From 7b7c02bcf2dd14737385196f30344e27939861aa Mon Sep 17 00:00:00 2001
From: Kwesi Rutledge <thesolitaryecrivain@gmail.com>
Date: Sun, 28 Sep 2025 21:53:23 -0400
Subject: [PATCH 01/19] started on more extensive README.md

---
 README.md | 11 +++++++++++
 1 file changed, 11 insertions(+)

diff --git a/README.md b/README.md
index 2b17da4..3b7642d 100644
--- a/README.md
+++ b/README.md
@@ -1,2 +1,13 @@
 # simplex
 A small library used to demonstrate the concepts of the Simplex algorithm in convex optimization.
+
+# Installation
+
+You can add this module to your package using:
+```bash
+go get github.com/MatProGo-dev/simplex
+```
+
+# Usage
+
+TBD
\ No newline at end of file

From 65738b4aea52633c89b0c693f15db71e52148635 Mon Sep 17 00:00:00 2001
From: Kwesi Rutledge <thesolitaryecrivain@gmail.com>
Date: Fri, 3 Oct 2025 00:26:26 -0400
Subject: [PATCH 02/19] Updated dependencies to less buggy SymbolicMath.go +
 MatProInterface.go

---
 go.mod | 4 ++--
 go.sum | 8 ++++----
 2 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/go.mod b/go.mod
index 583e021..c08390e 100644
--- a/go.mod
+++ b/go.mod
@@ -5,7 +5,7 @@ go 1.23.0
 toolchain go1.23.9
 
 require (
-	github.com/MatProGo-dev/MatProInterface.go v0.5.5
-	github.com/MatProGo-dev/SymbolicMath.go v0.2.4-1
+	github.com/MatProGo-dev/MatProInterface.go v0.5.6
+	github.com/MatProGo-dev/SymbolicMath.go v0.2.5
 	gonum.org/v1/gonum v0.16.0
 )
diff --git a/go.sum b/go.sum
index fca3c9b..168c097 100644
--- a/go.sum
+++ b/go.sum
@@ -1,6 +1,6 @@
-github.com/MatProGo-dev/MatProInterface.go v0.5.5 h1:mq4hxTXz9msY0hEKqrKLJB4Ne0jfv4itaZAx3LV/l7A=
-github.com/MatProGo-dev/MatProInterface.go v0.5.5/go.mod h1:UtPWsYyLFvssLYPZkiyMpgb9R9aTL8J4y1GfrM4phvc=
-github.com/MatProGo-dev/SymbolicMath.go v0.2.4-1 h1:SIj6oFJgavWtArs8toeHCPfxOefGMplWSkNvlR9P2Ac=
-github.com/MatProGo-dev/SymbolicMath.go v0.2.4-1/go.mod h1:tW8thj4pkaTV9lFNU3OCKmwQ3mZ2Eim6S4JpHRDfRvU=
+github.com/MatProGo-dev/MatProInterface.go v0.5.6 h1:rzoT536J0sWQEJttc3vSsJ/ESgEg95NU2SbtaaGmUs4=
+github.com/MatProGo-dev/MatProInterface.go v0.5.6/go.mod h1:o/uWBdqnA6YXq0enVlFEwM6raLnV2xC0liXqRe8FrPA=
+github.com/MatProGo-dev/SymbolicMath.go v0.2.5 h1:fGpwtywb2hUXvGKk1Te6PQEfHeVar5w05KTbc3wHj6A=
+github.com/MatProGo-dev/SymbolicMath.go v0.2.5/go.mod h1:tW8thj4pkaTV9lFNU3OCKmwQ3mZ2Eim6S4JpHRDfRvU=
 gonum.org/v1/gonum v0.16.0 h1:5+ul4Swaf3ESvrOnidPp4GZbzf0mxVQpDCYUQE7OJfk=
 gonum.org/v1/gonum v0.16.0/go.mod h1:fef3am4MQ93R2HHpKnLk4/Tbh/s0+wqD5nfa6Pnwy4E=

From ec8ae5c361fa356edb50162f76941d7aa5a96d8f Mon Sep 17 00:00:00 2001
From: Kwesi Rutledge <thesolitaryecrivain@gmail.com>
Date: Fri, 3 Oct 2025 00:26:46 -0400
Subject: [PATCH 03/19] Attempting to fix bug in how we solve from tableau

---
 algorithms/tableau/state.go    |  2 +-
 examples/gonum_bug1/try_bug.go | 92 ++++++++++++++++++++++++++++++++++
 2 files changed, 93 insertions(+), 1 deletion(-)
 create mode 100644 examples/gonum_bug1/try_bug.go

diff --git a/algorithms/tableau/state.go b/algorithms/tableau/state.go
index 84103cd..99a205f 100644
--- a/algorithms/tableau/state.go
+++ b/algorithms/tableau/state.go
@@ -288,7 +288,7 @@ func (state *TableauAlgorithmState) CalculateOptimalSolution() (mat.VecDense, er
 	// - The non-basic variables set to zero
 	A, b := state.A(), state.B()
 	numConstraints, _ := A.Dims()
-	numNonBasic := state.NumberOfVariables() - state.NumberOfConstraints()
+	numNonBasic := state.Tableau.NumberOfNonBasicVariables() //state.NumberOfVariables() - state.NumberOfConstraints()
 
 	// Augment the A and b matrices with the non-basic variable constraints
 	AAugmented := mat.NewDense(numConstraints+numNonBasic, numVars, nil)
diff --git a/examples/gonum_bug1/try_bug.go b/examples/gonum_bug1/try_bug.go
new file mode 100644
index 0000000..727c693
--- /dev/null
+++ b/examples/gonum_bug1/try_bug.go
@@ -0,0 +1,92 @@
+package main
+
+import (
+	"github.com/MatProGo-dev/MatProInterface.go/problem"
+	getKMatrix "github.com/MatProGo-dev/SymbolicMath.go/get/KMatrix"
+	getKVector "github.com/MatProGo-dev/SymbolicMath.go/get/KVector"
+	"github.com/MatProGo-dev/simplex/simplexSolver"
+	"gonum.org/v1/gonum/mat"
+)
+
+/*
+Description:
+
+	Builds a version of a linear programming problem mentioned in this issue in gonum:
+
+		https://github.com/gonum/gonum/issues/1914
+
+	This problem is very large and was causing issues in Gonum's LP solver.
+
+	We will use this problem to test our own simplex solver implementation.
+*/
+func BuildOptimizationProblem() problem.OptimizationProblem {
+	// setup
+	varCount := 57
+	out := problem.NewProblem("Gonum Bug LP Problem")
+
+	// Create the variables
+	x := out.AddVariableVector(varCount)
+
+	// Create the objective
+	c := getKVector.From(
+		[]float64{10, 5, 7, 10, 10, 5, 20, 20, 20, 20, 7, 5, 10, 80, 80, 10, 5, 5, 80, 80, 10, 80, 10, 7, 10, 10, 80, 7, 10, 20, 10, 7, 10, 7, 10, 15, 10, 10, 80, 10, 5, 7, 5, 10, 20, 10, 5, 10, 80, 80, 5, 10, 7, 7, 10, 5, 7},
+	)
+	out.SetObjective(
+		c.Transpose().Multiply(x),
+		problem.SenseMinimize,
+	)
+
+	// Create the constraints
+	// - Linear Equality Constraints
+	b := getKVector.From(
+		[]float64{38, 5, 2, 33, 28, 14, 2, 48, 8, 133, 117, 34, 48, 20, 16, 50, 30, 75, 10, 40, 6, 70, 10, 5, 167, 13, 2, 118, 12, 98, 67, 157, 55, 2, 4, 4, 25, 4},
+	)
+
+	Abuf := []float64{
+		1, 0.95, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.95, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0.95, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0.95, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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+	A := mat.NewDense(38, varCount, Abuf)
+
+	out.Constraints = append(
+		out.Constraints,
+		getKMatrix.From(A).Multiply(x).Eq(b),
+	)
+
+	// - Linear Inequality Constraints
+	h := getKVector.From(
+		[]float64{3370, 1031, 2350, 2289, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
+	)
+	Gbuf := []float64{1, 0, 0, 1, 1, 0, 2, 2, 0, 2, 0, 0, 1, 0, 8, 1, 0, 0, 8, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 2, 0, 0, 1, 0, 8, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, 8, 1, 0, 0, 1, 8, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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+	G := mat.NewDense(6+varCount, varCount, Gbuf)
+
+	out.Constraints = append(
+		out.Constraints,
+		getKMatrix.From(G).Multiply(x).LessEq(h),
+	)
+
+	return *out
+
+}
+
+func main() {
+	// This is just a placeholder to make the package "main" valid.
+	trickyProblem := BuildOptimizationProblem()
+
+	// Use solver to solve the problem
+	solver := simplexSolver.New("Simplex Solver Example")
+	solver.IterationLimit = 100
+
+	// Solve the problem
+	solution, err := solver.Solve(trickyProblem)
+	if err != nil {
+		panic(err)
+	}
+
+	// Print the solution
+	solutionMessage, _ := solution.Status.ToMessage()
+	println("Solution Status: ", solutionMessage)
+	println("Objective Value: ", solution.Objective)
+	println("Variable Values: ")
+	for varName, varValue := range solution.Values {
+		println("  ", varName, ": ", varValue)
+	}
+}

