From 5c33eded36a128a780f04ad81e962edde37021fe Mon Sep 17 00:00:00 2001
From: Arnav Kapoor <kapoorarnav43@gmail.com>
Date: Tue, 18 Nov 2025 02:53:33 +0530
Subject: [PATCH 01/17] Problem 9 and 10

---
 src/ADNLPProblems/toint.jl | 35 +++++++++++++++++++++++++++++
 src/ADNLPProblems/trig.jl  | 35 +++++++++++++++++++++++++++++
 src/Meta/toint.jl          | 27 ++++++++++++++++++++++
 src/Meta/trig.jl           | 27 ++++++++++++++++++++++
 src/PureJuMP/toint.jl      | 46 ++++++++++++++++++++++++++++++++++++++
 src/PureJuMP/trig.jl       | 40 +++++++++++++++++++++++++++++++++
 6 files changed, 210 insertions(+)
 create mode 100644 src/ADNLPProblems/toint.jl
 create mode 100644 src/ADNLPProblems/trig.jl
 create mode 100644 src/Meta/toint.jl
 create mode 100644 src/Meta/trig.jl
 create mode 100644 src/PureJuMP/toint.jl
 create mode 100644 src/PureJuMP/trig.jl

diff --git a/src/ADNLPProblems/toint.jl b/src/ADNLPProblems/toint.jl
new file mode 100644
index 00000000..ccdc9847
--- /dev/null
+++ b/src/ADNLPProblems/toint.jl
@@ -0,0 +1,35 @@
+export toint
+
+function toint(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
+  function f(x; n = length(x))
+    n_local = n
+    s = zero(T)
+    for i = 1:n_local
+      xi = x[i]
+      ci = 1 + (i / 10)
+
+      jlo = max(1, i - 2)
+      jhi = min(n_local, i + 2)
+      for j = jlo:jhi
+        aij = 5 * (1 + mod(i, 5) + mod(j, 5))
+        bij = (i + j) / 10
+        cj = (1 + j) / 10
+        s += aij * sin(bij + ci * xi + cj * x[j])
+      end
+
+      if iseven(n_local)
+        j = i + (n_local ÷ 2)
+        if 1 <= j <= n_local
+          aij = 5 * (1 + mod(i, 5) + mod(j, 5))
+          bij = (i + j) / 10
+          cj = (1 + j) / 10
+          s += aij * sin(bij + ci * xi + cj * x[j])
+        end
+      end
+    end
+    return s / T(n_local)
+  end
+
+  x0 = fill(1, n)
+  return ADNLPModels.ADNLPModel(f, x0, name = "toint"; kwargs...)
+end
diff --git a/src/ADNLPProblems/trig.jl b/src/ADNLPProblems/trig.jl
new file mode 100644
index 00000000..622fa6da
--- /dev/null
+++ b/src/ADNLPProblems/trig.jl
@@ -0,0 +1,35 @@
+export trig
+
+function trig(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
+  function f(x; n = length(x))
+    n_local = n
+    s = zero(T)
+    for i = 1:n_local
+      xi = x[i]
+      term = T(i) * (one(T) - cos(xi))
+
+      jlo = max(1, i - 2)
+      jhi = min(n_local, i + 2)
+      for j = jlo:jhi
+        aij = 5 * (1 + (mod(i, 5)) + (mod(j, 5)))
+        bij = (i + j) // 10
+        term += aij * sin(x[j]) + bij * cos(x[j])
+      end
+
+      if iseven(n_local)
+        j = i + (n_local ÷ 2)
+        if 1 <= j <= n_local
+          aij = 5 * (1 + (mod(i, 5)) + (mod(j, 5)))
+          bij = (i + j) // 10
+          term += aij * sin(x[j]) + bij * cos(x[j])
+        end
+      end
+
+      s += term
+    end
+    return s / T(n_local)
+  end
+
+  x0 = fill(1 / n, n)
+  return ADNLPModels.ADNLPModel(f, x0, name = "trig"; kwargs...)
+end
diff --git a/src/Meta/toint.jl b/src/Meta/toint.jl
new file mode 100644
index 00000000..b01aaa0d
--- /dev/null
+++ b/src/Meta/toint.jl
@@ -0,0 +1,27 @@
+toint_meta = Dict(
+  :nvar => 100,
+  :variable_nvar => true,
+  :ncon => 0,
+  :variable_ncon => false,
+  :minimize => true,
+  :name => "toint",
+  :has_equalities_only => false,
+  :has_inequalities_only => false,
+  :has_bounds => false,
+  :has_fixed_variables => false,
+  :objtype => :other,
+  :contype => :unconstrained,
+  :best_known_lower_bound => -Inf,
+  :best_known_upper_bound => 0.0,
+  :is_feasible => true,
+  :defined_everywhere => missing,
+  :origin => :unknown,
+)
+
+get_toint_nvar(; n::Integer = default_nvar, kwargs...) = n
+get_toint_ncon(; n::Integer = default_nvar, kwargs...) = 0
+get_toint_nlin(; n::Integer = default_nvar, kwargs...) = 0
+get_toint_nnln(; n::Integer = default_nvar, kwargs...) = 0
