents(q))
+    for (c, d) in zip(AbstractAlgebra.coefficients(q), AbstractAlgebra.exponent_vectors(q))
       push_term!(ctx, kk(c), ee+d)
     end
   end
diff --git a/src/Rings/mpolyquo-localizations.jl b/src/Rings/mpolyquo-localizations.jl
index 5294ea50c6ad..f9357af03df5 100644
--- a/src/Rings/mpolyquo-localizations.jl
+++ b/src/Rings/mpolyquo-localizations.jl
@@ -620,7 +620,7 @@ function is_zero_divisor(f::MPolyQuoLocRingElem{<:Field})
   # once more functionality is working, it will actually do stuff and
   # the above signature can be widened.
   if is_constant(lifted_numerator(f)) && is_constant(lifted_denominator(f))
-    c = first(coefficients(lift(numerator(f))))
+    c = first(AbstractAlgebra.coefficients(lift(numerator(f))))
     return is_zero_divisor(c)
   end
   return !is_zero(quotient(ideal(parent(f), zero(f)), ideal(parent(f), f)))
@@ -1378,7 +1378,7 @@ end
   gb = groebner_basis(J, ordering=oo)
 
   # TODO: Speed up and use build context.
-  res_gens = elem_type(A)[f for f in gb if all(e -> is_zero(view(e, 1:(n+r))), exponents(f))]
+  res_gens = elem_type(A)[f for f in gb if all(e -> is_zero(view(e, 1:(n+r))), AbstractAlgebra.exponent_vectors(f))]
   img_gens2 = vcat([zero(R) for i in 1:(n+r)], gens(R))
   result = ideal(R, elem_type(R)[evaluate(g, img_gens2) for g in res_gens])
   return result
@@ -2779,7 +2779,7 @@ function _evaluate_with_build_ctx(
   r = ngens(cod_ring)
   kk = coefficient_ring(cod_ring)
   ctx = MPolyBuildCtx(cod_ring)
-  for (q, e) in zip(coefficients(p), exponents(p))
+  for (q, e) in zip(AbstractAlgebra.coefficients(p), AbstractAlgebra.exponent_vectors(p))
     ee = [0 for _ in 1:r]
     for (i, k) in enumerate(e)
       ee[ind[i]] = k
@@ -2794,13 +2794,13 @@ end
 # The following methods are only safe, because they are called 
 # exclusively in a setup where variables map to variables 
 # and no denominators are introduced. 
-_coefficients(x::MPolyRingElem) = coefficients(x)
-_coefficients(x::MPolyQuoRingElem) = coefficients(lift(x))
-_coefficients(x::MPolyLocRingElem) = coefficients(numerator(x))
-_coefficients(x::MPolyQuoLocRingElem) = coefficients(lifted_numerator(x))
-
-_exponents(x::MPolyRingElem) = exponents(x)
-_exponents(x::MPolyQuoRingElem) = exponents(lift(x))
-_exponents(x::MPolyLocRingElem) = exponents(numerator(x))
-_exponents(x::MPolyQuoLocRingElem) = exponents(lifted_numerator(x))
+_coefficients(x::MPolyRingElem) = AbstractAlgebra.coefficients(x)
+_coefficients(x::MPolyQuoRingElem) = AbstractAlgebra.coefficients(lift(x))
+_coefficients(x::MPolyLocRingElem) = AbstractAlgebra.coefficients(numerator(x))
+_coefficients(x::MPolyQuoLocRingElem) = AbstractAlgebra.coefficients(lifted_numerator(x))
+
+_exponents(x::MPolyRingElem) = AbstractAlgebra.exponent_vectors(x)
+_exponents(x::MPolyQuoRingElem) = AbstractAlgebra.exponent_vectors(lift(x))
+_exponents(x::MPolyLocRingElem) = AbstractAlgebra.exponent_vectors(numerator(x))
+_exponents(x::MPolyQuoLocRingElem) = AbstractAlgebra.exponent_vectors(lifted_numerator(x))
 

From 1892dabb2729ffa2f14b1b090350ffd2d01338d3 Mon Sep 17 00:00:00 2001
From: Simon Brandhorst <brandhorst@math.uni-sb.de>
Date: Tue, 1 Oct 2024 15:21:40 +0200
Subject: [PATCH 22/22] Update src/Rings/MPolyMap/MPolyAnyMap.jl

---
 src/Rings/MPolyMap/MPolyAnyMap.jl | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/src/Rings/MPolyMap/MPolyAnyMap.jl b/src/Rings/MPolyMap/MPolyAnyMap.jl
index 009cebd8380f..8394cbb8f749 100644
--- a/src/Rings/MPolyMap/MPolyAnyMap.jl
+++ b/src/Rings/MPolyMap/MPolyAnyMap.jl
@@ -64,7 +64,8 @@ const _DomainTypes = Union{MPolyRing, MPolyQuoRing}
     # call the inner one with this argument set to `false`. This way the check 
     # can safely be disabled.
     if check_for_mapping_of_vars && all(_is_gen, img_gens) && _allunique(img_gens)
-      result.variable_indices = [findfirst(==(x), gens(codomain)) for x in img_gens]
+      gens_codomain = gens(codomain)
+      result.variable_indices = [findfirst(==(x), gens_codomain) for x in img_gens]
     end
     return result
   end