From 5b5c414844268a50c4deb7d4210f7a1e4de9039b Mon Sep 17 00:00:00 2001
From: Kwesi Rutledge <thesolitaryecrivain@gmail.com>
Date: Sat, 4 Oct 2025 14:07:48 -0400
Subject: [PATCH 04/19] Upgraded package dependencies + introduced simplex
 solution object

---
 algorithms/algorithm_interface.go             |  3 +-
 algorithms/stanford/stanford.go               | 30 ++++++++++---------
 algorithms/tableau/state.go                   | 13 ++++----
 algorithms/tableau/tableau_algo.go            | 13 ++++----
 .../tableau/termination/termination_types.go  | 12 ++++----
 examples/gonum_bug1/try_bug.go                |  2 +-
 .../the_simplex_method_part_ii.go             |  2 +-
 go.mod                                        |  2 +-
 go.sum                                        |  2 ++
 simplexSolver/solver.go                       |  5 ++--
 solution/simplex_solution.go                  |  9 ++++++
 11 files changed, 55 insertions(+), 38 deletions(-)
 create mode 100644 solution/simplex_solution.go

diff --git a/algorithms/algorithm_interface.go b/algorithms/algorithm_interface.go
index 46625bb..64a3e96 100644
--- a/algorithms/algorithm_interface.go
+++ b/algorithms/algorithm_interface.go
@@ -2,9 +2,10 @@ package algorithms
 
 import (
 	"github.com/MatProGo-dev/MatProInterface.go/problem"
+	simplex_solution "github.com/MatProGo-dev/simplex/solution"
 )
 
 type AlgorithmInterface interface {
 	// Solves the provided optimization problem.
-	Solve(prob problem.OptimizationProblem) (problem.Solution, error)
+	Solve(prob problem.OptimizationProblem) (simplex_solution.SimplexSolution, error)
 }
diff --git a/algorithms/stanford/stanford.go b/algorithms/stanford/stanford.go
index badaabe..089192f 100644
--- a/algorithms/stanford/stanford.go
+++ b/algorithms/stanford/stanford.go
@@ -4,7 +4,9 @@ import (
 	"fmt"
 
 	"github.com/MatProGo-dev/MatProInterface.go/problem"
+	solution_status "github.com/MatProGo-dev/MatProInterface.go/solution/status"
 	"github.com/MatProGo-dev/SymbolicMath.go/symbolic"
+	simplex_solution "github.com/MatProGo-dev/simplex/solution"
 	"github.com/MatProGo-dev/simplex/utils"
 	"gonum.org/v1/gonum/mat"
 )
@@ -178,11 +180,11 @@ Description:
 	- The values of the basic variables
 	- The values of the non-basic variables
 */
-func (algo *StanfordAlgorithm) ComputeSolutionFromState(state StanfordAlgorithmState) (problem.Solution, error) {
+func (algo *StanfordAlgorithm) ComputeSolutionFromState(state StanfordAlgorithmState) (simplex_solution.SimplexSolution, error) {
 	// Setup
 	fmt.Printf("Computing solution from state...\n")
-	solution := problem.Solution{
-		Status: problem.OptimizationStatus_OPTIMAL,
+	solution := simplex_solution.SimplexSolution{
+		Status: solution_status.OPTIMAL,
 	}
 
 	// Compute the feasible solution of the basic variables
@@ -200,18 +202,18 @@ func (algo *StanfordAlgorithm) ComputeSolutionFromState(state StanfordAlgorithmS
 
 	// Set the values of the basic variables
 	for ii, bv := range state.BasicVariables {
-		solution.Values[bv.ID] = xBasic.AtVec(ii)
+		solution.VariableValues[bv.ID] = xBasic.AtVec(ii)
 	}
 
 	// Set the values of the non-basic variables
 	for jj, nv := range state.GetNonBasicVariables() {
-		solution.Values[nv.ID] = state.NonBasicValues.AtVec(jj)
+		solution.VariableValues[nv.ID] = state.NonBasicValues.AtVec(jj)
 	}
 
 	return solution, nil
 }
 
-func (algo *StanfordAlgorithm) Solve(initialState StanfordAlgorithmState) (problem.Solution, error) {
+func (algo *StanfordAlgorithm) Solve(initialState StanfordAlgorithmState) (simplex_solution.SimplexSolution, error) {
 	// Setup
 	var stateII StanfordAlgorithmState = initialState
 
@@ -221,7 +223,7 @@ func (algo *StanfordAlgorithm) Solve(initialState StanfordAlgorithmState) (probl
 		// Test for Termination
 		r, err := stateII.GetReducedCostVector()
 		if err != nil {
-			return problem.Solution{}, fmt.Errorf(
+			return simplex_solution.SimplexSolution{}, fmt.Errorf(
 				"StanfordAlgorithm: Failed to get reduced cost vector (%v) at iteration #%v",
 				err,
 				iter,
@@ -248,7 +250,7 @@ func (algo *StanfordAlgorithm) Solve(initialState StanfordAlgorithmState) (probl
 		var ABasicInv mat.Dense
 		ABasic, err := stateII.ABasic()
 		if err != nil {
-			return problem.Solution{}, fmt.Errorf("StanfordAlgorithm: Failed to get ABasic matrix (%v)", err)
+			return simplex_solution.SimplexSolution{}, fmt.Errorf("StanfordAlgorithm: Failed to get ABasic matrix (%v)", err)
 		}
 		ABasicInv.Inverse(ABasic)
 		var ABasicAe mat.VecDense
@@ -263,7 +265,7 @@ func (algo *StanfordAlgorithm) Solve(initialState StanfordAlgorithmState) (probl
 			}
 		}
 		if objectiveIsUnboundedBelow {
-			return problem.Solution{}, fmt.Errorf(
+			return simplex_solution.SimplexSolution{}, fmt.Errorf(
 				"StanfordAlgorithm: Objective function is unbounded below, no solution exists at iteration %d",
 				iter,
 			)
@@ -274,13 +276,13 @@ func (algo *StanfordAlgorithm) Solve(initialState StanfordAlgorithmState) (probl
 		// Compute the feasible Solution of the Basic variables
 		xBasicII, err := algo.ComputeFeasibleBasicSolution(stateII)
 		if err != nil {
-			return problem.Solution{}, err
+			return simplex_solution.SimplexSolution{}, err
 		}
 
 		// Compute the value of the objective function
 		objII, err := algo.ComputeObjectiveFunctionValueWithFeasibleBasicSolution(stateII, xBasicII)
 		if err != nil {
-			return problem.Solution{}, err
+			return simplex_solution.SimplexSolution{}, err
 		}
 		fmt.Printf("Iteration %d: Basic Solution: %v, Objective Value: %f\n", iter, xBasicII, objII)
 
@@ -290,13 +292,13 @@ func (algo *StanfordAlgorithm) Solve(initialState StanfordAlgorithmState) (probl
 		// Check if the solution is optimal
 
 		if iter == algo.IterationLimit {
-			return problem.Solution{
+			return simplex_solution.SimplexSolution{
 				Objective: objII,
-				Status:    problem.OptimizationStatus_ITERATION_LIMIT,
+				Status:    solution_status.ITERATION_LIMIT,
 			}, nil
 		}
 
 	}
 
-	return problem.Solution{}, nil
+	return simplex_solution.SimplexSolution{}, nil
 }
diff --git a/algorithms/tableau/state.go b/algorithms/tableau/state.go
index 99a205f..a929e87 100644
--- a/algorithms/tableau/state.go
+++ b/algorithms/tableau/state.go
@@ -3,10 +3,11 @@ package tableau_algorithm1
 import (
 	"fmt"
 