+get_toint_nequ(; n::Integer = default_nvar, kwargs...) = 0
+get_toint_nineq(; n::Integer = default_nvar, kwargs...) = 0
+get_toint_nls_nequ(; n::Integer = default_nvar, kwargs...) = 2 * n
diff --git a/src/Meta/trig.jl b/src/Meta/trig.jl
new file mode 100644
index 00000000..731a7bef
--- /dev/null
+++ b/src/Meta/trig.jl
@@ -0,0 +1,27 @@
+trig_meta = Dict(
+  :nvar => 100,
+  :variable_nvar => true,
+  :ncon => 0,
+  :variable_ncon => false,
+  :minimize => true,
+  :name => "trig",
+  :has_equalities_only => false,
+  :has_inequalities_only => false,
+  :has_bounds => false,
+  :has_fixed_variables => false,
+  :objtype => :other,
+  :contype => :unconstrained,
+  :best_known_lower_bound => -Inf,
+  :best_known_upper_bound => 0.0,
+  :is_feasible => true,
+  :defined_everywhere => missing,
+  :origin => :unknown,
+)
+
+get_trig_nvar(; n::Integer = default_nvar, kwargs...) = n
+get_trig_ncon(; n::Integer = default_nvar, kwargs...) = 0
+get_trig_nlin(; n::Integer = default_nvar, kwargs...) = 0
+get_trig_nnln(; n::Integer = default_nvar, kwargs...) = 0
+get_trig_nequ(; n::Integer = default_nvar, kwargs...) = 0
+get_trig_nineq(; n::Integer = default_nvar, kwargs...) = 0
+get_trig_nls_nequ(; n::Integer = default_nvar, kwargs...) = 2 * n
diff --git a/src/PureJuMP/toint.jl b/src/PureJuMP/toint.jl
new file mode 100644
index 00000000..a967cc27
--- /dev/null
+++ b/src/PureJuMP/toint.jl
@@ -0,0 +1,46 @@
+# Toint trigonometric function
+#
+#   Problem 10 in
+#   L. Luksan, C. Matonoha and J. Vlcek
+#   Sparse Test Problems for Unconstrained Optimization,
+#   Technical Report 1064,
+#   Institute of Computer Science,
+#   Academy of Science of the Czech Republic
+#
+#   https://www.researchgate.net/publication/325314400_Sparse_Test_Problems_for_Unconstrained_Optimization
+#
+export toint
+
+function toint(args...; n::Int = default_nvar, kwargs...)
+  model = Model()
+  @variable(model, x[i = 1:n], start = 1)
+
+  @objective(
+    model,
+    Min,
+    (1 / n) * sum(begin
+      ci = 1 + i / 10
+      s = zero(Float64)
+      jlo = max(1, i - 2)
+      jhi = min(n, i + 2)
+      for j = jlo:jhi
+        aij = 5 * (1 + mod(i, 5) + mod(j, 5))
+        bij = (i + j) / 10
+        cj = 1 + j / 10
+        s += aij * sin(bij + ci * x[i] + cj * x[j])
+      end
+      if iseven(n)
+        j = i + (n ÷ 2)
+        if 1 <= j <= n
+          aij = 5 * (1 + mod(i, 5) + mod(j, 5))
+          bij = (i + j) / 10
+          cj = 1 + j / 10
+          s += aij * sin(bij + ci * x[i] + cj * x[j])
+        end
+      end
+      s
+    end for i = 1:n)
+  )
+
+  return model
+end
diff --git a/src/PureJuMP/trig.jl b/src/PureJuMP/trig.jl
new file mode 100644
index 00000000..a135b21f
--- /dev/null
+++ b/src/PureJuMP/trig.jl
@@ -0,0 +1,40 @@
+# Another trigonometric function
+#
+#   Problem 9 in
+#   L. Luksan, C. Matonoha and J. Vlcek
+#   Sparse Test Problems for Unconstrained Optimization,
+#   Technical Report 1064,
+#   Institute of Computer Science,
+#   Academy of Science of the Czech Republic
+#
+#   https://www.researchgate.net/publication/325314400_Sparse_Test_Problems_for_Unconstrained_Optimization
+#
+export trig
+
+function trig(args...; n::Int = default_nvar, kwargs...)
+  model = Model()
+  @variable(model, x[i = 1:n], start = 1 / n)
+
+  @objective(
+    model,
+    Min,
+    (1 / n) * sum(
+      i * (1 - cos(x[i])) +
+      sum(
+        5 * (1 + mod(i, 5) + mod(j, 5)) * sin(x[j]) + (i + j) / 10 * cos(x[j]) for
+        j = max(1, i - 2):min(n, i + 2)
+      ) +
+      (
+        iseven(n) ?
+        (
+          let j = i + (n ÷ 2);
+            (1 <= j <= n) ?
+            (5 * (1 + mod(i, 5) + mod(j, 5)) * sin(x[j]) + (i + j) / 10 * cos(x[j])) : 0
+          end
+        ) : 0
+      ) for i = 1:n
+    )
+  )
+
+  return model
+end