-	"github.com/MatProGo-dev/MatProInterface.go/problem"
+	solution_status "github.com/MatProGo-dev/MatProInterface.go/solution/status"
 	"github.com/MatProGo-dev/SymbolicMath.go/symbolic"
 	"github.com/MatProGo-dev/simplex/algorithms"
 	"github.com/MatProGo-dev/simplex/algorithms/tableau/selection"
+	simplex_solution "github.com/MatProGo-dev/simplex/solution"
 	"github.com/MatProGo-dev/simplex/utils"
 	"gonum.org/v1/gonum/mat"
 )
@@ -341,13 +342,13 @@ func (state *TableauAlgorithmState) CreateOptimalValuesMap() (map[uint64]float64
 	return solutionMap, nil
 }
 
-func (state *TableauAlgorithmState) ToSolution(currentStatus problem.OptimizationStatus) problem.Solution {
+func (state *TableauAlgorithmState) ToSolution(currentStatus solution_status.SolutionStatus) simplex_solution.SimplexSolution {
 	// Construct Solution Map
 
 	// Assemble Solution Output
-	return problem.Solution{
-		Values:    map[uint64]float64{},
-		Objective: -1.0,
-		Status:    currentStatus,
+	return simplex_solution.SimplexSolution{
+		VariableValues: map[uint64]float64{},
+		Objective:      -1.0,
+		Status:         currentStatus,
 	}
 }
diff --git a/algorithms/tableau/tableau_algo.go b/algorithms/tableau/tableau_algo.go
index a2c25a6..30b3587 100644
--- a/algorithms/tableau/tableau_algo.go
+++ b/algorithms/tableau/tableau_algo.go
@@ -5,6 +5,7 @@ import (
 
 	"github.com/MatProGo-dev/MatProInterface.go/problem"
 	tableau_termination "github.com/MatProGo-dev/simplex/algorithms/tableau/termination"
+	simplex_solution "github.com/MatProGo-dev/simplex/solution"
 	"github.com/MatProGo-dev/simplex/utils"
 	"gonum.org/v1/gonum/mat"
 )
@@ -33,13 +34,13 @@ func (algo *TableauAlgorithm) CheckTerminationConditions(state TableauAlgorithmS
 	return tableau_termination.DidNotTerminate, nil
 }
 
-func (algo *TableauAlgorithm) Solve(prob problem.OptimizationProblem) (problem.Solution, error) {
+func (algo *TableauAlgorithm) Solve(prob problem.OptimizationProblem) (simplex_solution.SimplexSolution, error) {
 	// Setup
 
 	// Create initial Tableau state from the problem
 	initialTableau, err := utils.GetInitialTableauFrom(&prob)
 	if err != nil {
-		return problem.Solution{}, fmt.Errorf("there was an issue creating the initial tableau: %v", err)
+		return simplex_solution.SimplexSolution{}, fmt.Errorf("there was an issue creating the initial tableau: %v", err)
 	}
 	stateII := TableauAlgorithmState{
 		Tableau:        &initialTableau,
@@ -47,12 +48,12 @@ func (algo *TableauAlgorithm) Solve(prob problem.OptimizationProblem) (problem.S
 	}
 
 	// Loop
-	sol := problem.Solution{}
+	sol := simplex_solution.SimplexSolution{}
 	for iter := 0; iter < algo.IterationLimit; iter++ {
 		// Test for Termination
 		condition, err := algo.CheckTerminationConditions(stateII)
 		if err != nil {
-			return problem.Solution{},
+			return simplex_solution.SimplexSolution{},
 				fmt.Errorf(
 					"There was an issue checking the termination condition at iteration %v: %v",
 					iter,
@@ -70,7 +71,7 @@ func (algo *TableauAlgorithm) Solve(prob problem.OptimizationProblem) (problem.S
 						err,
 					)
 			}
-			sol.Values, err = stateII.CreateOptimalValuesMap()
+			sol.VariableValues, err = stateII.CreateOptimalValuesMap()
 			if err != nil {
 				return sol,
 					fmt.Errorf(
@@ -89,7 +90,7 @@ func (algo *TableauAlgorithm) Solve(prob problem.OptimizationProblem) (problem.S
 		// Update the state
 		stateII, err = stateII.CalculateNextState()
 		if err != nil {
-			return problem.Solution{},
+			return simplex_solution.SimplexSolution{},
 				fmt.Errorf(
 					"There was an issue updating the state at iteration %v: %v",
 					iter,
diff --git a/algorithms/tableau/termination/termination_types.go b/algorithms/tableau/termination/termination_types.go
index 0a3bb80..1cf15cd 100644
--- a/algorithms/tableau/termination/termination_types.go
+++ b/algorithms/tableau/termination/termination_types.go
@@ -1,7 +1,7 @@
 package tableau_termination
 
 import (
-	"github.com/MatProGo-dev/MatProInterface.go/problem"
+	solution_status "github.com/MatProGo-dev/MatProInterface.go/solution/status"
 )
 
 type TerminationType string
@@ -10,15 +10,15 @@ const DidNotTerminate TerminationType = "Did Not Terminate"
 const MaximumIterationsReached TerminationType = "Maximum Iterations Reached"
 const OptimalSolutionFound TerminationType = "Optimal Solution Found"
 
-func (tt TerminationType) ToOptimizationStatus() problem.OptimizationStatus {
+func (tt TerminationType) ToOptimizationStatus() solution_status.SolutionStatus {
 	switch tt {
 	case DidNotTerminate:
-		return problem.OptimizationStatus_INPROGRESS
+		return solution_status.INPROGRESS
 	case MaximumIterationsReached:
-		return problem.OptimizationStatus_ITERATION_LIMIT
+		return solution_status.ITERATION_LIMIT
 	case OptimalSolutionFound:
-		return problem.OptimizationStatus_OPTIMAL
+		return solution_status.OPTIMAL
 	default:
-		return problem.OptimizationStatus_INPROGRESS
+		return solution_status.INPROGRESS
 	}
 }
diff --git a/examples/gonum_bug1/try_bug.go b/examples/gonum_bug1/try_bug.go
index 727c693..cf2bb7c 100644
--- a/examples/gonum_bug1/try_bug.go
+++ b/examples/gonum_bug1/try_bug.go
@@ -86,7 +86,7 @@ func main() {
 	println("Solution Status: ", solutionMessage)
 	println("Objective Value: ", solution.Objective)
 	println("Variable Values: ")
-	for varName, varValue := range solution.Values {
+	for varName, varValue := range solution.VariableValues {
 		println("  ", varName, ": ", varValue)
 	}
 }
diff --git a/examples/sergiy_butenko1/the_simplex_method_part_ii.go b/examples/sergiy_butenko1/the_simplex_method_part_ii.go
index ba062a9..3d15c23 100644
--- a/examples/sergiy_butenko1/the_simplex_method_part_ii.go
+++ b/examples/sergiy_butenko1/the_simplex_method_part_ii.go
@@ -27,7 +27,7 @@ func main() {
 	println("Solution Status: ", solutionMessage)
 	println("Objective Value: ", solution.Objective)
 	println("Variable Values: ")
-	for varName, varValue := range solution.Values {
+	for varName, varValue := range solution.VariableValues {
 		println("  ", varName, ": ", varValue)
 	}
 }
diff --git a/go.mod b/go.mod
index c08390e..18de501 100644
--- a/go.mod
+++ b/go.mod
@@ -5,7 +5,7 @@ go 1.23.0
 toolchain go1.23.9
 
 require (
-	github.com/MatProGo-dev/MatProInterface.go v0.5.6
+	github.com/MatProGo-dev/MatProInterface.go v0.6.0
 	github.com/MatProGo-dev/SymbolicMath.go v0.2.5
 	gonum.org/v1/gonum v0.16.0
 )
diff --git a/go.sum b/go.sum
index 168c097..f772359 100644
--- a/go.sum
+++ b/go.sum
@@ -1,5 +1,7 @@
 github.com/MatProGo-dev/MatProInterface.go v0.5.6 h1:rzoT536J0sWQEJttc3vSsJ/ESgEg95NU2SbtaaGmUs4=
 github.com/MatProGo-dev/MatProInterface.go v0.5.6/go.mod h1:o/uWBdqnA6YXq0enVlFEwM6raLnV2xC0liXqRe8FrPA=
+github.com/MatProGo-dev/MatProInterface.go v0.6.0 h1:x3hQwl5Hz1Z+ZuTlaQlMfdjvaQqjmc9agJkF7FIBR4U=
+github.com/MatProGo-dev/MatProInterface.go v0.6.0/go.mod h1:o/uWBdqnA6YXq0enVlFEwM6raLnV2xC0liXqRe8FrPA=
 github.com/MatProGo-dev/SymbolicMath.go v0.2.5 h1:fGpwtywb2hUXvGKk1Te6PQEfHeVar5w05KTbc3wHj6A=
 github.com/MatProGo-dev/SymbolicMath.go v0.2.5/go.mod h1:tW8thj4pkaTV9lFNU3OCKmwQ3mZ2Eim6S4JpHRDfRvU=
 gonum.org/v1/gonum v0.16.0 h1:5+ul4Swaf3ESvrOnidPp4GZbzf0mxVQpDCYUQE7OJfk=
diff --git a/simplexSolver/solver.go b/simplexSolver/solver.go
index e0c9fa4..4277a53 100644
--- a/simplexSolver/solver.go
+++ b/simplexSolver/solver.go
@@ -6,6 +6,7 @@ import (
 	"github.com/MatProGo-dev/MatProInterface.go/problem"
 	"github.com/MatProGo-dev/simplex/algorithms"
 	tableau_algorithm1 "github.com/MatProGo-dev/simplex/algorithms/tableau"
+	simplex_solution "github.com/MatProGo-dev/simplex/solution"
 )
 
 type SimplexSolver struct {
@@ -39,13 +40,13 @@ func (solver *SimplexSolver) CreateAlgorithm(algoType algorithms.AlgorithmType)
 	}
 }
 
-func (solver *SimplexSolver) Solve(prob problem.OptimizationProblem) (problem.Solution, error) {
+func (solver *SimplexSolver) Solve(prob problem.OptimizationProblem) (simplex_solution.SimplexSolution, error) {
 	// Setup
 
 	// Choose Algorithm
 	algo, err := solver.CreateAlgorithm(solver.Algorithm)
 	if err != nil {
-		return problem.Solution{}, fmt.Errorf(
+		return simplex_solution.SimplexSolution{}, fmt.Errorf(
 			"The Solve() function was given an unknown solver type: %v",
 			solver.Algorithm,
 		)
diff --git a/solution/simplex_solution.go b/solution/simplex_solution.go
new file mode 100644
index 0000000..bced66b
--- /dev/null
+++ b/solution/simplex_solution.go
@@ -0,0 +1,9 @@
+package simplex_solution
+
+import solution_status "github.com/MatProGo-dev/MatProInterface.go/solution/status"
+
+type SimplexSolution struct {
+	VariableValues map[uint64]float64
+	Objective      float64
+	Status         solution_status.SolutionStatus
+}

From fb0ed9fc89da5fd30ae209169ed7c65692cb8f0b Mon Sep 17 00:00:00 2001
From: Kwesi Rutledge <thesolitaryecrivain@gmail.com>
Date: Sat, 4 Oct 2025 14:19:18 -0400
Subject: [PATCH 05/19] Added iterations field to SimplexSolution

---
 algorithms/tableau/state.go                   | 40 +++++++++++++++----
 algorithms/tableau/tableau_algo.go            | 17 ++------
 examples/gonum_bug1/try_bug.go                |  1 +
 .../the_simplex_method_part_ii.go             |  1 +
 solution/simplex_solution.go                  |  1 +
 5 files changed, 39 insertions(+), 21 deletions(-)

diff --git a/algorithms/tableau/state.go b/algorithms/tableau/state.go
index a929e87..19c381c 100644
--- a/algorithms/tableau/state.go
+++ b/algorithms/tableau/state.go
@@ -3,10 +3,10 @@ package tableau_algorithm1
 import (
 	"fmt"
 
-	solution_status "github.com/MatProGo-dev/MatProInterface.go/solution/status"
 	"github.com/MatProGo-dev/SymbolicMath.go/symbolic"
 	"github.com/MatProGo-dev/simplex/algorithms"
 	"github.com/MatProGo-dev/simplex/algorithms/tableau/selection"
+	tableau_termination "github.com/MatProGo-dev/simplex/algorithms/tableau/termination"
 	simplex_solution "github.com/MatProGo-dev/simplex/solution"
 	"github.com/MatProGo-dev/simplex/utils"
 	"gonum.org/v1/gonum/mat"
@@ -342,13 +342,37 @@ func (state *TableauAlgorithmState) CreateOptimalValuesMap() (map[uint64]float64
 	return solutionMap, nil
 }
 
-func (state *TableauAlgorithmState) ToSolution(currentStatus solution_status.SolutionStatus) simplex_solution.SimplexSolution {
-	// Construct Solution Map
+func (state *TableauAlgorithmState) ToSolution(condition tableau_termination.TerminationType) (simplex_solution.SimplexSolution, error) {
+	// Create container for solution
+	var sol simplex_solution.SimplexSolution
+	var err error
 
-	// Assemble Solution Output
-	return simplex_solution.SimplexSolution{
-		VariableValues: map[uint64]float64{},
-		Objective:      -1.0,
-		Status:         currentStatus,
+	// Construct Solution Status
+	sol.Status = condition.ToOptimizationStatus()
+
+	// Construct Iteration Count
+	sol.Iterations = state.IterationCount
+
+	// Construct Objective Value
+	sol.Objective, err = state.CurrentObjectiveValue()
+	if err != nil {
+		return sol,
+			fmt.Errorf(
+				"There was an issue getting the objective value at termination: %v",
+				err,
+			)
 	}
+
+	// Construct Variable map
+	sol.VariableValues, err = state.CreateOptimalValuesMap()
+	if err != nil {
+		return sol,
+			fmt.Errorf(
+				"There was an issue creating the optimal values map at termination: %v",
+				err,
+			)
+	}
+
+	// Assemble Solution Output
+	return sol, nil
 }
diff --git a/algorithms/tableau/tableau_algo.go b/algorithms/tableau/tableau_algo.go
index 30b3587..ad6e8aa 100644
--- a/algorithms/tableau/tableau_algo.go
+++ b/algorithms/tableau/tableau_algo.go
@@ -62,24 +62,15 @@ func (algo *TableauAlgorithm) Solve(prob problem.OptimizationProblem) (simplex_s
 		}
 
 		if condition != tableau_termination.DidNotTerminate {
-			sol.Status = condition.ToOptimizationStatus()
-			sol.Objective, err = stateII.CurrentObjectiveValue()
+			sol, err = stateII.ToSolution(condition)
 			if err != nil {
-				return sol,
+				return simplex_solution.SimplexSolution{},
 					fmt.Errorf(
-						"There was an issue getting the objective value at termination: %v",
+						"There was an issue converting the final state to a solution at iteration %v: %v",
+						iter,
 						err,
 					)
 			}
-			sol.VariableValues, err = stateII.CreateOptimalValuesMap()
-			if err != nil {
-				return sol,
-					fmt.Errorf(
-						"There was an issue creating the optimal values map at termination: %v",
-						err,
-					)
-			}
-
 			// Exit the loop
 			break
 		}
diff --git a/examples/gonum_bug1/try_bug.go b/examples/gonum_bug1/try_bug.go
index cf2bb7c..a7f6f29 100644
--- a/examples/gonum_bug1/try_bug.go
+++ b/examples/gonum_bug1/try_bug.go
@@ -85,6 +85,7 @@ func main() {
 	solutionMessage, _ := solution.Status.ToMessage()
 	println("Solution Status: ", solutionMessage)
 	println("Objective Value: ", solution.Objective)
+	println("Number of Iterations: ", solution.Iterations)
 	println("Variable Values: ")
 	for varName, varValue := range solution.VariableValues {
 		println("  ", varName, ": ", varValue)
diff --git a/examples/sergiy_butenko1/the_simplex_method_part_ii.go b/examples/sergiy_butenko1/the_simplex_method_part_ii.go
index 3d15c23..d9eed9d 100644
--- a/examples/sergiy_butenko1/the_simplex_method_part_ii.go
+++ b/examples/sergiy_butenko1/the_simplex_method_part_ii.go
@@ -26,6 +26,7 @@ func main() {
 	solutionMessage, _ := solution.Status.ToMessage()
 	println("Solution Status: ", solutionMessage)
 	println("Objective Value: ", solution.Objective)
+	println("Number of Iterations: ", solution.Iterations)
 	println("Variable Values: ")
 	for varName, varValue := range solution.VariableValues {
 		println("  ", varName, ": ", varValue)
diff --git a/solution/simplex_solution.go b/solution/simplex_solution.go
index bced66b..e6db9f5 100644
--- a/solution/simplex_solution.go
+++ b/solution/simplex_solution.go
@@ -6,4 +6,5 @@ type SimplexSolution struct {
 	VariableValues map[uint64]float64
 	Objective      float64
 	Status         solution_status.SolutionStatus
+	Iterations     int
 }