From 7cffe7dbbcd1676f78b263171ddd401171a32141 Mon Sep 17 00:00:00 2001
From: Arnav Kapoor <kapoorarnav43@gmail.com>
Date: Tue, 18 Nov 2025 02:57:26 +0530
Subject: [PATCH 02/17] feat(trigb): add banded trigonometric problem (Meta,
 ADNLP, PureJuMP)

---
 src/ADNLPProblems/trigb.jl | 24 ++++++++++++++++++++++++
 src/Meta/trigb.jl          | 27 +++++++++++++++++++++++++++
 src/PureJuMP/trigb.jl      | 22 ++++++++++++++++++++++
 3 files changed, 73 insertions(+)
 create mode 100644 src/ADNLPProblems/trigb.jl
 create mode 100644 src/Meta/trigb.jl
 create mode 100644 src/PureJuMP/trigb.jl

diff --git a/src/ADNLPProblems/trigb.jl b/src/ADNLPProblems/trigb.jl
new file mode 100644
index 00000000..950031b0
--- /dev/null
+++ b/src/ADNLPProblems/trigb.jl
@@ -0,0 +1,24 @@
+export trigb
+
+function trigb(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
+  # Band-limited trigonometric objective
+  # F(x) = sum_{i=1}^n i * [ (1 - cos(x_i)) + sin(x_{i-1}) - sin(x_{i+1}) ]
+  # with boundary values x_0 = x_{n+1} = 0
+
+  function f(x; n = length(x))
+    n_local = n
+    s = zero(T)
+    for i in 1:n_local
+      xi = x[i]
+      left = (i == 1) ? zero(T) : x[i - 1]
+      right = (i == n_local) ? zero(T) : x[i + 1]
+      term = T(i) * ( (one(T) - cos(xi)) + sin(left) - sin(right) )
+      s += term
+    end
+    return s
+  end
+
+  # default initial guess: xbar_i = 1 (use type-generic one(T))
+  x0 = fill(one(T), n)
+  return ADNLPModels.ADNLPModel(f, x0, name = "trigb"; kwargs...)
+end
diff --git a/src/Meta/trigb.jl b/src/Meta/trigb.jl
new file mode 100644
index 00000000..8ae0e399
--- /dev/null
+++ b/src/Meta/trigb.jl
@@ -0,0 +1,27 @@
+trigb_meta = Dict(
+  :nvar => 100,
+  :variable_nvar => true,
+  :ncon => 0,
+  :variable_ncon => false,
+  :minimize => true,
+  :name => "trigb",
+  :has_equalities_only => false,
+  :has_inequalities_only => false,
+  :has_bounds => false,
+  :has_fixed_variables => false,
+  :objtype => :other,
+  :contype => :unconstrained,
+  :best_known_lower_bound => -Inf,
+  :best_known_upper_bound => 0.0,
+  :is_feasible => true,
+  :defined_everywhere => missing,
+  :origin => :unknown,
+)
+
+get_trigb_nvar(; n::Integer = default_nvar, kwargs...) = n
+get_trigb_ncon(; n::Integer = default_nvar, kwargs...) = 0
+get_trigb_nlin(; n::Integer = default_nvar, kwargs...) = 0
+get_trigb_nnln(; n::Integer = default_nvar, kwargs...) = 0
+get_trigb_nequ(; n::Integer = default_nvar, kwargs...) = 0
+get_trigb_nineq(; n::Integer = default_nvar, kwargs...) = 0
+get_trigb_nls_nequ(; n::Integer = default_nvar, kwargs...) = 2 * n
diff --git a/src/PureJuMP/trigb.jl b/src/PureJuMP/trigb.jl
new file mode 100644
index 00000000..dd7080b2
--- /dev/null
+++ b/src/PureJuMP/trigb.jl
@@ -0,0 +1,22 @@
+## Banded trigonometric problem (Problem 16)
+## F(x) = sum_{i=1}^n i * [ (1 - cos(x_i)) + sin(x_{i-1}) - sin(x_{i+1}) ]
+## boundary: x_0 = x_{n+1} = 0
+
+export trigb
+
+function trigb(args...; n::Int = default_nvar, kwargs...)
+  model = Model()
+  @variable(model, x[i = 1:n], start = 1.0)
+
+  @objective(model, Min,
+    sum(
+      i * (
+        (1 - cos(x[i])) +
+        ((i == 1) ? sin(0.0) : sin(x[i - 1])) -
+        ((i == n) ? sin(0.0) : sin(x[i + 1]))
+      ) for i = 1:n
+    )
+  )
+
+  return model
+end

From efc78aba97f61086579280815e741252df603abf Mon Sep 17 00:00:00 2001
From: Arnav Kapoor <kapoorarnav43@gmail.com>
Date: Tue, 18 Nov 2025 03:06:37 +0530
Subject: [PATCH 03/17] trigb.jl

---
 src/ADNLPProblems/trigb.jl | 11 +++--------
 src/PureJuMP/trigb.jl      | 22 +++++++++++++++-------
 2 files changed, 18 insertions(+), 15 deletions(-)

diff --git a/src/ADNLPProblems/trigb.jl b/src/ADNLPProblems/trigb.jl
index 950031b0..14472bdd 100644
--- a/src/ADNLPProblems/trigb.jl
+++ b/src/ADNLPProblems/trigb.jl
@@ -1,24 +1,19 @@
 export trigb
 
 function trigb(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
-  # Band-limited trigonometric objective
-  # F(x) = sum_{i=1}^n i * [ (1 - cos(x_i)) + sin(x_{i-1}) - sin(x_{i+1}) ]
-  # with boundary values x_0 = x_{n+1} = 0
-
   function f(x; n = length(x))
     n_local = n
     s = zero(T)
-    for i in 1:n_local
+    for i = 1:n_local
       xi = x[i]
       left = (i == 1) ? zero(T) : x[i - 1]
       right = (i == n_local) ? zero(T) : x[i + 1]
-      term = T(i) * ( (one(T) - cos(xi)) + sin(left) - sin(right) )
+      term = i * (1 - cos(xi) + sin(left) - sin(right))
       s += term
     end
     return s
   end
 
-  # default initial guess: xbar_i = 1 (use type-generic one(T))
-  x0 = fill(one(T), n)
+  x0 = fill(1, n)
   return ADNLPModels.ADNLPModel(f, x0, name = "trigb"; kwargs...)
 end
diff --git a/src/PureJuMP/trigb.jl b/src/PureJuMP/trigb.jl
index dd7080b2..410de53d 100644
--- a/src/PureJuMP/trigb.jl
+++ b/src/PureJuMP/trigb.jl
@@ -1,18 +1,26 @@
-## Banded trigonometric problem (Problem 16)
-## F(x) = sum_{i=1}^n i * [ (1 - cos(x_i)) + sin(x_{i-1}) - sin(x_{i+1}) ]
-## boundary: x_0 = x_{n+1} = 0
-
+## Banded trigonometric problem
+#
+#   Problem 16 in
+#   L. Luksan, C. Matonoha and J. Vlcek
+#   Sparse Test Problems for Unconstrained Optimization,
+#   Technical Report 1064,
+#   Institute of Computer Science,
+#   Academy of Science of the Czech Republic
+#
+#   https://www.researchgate.net/publication/325314400_Sparse_Test_Problems_for_Unconstrained_Optimization
+#
 export trigb
 
 function trigb(args...; n::Int = default_nvar, kwargs...)
   model = Model()
   @variable(model, x[i = 1:n], start = 1.0)
 
-  @objective(model, Min,
+  @objective(
+    model,
+    Min,
     sum(
       i * (
-        (1 - cos(x[i])) +
-        ((i == 1) ? sin(0.0) : sin(x[i - 1])) -
+        (1 - cos(x[i])) + ((i == 1) ? sin(0.0) : sin(x[i - 1])) -
         ((i == n) ? sin(0.0) : sin(x[i + 1]))
       ) for i = 1:n
     )