From 4096194d2259f278b839cd1bf6be4b9572b66809 Mon Sep 17 00:00:00 2001
From: Kwesi Rutledge <thesolitaryecrivain@gmail.com>
Date: Sat, 4 Oct 2025 14:45:45 -0400
Subject: [PATCH 06/19] Improved the documentation of the `SimplexSolution`

Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>
---
 solution/simplex_solution.go | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/solution/simplex_solution.go b/solution/simplex_solution.go
index bced66b..0cbebaa 100644
--- a/solution/simplex_solution.go
+++ b/solution/simplex_solution.go
@@ -2,8 +2,14 @@ package simplex_solution
 
 import solution_status "github.com/MatProGo-dev/MatProInterface.go/solution/status"
 
+// SimplexSolution represents the result of solving a linear program using the simplex method.
+// It contains the values of the decision variables, the objective value, and the solution status.
 type SimplexSolution struct {
+	// VariableValues maps variable IDs (as uint64) to their solution values.
+	// The uint64 key typically represents the unique identifier or index of a variable in the model.
 	VariableValues map[uint64]float64
+	// Objective is the value of the objective function at the solution.
 	Objective      float64
+	// Status indicates the status of the solution (e.g., optimal, infeasible).
 	Status         solution_status.SolutionStatus
 }

From 4ea1230c35c04c2d37f2ecb73add11fbb30c990b Mon Sep 17 00:00:00 2001
From: Kwesi Rutledge <thesolitaryecrivain@gmail.com>
Date: Sat, 4 Oct 2025 14:46:10 -0400
Subject: [PATCH 07/19] Remove commented code

Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>
---
 algorithms/tableau/state.go | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/algorithms/tableau/state.go b/algorithms/tableau/state.go
index a929e87..395ca55 100644
--- a/algorithms/tableau/state.go
+++ b/algorithms/tableau/state.go
@@ -289,7 +289,7 @@ func (state *TableauAlgorithmState) CalculateOptimalSolution() (mat.VecDense, er
 	// - The non-basic variables set to zero
 	A, b := state.A(), state.B()
 	numConstraints, _ := A.Dims()
-	numNonBasic := state.Tableau.NumberOfNonBasicVariables() //state.NumberOfVariables() - state.NumberOfConstraints()
+	numNonBasic := state.Tableau.NumberOfNonBasicVariables()
 
 	// Augment the A and b matrices with the non-basic variable constraints
 	AAugmented := mat.NewDense(numConstraints+numNonBasic, numVars, nil)

From e9b2b4dfda8ed3b4e5448f85c148463061b73af1 Mon Sep 17 00:00:00 2001
From: Kwesi Rutledge <thesolitaryecrivain@gmail.com>
Date: Sat, 4 Oct 2025 14:47:17 -0400
Subject: [PATCH 08/19] Tried to debug the new example

---
 algorithms/tableau/state.go    | 8 +++-----
 examples/gonum_bug1/try_bug.go | 8 ++++++++
 utils/tableau.go               | 2 ++
 3 files changed, 13 insertions(+), 5 deletions(-)

diff --git a/algorithms/tableau/state.go b/algorithms/tableau/state.go
index 19c381c..53d9c33 100644
--- a/algorithms/tableau/state.go
+++ b/algorithms/tableau/state.go
@@ -297,16 +297,14 @@ func (state *TableauAlgorithmState) CalculateOptimalSolution() (mat.VecDense, er
 	bAugmented := mat.NewVecDense(numConstraints+numNonBasic, nil)
 	bAugmented.CopyVec(b)
 
-	fmt.Println("A: ", mat.Formatted(AAugmented))
-
 	// Add the non-basic variable constraints
 	nonBasicVars := state.GetNonBasicVariables()
 	for ii, v := range nonBasicVars {
-		fmt.Println("Adding non-basic variable constraint for variable: ", v)
+		// fmt.Println("Adding non-basic variable constraint for variable: ", v)
 		// Find the index of the variable in the tableau
 		vIdxInTableau, _ := symbolic.FindInSlice(v, state.Tableau.Variables)
-		fmt.Println("vIdxInTableau: ", vIdxInTableau)
-		fmt.Println("Targeted row: ", numConstraints+ii)
+		// fmt.Println("vIdxInTableau: ", vIdxInTableau)
+		// fmt.Println("Targeted row: ", numConstraints+ii)
 		AAugmented.Set(numConstraints+ii, vIdxInTableau, 1.0)
 	}
 	// b is already zero in the new rows, so we don't need to set anything in bAugmented
diff --git a/examples/gonum_bug1/try_bug.go b/examples/gonum_bug1/try_bug.go
index a7f6f29..56d8bb8 100644
--- a/examples/gonum_bug1/try_bug.go
+++ b/examples/gonum_bug1/try_bug.go
@@ -4,6 +4,7 @@ import (
 	"github.com/MatProGo-dev/MatProInterface.go/problem"
 	getKMatrix "github.com/MatProGo-dev/SymbolicMath.go/get/KMatrix"
 	getKVector "github.com/MatProGo-dev/SymbolicMath.go/get/KVector"
+	"github.com/MatProGo-dev/SymbolicMath.go/symbolic"
 	"github.com/MatProGo-dev/simplex/simplexSolver"
 	"gonum.org/v1/gonum/mat"
 )
@@ -90,4 +91,11 @@ func main() {
 	for varName, varValue := range solution.VariableValues {
 		println("  ", varName, ": ", varValue)
 	}
+
+	// Construct Variable Values map in terms of map[symbolic.Variable] float64
+	varValues := make(map[symbolic.Variable]float64)
+	for varID, varValue := range solution.VariableValues {
+		// Extract variable form problem that has the same ID
+		varValues[symbolic.NewVariable(varName)] = varValue
+	}
 }
diff --git a/utils/tableau.go b/utils/tableau.go
index 6562ae6..6bd892f 100644
--- a/utils/tableau.go
+++ b/utils/tableau.go
@@ -446,6 +446,8 @@ func (tableau *Tableau) CanNotBeImproved() bool {
 	// Get the coefficients of the non-basic variables
 	c := tableau.C()
 
+	fmt.Println("c =", c)
+
 	// Check if all coefficients are less than or equal to zero
 	for ii := 0; ii < c.Len(); ii++ {
 		if c.AtVec(ii) < 0 {

From 16d1b2a88f9d0f4cd81ffcd4e709bbd3e5766ea2 Mon Sep 17 00:00:00 2001
From: Kwesi Rutledge <thesolitaryecrivain@gmail.com>
Date: Sat, 4 Oct 2025 14:47:48 -0400
Subject: [PATCH 09/19] Cleaning up unused code in example

---
 examples/gonum_bug1/try_bug.go | 8 --------
 1 file changed, 8 deletions(-)

diff --git a/examples/gonum_bug1/try_bug.go b/examples/gonum_bug1/try_bug.go
index 56d8bb8..a7f6f29 100644
--- a/examples/gonum_bug1/try_bug.go
+++ b/examples/gonum_bug1/try_bug.go
@@ -4,7 +4,6 @@ import (
 	"github.com/MatProGo-dev/MatProInterface.go/problem"
 	getKMatrix "github.com/MatProGo-dev/SymbolicMath.go/get/KMatrix"
 	getKVector "github.com/MatProGo-dev/SymbolicMath.go/get/KVector"
-	"github.com/MatProGo-dev/SymbolicMath.go/symbolic"
 	"github.com/MatProGo-dev/simplex/simplexSolver"
 	"gonum.org/v1/gonum/mat"
 )
@@ -91,11 +90,4 @@ func main() {
 	for varName, varValue := range solution.VariableValues {
 		println("  ", varName, ": ", varValue)
 	}
-
-	// Construct Variable Values map in terms of map[symbolic.Variable] float64
-	varValues := make(map[symbolic.Variable]float64)
-	for varID, varValue := range solution.VariableValues {
-		// Extract variable form problem that has the same ID
-		varValues[symbolic.NewVariable(varName)] = varValue
-	}
 }