From 04c8ad10aa9bb47e5c61524586b15cc4409bb922 Mon Sep 17 00:00:00 2001
From: Arnav Kapoor <kapoorarnav43@gmail.com>
Date: Tue, 18 Nov 2025 15:51:11 +0530
Subject: [PATCH 04/17] Update trig.jl

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

diff --git a/src/ADNLPProblems/trig.jl b/src/ADNLPProblems/trig.jl
index 622fa6da..d69fafdd 100644
--- a/src/ADNLPProblems/trig.jl
+++ b/src/ADNLPProblems/trig.jl
@@ -6,21 +6,21 @@ function trig(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where
     s = zero(T)
     for i = 1:n_local
       xi = x[i]
-      term = T(i) * (one(T) - cos(xi))
+      term = i * (1 - cos(xi))
 
       jlo = max(1, i - 2)
       jhi = min(n_local, i + 2)
       for j = jlo:jhi
-        aij = 5 * (1 + (mod(i, 5)) + (mod(j, 5)))
-        bij = (i + j) // 10
+        aij = 5 * (1 + mod(i, 5) + mod(j, 5))
+        bij = (i + j) / 10
         term += aij * sin(x[j]) + bij * cos(x[j])
       end
 
       if iseven(n_local)
         j = i + (n_local ÷ 2)
         if 1 <= j <= n_local
-          aij = 5 * (1 + (mod(i, 5)) + (mod(j, 5)))
-          bij = (i + j) // 10
+          aij = 5 * (1 + mod(i, 5) + mod(j, 5))
+          bij = (i + j) / 10
           term += aij * sin(x[j]) + bij * cos(x[j])
         end
       end

From eb71f89aeef23cef133eca0b0700dece377f572b Mon Sep 17 00:00:00 2001
From: Arnav Kapoor <kapoorarnav43@gmail.com>
Date: Tue, 18 Nov 2025 18:58:37 +0530
Subject: [PATCH 05/17] Apply suggestions from code review

Co-authored-by: Tangi Migot <tangi.migot@gmail.com>
---
 src/ADNLPProblems/toint.jl |  3 +--
 src/ADNLPProblems/trig.jl  | 10 +++-------
 src/ADNLPProblems/trigb.jl |  8 +++-----
 src/Meta/trigb.jl          |  1 -
 src/PureJuMP/trigb.jl      |  4 ++--
 5 files changed, 9 insertions(+), 17 deletions(-)

diff --git a/src/ADNLPProblems/toint.jl b/src/ADNLPProblems/toint.jl
index ccdc9847..a4e9b310 100644
--- a/src/ADNLPProblems/toint.jl
+++ b/src/ADNLPProblems/toint.jl
@@ -2,7 +2,6 @@ export toint
 
 function toint(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
   function f(x; n = length(x))
-    n_local = n
     s = zero(T)
     for i = 1:n_local
       xi = x[i]
@@ -30,6 +29,6 @@ function toint(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) wher
     return s / T(n_local)
   end
 
-  x0 = fill(1, n)
+  x0 = fill(one(T), n)
   return ADNLPModels.ADNLPModel(f, x0, name = "toint"; kwargs...)
 end
diff --git a/src/ADNLPProblems/trig.jl b/src/ADNLPProblems/trig.jl
index d69fafdd..9f5805c4 100644
--- a/src/ADNLPProblems/trig.jl
+++ b/src/ADNLPProblems/trig.jl
@@ -2,15 +2,11 @@ export trig
 
 function trig(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
   function f(x; n = length(x))
-    n_local = n
     s = zero(T)
     for i = 1:n_local
-      xi = x[i]
       term = i * (1 - cos(xi))
 
-      jlo = max(1, i - 2)
-      jhi = min(n_local, i + 2)
-      for j = jlo:jhi
+      for j = max(1, i - 2):min(n, i + 2)
         aij = 5 * (1 + mod(i, 5) + mod(j, 5))
         bij = (i + j) / 10
         term += aij * sin(x[j]) + bij * cos(x[j])
@@ -27,9 +23,9 @@ function trig(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where
 
       s += term
     end
-    return s / T(n_local)
+    return s / n
   end
 
-  x0 = fill(1 / n, n)
+  x0 = fill(one(T) / n, n)
   return ADNLPModels.ADNLPModel(f, x0, name = "trig"; kwargs...)
 end
diff --git a/src/ADNLPProblems/trigb.jl b/src/ADNLPProblems/trigb.jl
index 14472bdd..cd2d63fa 100644
--- a/src/ADNLPProblems/trigb.jl
+++ b/src/ADNLPProblems/trigb.jl
@@ -2,18 +2,16 @@ export trigb
 
 function trigb(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
   function f(x; n = length(x))
-    n_local = n
     s = zero(T)
     for i = 1:n_local
-      xi = x[i]
-      left = (i == 1) ? zero(T) : x[i - 1]
-      right = (i == n_local) ? zero(T) : x[i + 1]
+      xim = (i == 1) ? zero(T) : x[i - 1]
+      xip = (i == n_local) ? zero(T) : x[i + 1]
       term = i * (1 - cos(xi) + sin(left) - sin(right))
       s += term
     end
     return s
   end
 
-  x0 = fill(1, n)
+  x0 = fill(one(T), n)
   return ADNLPModels.ADNLPModel(f, x0, name = "trigb"; kwargs...)
 end
diff --git a/src/Meta/trigb.jl b/src/Meta/trigb.jl
index 8ae0e399..c648cb7a 100644
--- a/src/Meta/trigb.jl
+++ b/src/Meta/trigb.jl
@@ -24,4 +24,3 @@ get_trigb_nlin(; n::Integer = default_nvar, kwargs...) = 0
 get_trigb_nnln(; n::Integer = default_nvar, kwargs...) = 0
 get_trigb_nequ(; n::Integer = default_nvar, kwargs...) = 0
 get_trigb_nineq(; n::Integer = default_nvar, kwargs...) = 0
-get_trigb_nls_nequ(; n::Integer = default_nvar, kwargs...) = 2 * n
diff --git a/src/PureJuMP/trigb.jl b/src/PureJuMP/trigb.jl
index 410de53d..db272be1 100644
--- a/src/PureJuMP/trigb.jl
+++ b/src/PureJuMP/trigb.jl
@@ -20,8 +20,8 @@ function trigb(args...; n::Int = default_nvar, kwargs...)
     Min,
     sum(
       i * (
-        (1 - cos(x[i])) + ((i == 1) ? sin(0.0) : sin(x[i - 1])) -
-        ((i == n) ? sin(0.0) : sin(x[i + 1]))
+        (1 - cos(x[i])) + ((i == 1) ? sin(0) : sin(x[i - 1])) -
+        ((i == n) ? sin(0) : sin(x[i + 1]))
       ) for i = 1:n
     )
   )