From 6df1ba7f38597c340d4d29ee0618463dd0385580 Mon Sep 17 00:00:00 2001
From: Kwesi Rutledge <thesolitaryecrivain@gmail.com>
Date: Wed, 15 Oct 2025 20:52:54 -0400
Subject: [PATCH 10/19] Upgraded MatProInterface.go interface

---
 go.mod |  4 ++--
 go.sum | 12 ++++++------
 2 files changed, 8 insertions(+), 8 deletions(-)

diff --git a/go.mod b/go.mod
index 18de501..a602e97 100644
--- a/go.mod
+++ b/go.mod
@@ -5,7 +5,7 @@ go 1.23.0
 toolchain go1.23.9
 
 require (
-	github.com/MatProGo-dev/MatProInterface.go v0.6.0
-	github.com/MatProGo-dev/SymbolicMath.go v0.2.5
+	github.com/MatProGo-dev/MatProInterface.go v0.6.4
+	github.com/MatProGo-dev/SymbolicMath.go v0.2.6
 	gonum.org/v1/gonum v0.16.0
 )
diff --git a/go.sum b/go.sum
index f772359..48fd2a7 100644
--- a/go.sum
+++ b/go.sum
@@ -1,8 +1,8 @@
-github.com/MatProGo-dev/MatProInterface.go v0.5.6 h1:rzoT536J0sWQEJttc3vSsJ/ESgEg95NU2SbtaaGmUs4=
-github.com/MatProGo-dev/MatProInterface.go v0.5.6/go.mod h1:o/uWBdqnA6YXq0enVlFEwM6raLnV2xC0liXqRe8FrPA=
-github.com/MatProGo-dev/MatProInterface.go v0.6.0 h1:x3hQwl5Hz1Z+ZuTlaQlMfdjvaQqjmc9agJkF7FIBR4U=
-github.com/MatProGo-dev/MatProInterface.go v0.6.0/go.mod h1:o/uWBdqnA6YXq0enVlFEwM6raLnV2xC0liXqRe8FrPA=
-github.com/MatProGo-dev/SymbolicMath.go v0.2.5 h1:fGpwtywb2hUXvGKk1Te6PQEfHeVar5w05KTbc3wHj6A=
-github.com/MatProGo-dev/SymbolicMath.go v0.2.5/go.mod h1:tW8thj4pkaTV9lFNU3OCKmwQ3mZ2Eim6S4JpHRDfRvU=
+github.com/MatProGo-dev/MatProInterface.go v0.6.2 h1:DSHXN5OLtYUfBUx41jSkhIitZwfJ3VabmttP7eDCLQ0=
+github.com/MatProGo-dev/MatProInterface.go v0.6.2/go.mod h1:v7e1RkEpIX5F2l/AeDy04CCaVERBA7vGI8rjVItB3dc=
+github.com/MatProGo-dev/MatProInterface.go v0.6.4 h1:tjoDJMmAelPVXz7gZcdUJyLYpSd2Xb9Pbqlb5FOQmTc=
+github.com/MatProGo-dev/MatProInterface.go v0.6.4/go.mod h1:v7e1RkEpIX5F2l/AeDy04CCaVERBA7vGI8rjVItB3dc=
+github.com/MatProGo-dev/SymbolicMath.go v0.2.6 h1:0THkOKIjdjadIb9MHIUflk08U7tv17KvtQPOP3eMOfk=
+github.com/MatProGo-dev/SymbolicMath.go v0.2.6/go.mod h1:tW8thj4pkaTV9lFNU3OCKmwQ3mZ2Eim6S4JpHRDfRvU=
 gonum.org/v1/gonum v0.16.0 h1:5+ul4Swaf3ESvrOnidPp4GZbzf0mxVQpDCYUQE7OJfk=
 gonum.org/v1/gonum v0.16.0/go.mod h1:fef3am4MQ93R2HHpKnLk4/Tbh/s0+wqD5nfa6Pnwy4E=

From b3d2996dd4e645bbe7b05b2617414909508882d0 Mon Sep 17 00:00:00 2001
From: Kwesi Rutledge <thesolitaryecrivain@gmail.com>
Date: Wed, 15 Oct 2025 20:53:35 -0400
Subject: [PATCH 11/19] Upgraded usage of modified methods throughout simplex

---
 algorithms/tableau/state.go               | 62 ++++++++++++++---------
 algorithms/tableau/tableau_algo.go        |  4 +-
 solution/simplex_solution.go              | 30 +++++++++--
 testing/algorithms/stanford/state_test.go |  6 +--
 testing/algorithms/tableau/state_test.go  |  3 +-
 testing/utils/tableau_test.go             |  4 +-
 6 files changed, 73 insertions(+), 36 deletions(-)

diff --git a/algorithms/tableau/state.go b/algorithms/tableau/state.go
index 9fbd128..fe9a0e5 100644
--- a/algorithms/tableau/state.go
+++ b/algorithms/tableau/state.go
@@ -3,6 +3,8 @@ package tableau_algorithm1
 import (
 	"fmt"
 
+	"github.com/MatProGo-dev/MatProInterface.go/problem"
+	"github.com/MatProGo-dev/MatProInterface.go/solution"
 	"github.com/MatProGo-dev/SymbolicMath.go/symbolic"
 	"github.com/MatProGo-dev/simplex/algorithms"
 	"github.com/MatProGo-dev/simplex/algorithms/tableau/selection"
@@ -91,17 +93,6 @@ func (state *TableauAlgorithmState) CheckTerminationCondition() (bool, error) {
 	return true, nil
 }
 
-func (state *TableauAlgorithmState) CurrentObjectiveValue() (float64, error) {
-	// Input Checking
-	err := state.Check()
-	if err != nil {
-		return 0.0, err
-	}
-
-	// Setup
-	return state.Tableau.D(), nil
-}
-
 /*
 GetBasicVariables
 Description:
@@ -251,6 +242,8 @@ func (state *TableauAlgorithmState) CalculateNextState() (TableauAlgorithmState,
 		return TableauAlgorithmState{}, err
 	}
 
+	// fmt.Println("Calculating next state from tableau:", mat.Formatted(state.Tableau.AsCompressedMatrix))
+
 	// Select the pivot column and row (i.e., the entering and exiting variables in the tableau)
 	// Here, we use Bland's Rule to select the entering variable
 	// TODO(Kwesi): Make other rules available
@@ -260,6 +253,9 @@ func (state *TableauAlgorithmState) CalculateNextState() (TableauAlgorithmState,
 		return TableauAlgorithmState{}, fmt.Errorf("TableauAlgorithmState: Failed to select entering and exiting variables (%v)", err)
 	}
 
+	// fmt.Println("Entering variable index: ", enteringVarIdx, " (", state.Tableau.Variables[enteringVarIdx], ")")
+	// fmt.Println("Exiting variable index: ", exitingVarIdx, " (", state.Tableau.Variables[exitingVarIdx], ")")
+
 	// Create the new tableau
 	newTab, err := state.Tableau.Pivot(enteringVarIdx, exitingVarIdx)
 	if err != nil {
@@ -318,7 +314,7 @@ func (state *TableauAlgorithmState) CalculateOptimalSolution() (mat.VecDense, er
 	return *solutionVec, nil
 }
 
-func (state *TableauAlgorithmState) CreateOptimalValuesMap() (map[uint64]float64, error) {
+func (state *TableauAlgorithmState) CreateOptimalValuesMap(originalVariablesAsStandardFormExpressions map[symbolic.Variable]symbolic.Expression) (map[uint64]float64, error) {
 	// Input Checking
 	err := state.Check()
 	if err != nil {
@@ -331,16 +327,33 @@ func (state *TableauAlgorithmState) CreateOptimalValuesMap() (map[uint64]float64
 		return nil, err
 	}
 