From 2968284832ef134e4e4246536b826edcb086446b Mon Sep 17 00:00:00 2001
From: Arnav Kapoor <kapoorarnav43@gmail.com>
Date: Tue, 18 Nov 2025 23:29:26 +0530
Subject: [PATCH 06/17] removing unnecessary variables

---
 src/ADNLPProblems/toint.jl | 15 ++++++---------
 src/ADNLPProblems/trig.jl  | 16 +++++++---------
 src/ADNLPProblems/trigb.jl |  7 +++----
 src/PureJuMP/trigb.jl      |  9 ++++-----
 4 files changed, 20 insertions(+), 27 deletions(-)

diff --git a/src/ADNLPProblems/toint.jl b/src/ADNLPProblems/toint.jl
index a4e9b310..ce5505e2 100644
--- a/src/ADNLPProblems/toint.jl
+++ b/src/ADNLPProblems/toint.jl
@@ -3,22 +3,19 @@ export toint
 function toint(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
   function f(x; n = length(x))
     s = zero(T)
-    for i = 1:n_local
-      xi = x[i]
+    for i = 1:n
       ci = 1 + (i / 10)
 
-      jlo = max(1, i - 2)
-      jhi = min(n_local, i + 2)
-      for j = jlo:jhi
+      for j = max(1, i - 2):min(n, i + 2)
         aij = 5 * (1 + mod(i, 5) + mod(j, 5))
         bij = (i + j) / 10
         cj = (1 + j) / 10
         s += aij * sin(bij + ci * xi + cj * x[j])
       end
 
-      if iseven(n_local)
-        j = i + (n_local ÷ 2)
-        if 1 <= j <= n_local
+      if iseven(n)
+        j = i + (n ÷ 2)
+        if 1 <= j <= n
           aij = 5 * (1 + mod(i, 5) + mod(j, 5))
           bij = (i + j) / 10
           cj = (1 + j) / 10
@@ -26,7 +23,7 @@ function toint(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) wher
         end
       end
     end
-    return s / T(n_local)
+    return s / n
   end
 
   x0 = fill(one(T), n)
diff --git a/src/ADNLPProblems/trig.jl b/src/ADNLPProblems/trig.jl
index 9f5805c4..b4b4b9fd 100644
--- a/src/ADNLPProblems/trig.jl
+++ b/src/ADNLPProblems/trig.jl
@@ -3,25 +3,23 @@ export trig
 function trig(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
   function f(x; n = length(x))
     s = zero(T)
-    for i = 1:n_local
-      term = i * (1 - cos(xi))
+    for i = 1:n
+      s += i * (1 - cos(x[i]))
 
       for j = max(1, i - 2):min(n, i + 2)
         aij = 5 * (1 + mod(i, 5) + mod(j, 5))
         bij = (i + j) / 10
-        term += aij * sin(x[j]) + bij * cos(x[j])
+        s += aij * sin(x[j]) + bij * cos(x[j])
       end
 
-      if iseven(n_local)
-        j = i + (n_local ÷ 2)
-        if 1 <= j <= n_local
+      if iseven(n)
+        j = i + (n ÷ 2)
+        if 1 <= j <= n
           aij = 5 * (1 + mod(i, 5) + mod(j, 5))
           bij = (i + j) / 10
-          term += aij * sin(x[j]) + bij * cos(x[j])
+          s += aij * sin(x[j]) + bij * cos(x[j])
         end
       end
-
-      s += term
     end
     return s / n
   end
diff --git a/src/ADNLPProblems/trigb.jl b/src/ADNLPProblems/trigb.jl
index cd2d63fa..98339cfa 100644
--- a/src/ADNLPProblems/trigb.jl
+++ b/src/ADNLPProblems/trigb.jl
@@ -3,11 +3,10 @@ export trigb
 function trigb(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
   function f(x; n = length(x))
     s = zero(T)
-    for i = 1:n_local
+    for i = 1:n
       xim = (i == 1) ? zero(T) : x[i - 1]
-      xip = (i == n_local) ? zero(T) : x[i + 1]
-      term = i * (1 - cos(xi) + sin(left) - sin(right))
-      s += term
+      xip = (i == n) ? zero(T) : x[i + 1]
+      s += i * (1 - cos(x[i]) + sin(xim) - sin(xip))
     end
     return s
   end
diff --git a/src/PureJuMP/trigb.jl b/src/PureJuMP/trigb.jl
index db272be1..1eb24276 100644
--- a/src/PureJuMP/trigb.jl
+++ b/src/PureJuMP/trigb.jl
@@ -13,16 +13,15 @@ export trigb
 
 function trigb(args...; n::Int = default_nvar, kwargs...)
   model = Model()
-  @variable(model, x[i = 1:n], start = 1.0)
+  @variable(model, x[i = 1:n], start = 1)
 
   @objective(
     model,
     Min,
     sum(
-      i * (
-        (1 - cos(x[i])) + ((i == 1) ? sin(0) : sin(x[i - 1])) -
-        ((i == n) ? sin(0) : sin(x[i + 1]))
-      ) for i = 1:n
+      i *
+      ((1 - cos(x[i])) + ((i == 1) ? sin(0) : sin(x[i - 1])) - ((i == n) ? sin(0) : sin(x[i + 1])))
+      for i = 1:n
     )
   )
 

From 84f4991266eeb3ff04ad0889a133123966d43fe3 Mon Sep 17 00:00:00 2001
From: Arnav Kapoor <kapoorarnav43@gmail.com>
Date: Wed, 19 Nov 2025 00:16:39 +0530
Subject: [PATCH 07/17] fixing remaining mentions of xi variable

---
 src/ADNLPProblems/toint.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/ADNLPProblems/toint.jl b/src/ADNLPProblems/toint.jl
index ce5505e2..86c521e0 100644
--- a/src/ADNLPProblems/toint.jl
+++ b/src/ADNLPProblems/toint.jl
@@ -10,7 +10,7 @@ function toint(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) wher
         aij = 5 * (1 + mod(i, 5) + mod(j, 5))
         bij = (i + j) / 10
         cj = (1 + j) / 10
-        s += aij * sin(bij + ci * xi + cj * x[j])
+        s += aij * sin(bij + ci * x[i] + cj * x[j])
       end
 
       if iseven(n)
@@ -19,7 +19,7 @@ function toint(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) wher
           aij = 5 * (1 + mod(i, 5) + mod(j, 5))
           bij = (i + j) / 10
           cj = (1 + j) / 10
-          s += aij * sin(bij + ci * xi + cj * x[j])
+          s += aij * sin(bij + ci * x[i] + cj * x[j])
         end
       end
     end

From 71bca05dc9006d29af623dc26797bcf3c120ea4d Mon Sep 17 00:00:00 2001
From: Arnav Kapoor <kapoorarnav43@gmail.com>
Date: Wed, 19 Nov 2025 01:11:46 +0530
Subject: [PATCH 08/17] removing twice renditions

---
 src/ADNLPProblems/toint.jl | 10 ----------
 src/ADNLPProblems/trig.jl  |  9 ---------
 2 files changed, 19 deletions(-)

diff --git a/src/ADNLPProblems/toint.jl b/src/ADNLPProblems/toint.jl
index 86c521e0..f00b5d49 100644
--- a/src/ADNLPProblems/toint.jl
+++ b/src/ADNLPProblems/toint.jl
@@ -12,16 +12,6 @@ function toint(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) wher
         cj = (1 + j) / 10
         s += aij * sin(bij + ci * x[i] + cj * x[j])
       end
-
-      if iseven(n)
-        j = i + (n ÷ 2)
-        if 1 <= j <= n
-          aij = 5 * (1 + mod(i, 5) + mod(j, 5))
-          bij = (i + j) / 10
-          cj = (1 + j) / 10
-          s += aij * sin(bij + ci * x[i] + cj * x[j])
-        end
-      end
     end
     return s / n
   end
diff --git a/src/ADNLPProblems/trig.jl b/src/ADNLPProblems/trig.jl
index b4b4b9fd..a5310b51 100644
--- a/src/ADNLPProblems/trig.jl
+++ b/src/ADNLPProblems/trig.jl
@@ -11,15 +11,6 @@ function trig(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where
         bij = (i + j) / 10
         s += aij * sin(x[j]) + bij * cos(x[j])
       end
-
-      if iseven(n)
-        j = i + (n ÷ 2)
-        if 1 <= j <= n
-          aij = 5 * (1 + mod(i, 5) + mod(j, 5))
-          bij = (i + j) / 10
-          s += aij * sin(x[j]) + bij * cos(x[j])
-        end
-      end
     end
     return s / n
   end

From fff0281ced831d43e5d9d5bbd39b4af9acc4588e Mon Sep 17 00:00:00 2001
From: Arnav Kapoor <kapoorarnav43@gmail.com>
Date: Wed, 19 Nov 2025 01:13:49 +0530
Subject: [PATCH 09/17] meta

---
 src/Meta/toint.jl | 1 -
 src/Meta/trig.jl  | 1 -
 2 files changed, 2 deletions(-)

diff --git a/src/Meta/toint.jl b/src/Meta/toint.jl
index b01aaa0d..f8122081 100644
--- a/src/Meta/toint.jl
+++ b/src/Meta/toint.jl
@@ -24,4 +24,3 @@ get_toint_nlin(; n::Integer = default_nvar, kwargs...) = 0
 get_toint_nnln(; n::Integer = default_nvar, kwargs...) = 0
 get_toint_nequ(; n::Integer = default_nvar, kwargs...) = 0
 get_toint_nineq(; n::Integer = default_nvar, kwargs...) = 0
-get_toint_nls_nequ(; n::Integer = default_nvar, kwargs...) = 2 * n
diff --git a/src/Meta/trig.jl b/src/Meta/trig.jl
index 731a7bef..c64a2eca 100644
--- a/src/Meta/trig.jl
+++ b/src/Meta/trig.jl
@@ -24,4 +24,3 @@ get_trig_nlin(; n::Integer = default_nvar, kwargs...) = 0
 get_trig_nnln(; n::Integer = default_nvar, kwargs...) = 0
 get_trig_nequ(; n::Integer = default_nvar, kwargs...) = 0
 get_trig_nineq(; n::Integer = default_nvar, kwargs...) = 0
-get_trig_nls_nequ(; n::Integer = default_nvar, kwargs...) = 2 * n

From fbfe1e2673cbe66b9a75cb87308ae959a5b01512 Mon Sep 17 00:00:00 2001
From: Arnav Kapoor <kapoorarnav43@gmail.com>
Date: Wed, 19 Nov 2025 01:17:32 +0530
Subject: [PATCH 10/17] PureJuMP