-	// Create the map
-	solutionMap := map[uint64]float64{}
+	// Create the map between the STANDARD FORM variables and the optimal values
+	standardFormOptimalValues := map[symbolic.Variable]symbolic.Expression{}
 	for ii, v := range state.Tableau.Variables {
-		solutionMap[v.ID] = solutionVec.AtVec(ii)
+		standardFormOptimalValues[v] = symbolic.K(solutionVec.AtVec(ii))
+	}
+
+	// Create the map between the ORIGINAL variables and the optimal values
+	optimalValueMap := map[uint64]float64{}
+	for origVar, expr := range originalVariablesAsStandardFormExpressions {
+		// Evaluate the expression (which is equal to the original variable) using the solution map
+		value := expr.SubstituteAccordingTo(standardFormOptimalValues)
+		valAsK, ok := value.(symbolic.K)
+		if !ok {
+			return nil, fmt.Errorf("TableauAlgorithmState: Failed to evaluate optimal value for original variable %v", origVar)
+		}
+		// Add the value to the output map
+		optimalValueMap[origVar.ID] = float64(valAsK)
 	}
 
-	return solutionMap, nil
+	return optimalValueMap, nil
 }
 
-func (state *TableauAlgorithmState) ToSolution(condition tableau_termination.TerminationType) (simplex_solution.SimplexSolution, error) {
+func (state *TableauAlgorithmState) ToSolution(
+	condition tableau_termination.TerminationType,
+	varMap map[symbolic.Variable]symbolic.Expression,
+	originalProblem *problem.OptimizationProblem,
+) (simplex_solution.SimplexSolution, error) {
 	// Create container for solution
 	var sol simplex_solution.SimplexSolution
 	var err error
@@ -351,22 +364,25 @@ func (state *TableauAlgorithmState) ToSolution(condition tableau_termination.Ter
 	// Construct Iteration Count
 	sol.Iterations = state.IterationCount
 
-	// Construct Objective Value
-	sol.Objective, err = state.CurrentObjectiveValue()
+	// Attach original problem
+	sol.OriginalProblem = originalProblem
+
+	// Construct Variable map
+	sol.VariableValues, err = state.CreateOptimalValuesMap(varMap)
 	if err != nil {
 		return sol,
 			fmt.Errorf(
-				"There was an issue getting the objective value at termination: %v",
+				"There was an issue creating the optimal values map at termination: %v",
 				err,
 			)
 	}
 
-	// Construct Variable map
-	sol.VariableValues, err = state.CreateOptimalValuesMap()
+	// Construct Objective Value
+	sol.Objective, err = solution.GetOptimalObjectiveValue(&sol)
 	if err != nil {
 		return sol,
 			fmt.Errorf(
-				"There was an issue creating the optimal values map at termination: %v",
+				"There was an issue getting the objective value at termination: %v",
 				err,
 			)
 	}
diff --git a/algorithms/tableau/tableau_algo.go b/algorithms/tableau/tableau_algo.go
index ad6e8aa..fbd472c 100644
--- a/algorithms/tableau/tableau_algo.go
+++ b/algorithms/tableau/tableau_algo.go
@@ -38,7 +38,7 @@ func (algo *TableauAlgorithm) Solve(prob problem.OptimizationProblem) (simplex_s
 	// Setup
 
 	// Create initial Tableau state from the problem
-	initialTableau, err := utils.GetInitialTableauFrom(&prob)
+	initialTableau, mapFromOriginalVariablesToStandardFormVariables, err := utils.GetInitialTableauFrom(&prob)
 	if err != nil {
 		return simplex_solution.SimplexSolution{}, fmt.Errorf("there was an issue creating the initial tableau: %v", err)
 	}
@@ -62,7 +62,7 @@ func (algo *TableauAlgorithm) Solve(prob problem.OptimizationProblem) (simplex_s
 		}
 
 		if condition != tableau_termination.DidNotTerminate {
-			sol, err = stateII.ToSolution(condition)
+			sol, err = stateII.ToSolution(condition, mapFromOriginalVariablesToStandardFormVariables, &prob)
 			if err != nil {
 				return simplex_solution.SimplexSolution{},
 					fmt.Errorf(
diff --git a/solution/simplex_solution.go b/solution/simplex_solution.go
index 1b76829..403b5d6 100644
--- a/solution/simplex_solution.go
+++ b/solution/simplex_solution.go
@@ -1,6 +1,9 @@
 package simplex_solution
 
-import solution_status "github.com/MatProGo-dev/MatProInterface.go/solution/status"
+import (
+	"github.com/MatProGo-dev/MatProInterface.go/problem"
+	solution_status "github.com/MatProGo-dev/MatProInterface.go/solution/status"
+)
 
 // SimplexSolution represents the result of solving a linear program using the simplex method.
 // It contains the values of the decision variables, the objective value, and the solution status.
@@ -9,8 +12,27 @@ type SimplexSolution struct {
 	// The uint64 key typically represents the unique identifier or index of a variable in the model.
 	VariableValues map[uint64]float64
 	// Objective is the value of the objective function at the solution.
-	Objective      float64
+	Objective float64
 	// Status indicates the status of the solution (e.g., optimal, infeasible).
-	Status         solution_status.SolutionStatus
-	Iterations     int
+	Status     solution_status.SolutionStatus
+	Iterations int
+	// originalProblem is the original optimization problem that was solved to obtain this solution.
+	// It is included for reference and may be nil if not applicable.
+	OriginalProblem *problem.OptimizationProblem
+}
+
+func (sol *SimplexSolution) GetValueMap() map[uint64]float64 {
+	return sol.VariableValues
+}
+
+func (sol *SimplexSolution) GetOptimalValue() float64 {
+	return sol.Objective
+}
+
+func (sol *SimplexSolution) GetStatus() solution_status.SolutionStatus {
+	return sol.Status
+}
+
+func (sol *SimplexSolution) GetProblem() *problem.OptimizationProblem {
+	return sol.OriginalProblem
 }
diff --git a/testing/algorithms/stanford/state_test.go b/testing/algorithms/stanford/state_test.go
index 721995f..30bf0e5 100644
--- a/testing/algorithms/stanford/state_test.go
+++ b/testing/algorithms/stanford/state_test.go
@@ -16,7 +16,7 @@ func TestStanfordAlgorithmState_NonBasicVariables1(t *testing.T) {
 	exampleProblem1 := examples.GetTestProblem1()
 
 	// Create the problem in standard form
-	problemInStandardForm, slackVariables, err := exampleProblem1.ToLPStandardForm1()
+	problemInStandardForm, slackVariables, _, err := exampleProblem1.ToLPStandardForm1()
 	if err != nil {
 		t.Errorf("Expected no error, but got: %v", err)
 	}
@@ -80,7 +80,7 @@ func TestStanfordAlgorithmState_BasicVariables1(t *testing.T) {
 	exampleProblem1 := examples.GetTestProblem1()
 
 	// Create the problem in standard form
-	problemInStandardForm, slackVariables, err := exampleProblem1.ToLPStandardForm1()
+	problemInStandardForm, slackVariables, _, err := exampleProblem1.ToLPStandardForm1()
 	if err != nil {
 		t.Errorf("Expected no error, but got: %v", err)
 	}
@@ -147,7 +147,7 @@ func TestStanfordAlgorithmState_ReducedCostVector1(t *testing.T) {
 	exampleProblem1 := examples.GetTestProblem2()
 
 	// Create the problem in standard form
-	problemInStandardForm, slackVariables, err := exampleProblem1.ToLPStandardForm1()
+	problemInStandardForm, slackVariables, _, err := exampleProblem1.ToLPStandardForm1()
 	if err != nil {
 		t.Errorf("Expected no error, but got: %v", err)
 	}
diff --git a/testing/algorithms/tableau/state_test.go b/testing/algorithms/tableau/state_test.go
index de7d526..4d8c7a7 100644
--- a/testing/algorithms/tableau/state_test.go
+++ b/testing/algorithms/tableau/state_test.go
@@ -34,7 +34,7 @@ func TestTableau_CalculateOptimalSolution1(t *testing.T) {
 	// Use the optimization solver to solve the problem
 
 	// Create initial Tableau state from the problem
-	initialTableau, err := utils.GetInitialTableauFrom(testProblem)
+	initialTableau, _, err := utils.GetInitialTableauFrom(testProblem)
 	if err != nil {
 		t.Errorf("there was an issue creating the initial tableau: %v", err)
 	}
@@ -66,5 +66,4 @@ func TestTableau_CalculateOptimalSolution1(t *testing.T) {
 			t.Errorf("Expected solution value %v at index %d, but got %v", val, ii, solVec.AtVec(ii))
 		}
 	}
-
 }
diff --git a/testing/utils/tableau_test.go b/testing/utils/tableau_test.go
index 64740c1..2803efe 100644
--- a/testing/utils/tableau_test.go
+++ b/testing/utils/tableau_test.go
@@ -24,7 +24,7 @@ func TestGetInitialTableau1(t *testing.T) {
 	problemIn := examples.GetTestProblem3()
 