---
 src/PureJuMP/toint.jl | 13 +------------
 src/PureJuMP/trig.jl  |  9 ---------
 2 files changed, 1 insertion(+), 21 deletions(-)

diff --git a/src/PureJuMP/toint.jl b/src/PureJuMP/toint.jl
index a967cc27..f4ef653a 100644
--- a/src/PureJuMP/toint.jl
+++ b/src/PureJuMP/toint.jl
@@ -21,23 +21,12 @@ function toint(args...; n::Int = default_nvar, kwargs...)
     (1 / n) * sum(begin
       ci = 1 + i / 10
       s = zero(Float64)
-      jlo = max(1, i - 2)
-      jhi = min(n, i + 2)
-      for j = jlo:jhi
+      for j = max(1, i - 2):min(n, i + 2)
         aij = 5 * (1 + mod(i, 5) + mod(j, 5))
         bij = (i + j) / 10
         cj = 1 + j / 10
         s += aij * sin(bij + ci * x[i] + cj * x[j])
       end
-      if iseven(n)
-        j = i + (n ÷ 2)
-        if 1 <= j <= n
-          aij = 5 * (1 + mod(i, 5) + mod(j, 5))
-          bij = (i + j) / 10
-          cj = 1 + j / 10
-          s += aij * sin(bij + ci * x[i] + cj * x[j])
-        end
-      end
       s
     end for i = 1:n)
   )
diff --git a/src/PureJuMP/trig.jl b/src/PureJuMP/trig.jl
index a135b21f..14c3afd7 100644
--- a/src/PureJuMP/trig.jl
+++ b/src/PureJuMP/trig.jl
@@ -23,15 +23,6 @@ function trig(args...; n::Int = default_nvar, kwargs...)
       sum(
         5 * (1 + mod(i, 5) + mod(j, 5)) * sin(x[j]) + (i + j) / 10 * cos(x[j]) for
         j = max(1, i - 2):min(n, i + 2)
-      ) +
-      (
-        iseven(n) ?
-        (
-          let j = i + (n ÷ 2);
-            (1 <= j <= n) ?
-            (5 * (1 + mod(i, 5) + mod(j, 5)) * sin(x[j]) + (i + j) / 10 * cos(x[j])) : 0
-          end
-        ) : 0
       ) for i = 1:n
     )
   )

From 8d5e0905b0dd22d19c5ba6bca978befdfc54bfe4 Mon Sep 17 00:00:00 2001
From: Arnav Kapoor <kapoorarnav43@gmail.com>
Date: Wed, 19 Nov 2025 02:38:30 +0530
Subject: [PATCH 11/17] Update toint.jl

---
 src/ADNLPProblems/toint.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/ADNLPProblems/toint.jl b/src/ADNLPProblems/toint.jl
index f00b5d49..18d9805e 100644
--- a/src/ADNLPProblems/toint.jl
+++ b/src/ADNLPProblems/toint.jl
@@ -8,8 +8,8 @@ function toint(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) wher
 
       for j = max(1, i - 2):min(n, i + 2)
         aij = 5 * (1 + mod(i, 5) + mod(j, 5))
-        bij = (i + j) / 10
-        cj = (1 + j) / 10
+        bij = (i + j) // 10
+        cj = (1 + j) // 10
         s += aij * sin(bij + ci * x[i] + cj * x[j])
       end
     end

From e76e90e6acb6c8322e71a539cf9309ffafbe52fa Mon Sep 17 00:00:00 2001
From: Arnav Kapoor <kapoorarnav43@gmail.com>
Date: Wed, 19 Nov 2025 02:38:52 +0530
Subject: [PATCH 12/17] Update trig.jl

---
 src/ADNLPProblems/trig.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/ADNLPProblems/trig.jl b/src/ADNLPProblems/trig.jl
index a5310b51..6d6f3dd4 100644
--- a/src/ADNLPProblems/trig.jl
+++ b/src/ADNLPProblems/trig.jl
@@ -8,7 +8,7 @@ function trig(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where
 
       for j = max(1, i - 2):min(n, i + 2)
         aij = 5 * (1 + mod(i, 5) + mod(j, 5))
-        bij = (i + j) / 10
+        bij = (i + j) // 10
         s += aij * sin(x[j]) + bij * cos(x[j])
       end
     end

From 5e003e5621c3d39b5564eaab74e2d2ff4cc634cd Mon Sep 17 00:00:00 2001
From: Arnav Kapoor <kapoorarnav43@gmail.com>
Date: Wed, 19 Nov 2025 03:06:02 +0530
Subject: [PATCH 13/17] Update toint.jl

---
 src/ADNLPProblems/toint.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/ADNLPProblems/toint.jl b/src/ADNLPProblems/toint.jl
index 18d9805e..7a45473d 100644
--- a/src/ADNLPProblems/toint.jl
+++ b/src/ADNLPProblems/toint.jl
@@ -4,7 +4,7 @@ function toint(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) wher
   function f(x; n = length(x))
     s = zero(T)
     for i = 1:n
-      ci = 1 + (i / 10)
+      ci = 1 + (i // 10)
 
       for j = max(1, i - 2):min(n, i + 2)
         aij = 5 * (1 + mod(i, 5) + mod(j, 5))

From e5c988264785ad626d8396c5a9ebc758791367c0 Mon Sep 17 00:00:00 2001
From: Arnav Kapoor <kapoorarnav43@gmail.com>
Date: Mon, 24 Nov 2025 02:28:46 +0530
Subject: [PATCH 14/17] Update src/ADNLPProblems/toint.jl

Co-authored-by: Tangi Migot <tangi.migot@gmail.com>
---
 src/ADNLPProblems/toint.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/ADNLPProblems/toint.jl b/src/ADNLPProblems/toint.jl
index 7a45473d..6a6e3c51 100644
--- a/src/ADNLPProblems/toint.jl
+++ b/src/ADNLPProblems/toint.jl
@@ -9,7 +9,7 @@ function toint(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) wher
       for j = max(1, i - 2):min(n, i + 2)
         aij = 5 * (1 + mod(i, 5) + mod(j, 5))
         bij = (i + j) // 10
-        cj = (1 + j) // 10
+        cj = 1 + (j // 10)
         s += aij * sin(bij + ci * x[i] + cj * x[j])
       end
     end

From 8b80602410186f8fe7d356a9fe90f95cacffb2ab Mon Sep 17 00:00:00 2001
From: Arnav Kapoor <kapoorarnav43@gmail.com>
Date: Wed, 19 Nov 2025 02:11:27 +0530
Subject: [PATCH 15/17] fixing Float64 issue in toint and trig problems

---
 src/ADNLPProblems/toint.jl | 30 +++++++++++++++---------------
 1 file changed, 15 insertions(+), 15 deletions(-)

diff --git a/src/ADNLPProblems/toint.jl b/src/ADNLPProblems/toint.jl
index 6a6e3c51..081f4928 100644
--- a/src/ADNLPProblems/toint.jl
+++ b/src/ADNLPProblems/toint.jl
@@ -1,21 +1,21 @@
 export toint
 
 function toint(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
-  function f(x; n = length(x))
-    s = zero(T)
-    for i = 1:n
-      ci = 1 + (i // 10)
+	function f(x; n = length(x))
+		s = zero(T)
+		for i ∈ 1:n
+			ci = 1 + (i // 10)
 
-      for j = max(1, i - 2):min(n, i + 2)
-        aij = 5 * (1 + mod(i, 5) + mod(j, 5))
-        bij = (i + j) // 10
-        cj = 1 + (j // 10)
-        s += aij * sin(bij + ci * x[i] + cj * x[j])
-      end
-    end
-    return s / n
-  end
+			for j ∈ max(1, i-2):min(n, i+2)
+				aij = 5 * (1 + mod(i, 5) + mod(j, 5))
+				bij = (i + j) // 10
+				cj = (1 + j) // 10
+				s += aij * sin(bij + ci * x[i] + cj * x[j])
+			end
+		end
+		return s / n
+	end
 
-  x0 = fill(one(T), n)
-  return ADNLPModels.ADNLPModel(f, x0, name = "toint"; kwargs...)
+	x0 = fill(one(T), n)
+	return ADNLPModels.ADNLPModel(f, x0, name = "toint"; kwargs...)
 end

From 5f03f4734b7d66026cc265def3106c0a6783a0b5 Mon Sep 17 00:00:00 2001
From: Arnav Kapoor <kapoorarnav43@gmail.com>
Date: Mon, 24 Nov 2025 04:32:27 +0530
Subject: [PATCH 16/17] further changes

---
 src/ADNLPProblems/toint.jl | 6 +++++-
 src/PureJuMP/toint.jl      | 6 +++++-
 2 files changed, 10 insertions(+), 2 deletions(-)

diff --git a/src/ADNLPProblems/toint.jl b/src/ADNLPProblems/toint.jl
index 081f4928..4efaf232 100644
--- a/src/ADNLPProblems/toint.jl
+++ b/src/ADNLPProblems/toint.jl
@@ -5,8 +5,12 @@ function toint(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) wher
 		s = zero(T)
 		for i ∈ 1:n
 			ci = 1 + (i // 10)
+			js = max(1, i-2):min(n, i+2)
+				if iseven(n)
+					js = sort(collect(union(collect(js), [j for j in (i + n ÷ 2, i - n ÷ 2) if 1 <= j <= n])))
+				end
 
-			for j ∈ max(1, i-2):min(n, i+2)
+			for j ∈ js
 				aij = 5 * (1 + mod(i, 5) + mod(j, 5))
 				bij = (i + j) // 10
 				cj = (1 + j) // 10
diff --git a/src/PureJuMP/toint.jl b/src/PureJuMP/toint.jl
index f4ef653a..9b69af88 100644
--- a/src/PureJuMP/toint.jl
+++ b/src/PureJuMP/toint.jl
@@ -21,7 +21,11 @@ function toint(args...; n::Int = default_nvar, kwargs...)
     (1 / n) * sum(begin
       ci = 1 + i / 10
       s = zero(Float64)
-      for j = max(1, i - 2):min(n, i + 2)
+      js = max(1, i - 2):min(n, i + 2)
+      if iseven(n)
+        js = sort(collect(union(collect(js), [j for j in (i + n ÷ 2, i - n ÷ 2) if 1 <= j <= n])))
+      end
+      for j in js
         aij = 5 * (1 + mod(i, 5) + mod(j, 5))
         bij = (i + j) / 10
         cj = 1 + j / 10

From c626f5f2cd1f9a1d1d671dc0b90298aa30c1f1dc Mon Sep 17 00:00:00 2001
From: Arnav Kapoor <kapoorarnav43@gmail.com>
Date: Mon, 24 Nov 2025 05:00:50 +0530
Subject: [PATCH 17/17] trig changes

---
 src/ADNLPProblems/trig.jl | 6 +++++-
 src/PureJuMP/trig.jl      | 7 ++++---
 2 files changed, 9 insertions(+), 4 deletions(-)

diff --git a/src/ADNLPProblems/trig.jl b/src/ADNLPProblems/trig.jl
index 6d6f3dd4..722e449c 100644
--- a/src/ADNLPProblems/trig.jl
+++ b/src/ADNLPProblems/trig.jl
@@ -6,7 +6,11 @@ function trig(; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where
     for i = 1:n
       s += i * (1 - cos(x[i]))
 
-      for j = max(1, i - 2):min(n, i + 2)
+      js = max(1, i - 2):min(n, i + 2)
+      if iseven(n)
+        js = sort(collect(union(collect(js), [j for j in (i + n ÷ 2, i - n ÷ 2) if 1 <= j <= n])))
+      end
+      for j in js
         aij = 5 * (1 + mod(i, 5) + mod(j, 5))
         bij = (i + j) // 10
         s += aij * sin(x[j]) + bij * cos(x[j])
diff --git a/src/PureJuMP/trig.jl b/src/PureJuMP/trig.jl
index 14c3afd7..eb7abadc 100644
--- a/src/PureJuMP/trig.jl
+++ b/src/PureJuMP/trig.jl
@@ -20,9 +20,10 @@ function trig(args...; n::Int = default_nvar, kwargs...)
     Min,
     (1 / n) * sum(
       i * (1 - cos(x[i])) +
-      sum(
-        5 * (1 + mod(i, 5) + mod(j, 5)) * sin(x[j]) + (i + j) / 10 * cos(x[j]) for
-        j = max(1, i - 2):min(n, i + 2)
+      (
+        sum(5 * (1 + mod(i, 5) + mod(j, 5)) * sin(x[j]) + (i + j) / 10 * cos(x[j]) for j in (
+          iseven(n) ? sort(collect(union(collect(max(1, i - 2):min(n, i + 2)), [j for j in (i + n ÷ 2, i - n ÷ 2) if 1 <= j <= n]))) : max(1, i - 2):min(n, i + 2)
+        ))
       ) for i = 1:n
     )
   )