 	// Create the tableau using the initial state + problem in standard form
-	tableau, err := utils.GetInitialTableauFrom(problemIn)
+	tableau, _, err := utils.GetInitialTableauFrom(problemIn)
 	if err != nil {
 		t.Errorf("Expected no error, but got: %v", err)
 	}
@@ -83,7 +83,7 @@ func TestComputeFeasibleSolution1(t *testing.T) {
 	problemIn := examples.GetTestProblem3()
 
 	// Create the tableau
-	tableau, err := utils.GetInitialTableauFrom(problemIn)
+	tableau, _, err := utils.GetInitialTableauFrom(problemIn)
 	if err != nil {
 		t.Errorf("Expected no error, but got: %v", err)
 	}

From aca9aa1c6e4352f75001a48663fcb59e34f72d65 Mon Sep 17 00:00:00 2001
From: Kwesi Rutledge <thesolitaryecrivain@gmail.com>
Date: Wed, 15 Oct 2025 20:53:47 -0400
Subject: [PATCH 12/19] Fixing bug in SimplexMethod Tableau method

---
 algorithms/tableau/selection/blands_rule.go |  5 +++--
 examples/gonum_bug1/try_bug.go              |  2 +-
 utils/tableau.go                            | 16 +++++++++-------
 3 files changed, 13 insertions(+), 10 deletions(-)

diff --git a/algorithms/tableau/selection/blands_rule.go b/algorithms/tableau/selection/blands_rule.go
index 8cf3821..f901d67 100644
--- a/algorithms/tableau/selection/blands_rule.go
+++ b/algorithms/tableau/selection/blands_rule.go
@@ -3,6 +3,7 @@ package selection
 import (
 	"fmt"
 
+	"github.com/MatProGo-dev/SymbolicMath.go/symbolic"
 	"github.com/MatProGo-dev/simplex/utils"
 )
 
@@ -55,7 +56,7 @@ Description:
 func (br BlandsRule) SelectExitingVariable(tableau utils.Tableau, enteringVarIdx int) int {
 	// Setup
 	minIndex := -1
-	minRatio := -1.0
+	minRatio := float64(symbolic.Infinity)
 
 	// Get the relevant matrices
 	A := tableau.A()
@@ -74,7 +75,7 @@ func (br BlandsRule) SelectExitingVariable(tableau utils.Tableau, enteringVarIdx
 	// Iterate through the ratios and find the smallest one
 	for i, ratio := range ratios {
 		if ratio >= 0 { // Only consider valid ratios
-			if minRatio < 0 || ratio < minRatio || (ratio == minRatio && tableau.BasicVariableIndicies[i] < tableau.BasicVariableIndicies[minIndex]) {
+			if ratio < minRatio || (ratio == minRatio && tableau.BasicVariableIndicies[i] < tableau.BasicVariableIndicies[minIndex]) {
 				minRatio = ratio
 				minIndex = i
 			}
diff --git a/examples/gonum_bug1/try_bug.go b/examples/gonum_bug1/try_bug.go
index a7f6f29..6545d10 100644
--- a/examples/gonum_bug1/try_bug.go
+++ b/examples/gonum_bug1/try_bug.go
@@ -56,7 +56,7 @@ func BuildOptimizationProblem() problem.OptimizationProblem {
 		[]float64{3370, 1031, 2350, 2289, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 	)
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-	G := mat.NewDense(6+varCount, varCount, Gbuf)
+	G := mat.NewDense(63, varCount, Gbuf)
 
 	out.Constraints = append(
 		out.Constraints,
diff --git a/utils/tableau.go b/utils/tableau.go
index 6bd892f..b3188ea 100644
--- a/utils/tableau.go
+++ b/utils/tableau.go
@@ -348,28 +348,30 @@ Description:
 
 	This function computes the initial tableau of an
 */
-func GetInitialTableauFrom(problemIn *problem.OptimizationProblem) (Tableau, error) {
+func GetInitialTableauFrom(problemIn *problem.OptimizationProblem) (Tableau, map[symbolic.Variable]symbolic.Expression, error) {
 	// Input Processing
 	if problemIn == nil {
-		return Tableau{}, fmt.Errorf(
+		return Tableau{}, nil, fmt.Errorf(
 			"Check: tableau.Problem cannot be nil",
 		)
 	}
 
 	// Ensure that the problem is a linear program
 	if !problemIn.IsLinear() {
-		return Tableau{}, fmt.Errorf(
+		return Tableau{}, nil, fmt.Errorf(
 			"Check: the problem is not a linear program",
 		)
 	}
 
 	// Transform the problem into the standard form where all constraints
 	// are equality constraints
-	problemInStandardForm, slackVariables, err := problemIn.ToLPStandardForm2()
+	problemInStandardForm, slackVariables, mapFromOriginalVariablesToNewExpressions, err := problemIn.ToLPStandardForm2()
 	if err != nil {
-		return Tableau{}, err
+		return Tableau{}, nil, err
 	}
 
+	fmt.Println("Problem in standard form:", problemInStandardForm)
+
 	// Transform SlackVariables object into indicies
 	var slackVariableIndicies []int
 	for _, slackVar := range slackVariables {
@@ -381,7 +383,7 @@ func GetInitialTableauFrom(problemIn *problem.OptimizationProblem) (Tableau, err
 	// [ A | b ]
 	A, b, err := problemInStandardForm.LinearEqualityConstraintMatrices()
 	if err != nil {
-		return Tableau{}, err
+		return Tableau{}, mapFromOriginalVariablesToNewExpressions, err
 	}
 	Ab := symbolic.HStack(A, b)
 
@@ -408,7 +410,7 @@ func GetInitialTableauFrom(problemIn *problem.OptimizationProblem) (Tableau, err
 		AsCompressedMatrix:    &tableauMatCondensedAsDense,
 		Variables:             problemInStandardForm.Variables,
 		BasicVariableIndicies: slackVariableIndicies,
-	}, nil
+	}, mapFromOriginalVariablesToNewExpressions, nil
 }
 
 /*

From 941a32296112f5b56053746980a6ff4ee1275970 Mon Sep 17 00:00:00 2001
From: Kwesi Rutledge <thesolitaryecrivain@gmail.com>
Date: Wed, 15 Oct 2025 21:26:24 -0400
Subject: [PATCH 13/19] Added working box example

---
 algorithms/tableau/selection/blands_rule.go |  2 +
 examples/box1/box.go                        | 82 +++++++++++++++++++++
 2 files changed, 84 insertions(+)
 create mode 100644 examples/box1/box.go

diff --git a/algorithms/tableau/selection/blands_rule.go b/algorithms/tableau/selection/blands_rule.go
index f901d67..0aaa3cc 100644
--- a/algorithms/tableau/selection/blands_rule.go
+++ b/algorithms/tableau/selection/blands_rule.go
@@ -99,6 +99,8 @@ func (br BlandsRule) SelectEnteringAndExitingVariables(tableau utils.Tableau) (i
 		return -1, -1, nil // Optimal solution found, no entering variable
 	}
 
+	fmt.Println("Entering variable index:", enteringVarIdx)
+
 	// Select the exiting variable
 	exitingVarIdx := br.SelectExitingVariable(tableau, enteringVarIdx)
 	if exitingVarIdx == -1 {
diff --git a/examples/box1/box.go b/examples/box1/box.go
new file mode 100644
index 0000000..9780d98
--- /dev/null
+++ b/examples/box1/box.go
@@ -0,0 +1,82 @@
+package main
+
+import (
+	"github.com/MatProGo-dev/MatProInterface.go/problem"
+	getKVector "github.com/MatProGo-dev/SymbolicMath.go/get/KVector"
+	"github.com/MatProGo-dev/SymbolicMath.go/symbolic"
+	"github.com/MatProGo-dev/simplex/simplexSolver"
+)
+
+/*
+Description:
+
+	This function builds an optimization problem where we attempt to find
+	the optimal solution to a linear programming problem that is in a feasible
+	region that is a box.
+
+	The problem will be:
+
+	Minimize:  x1 + 2*x2
+	Subject to:
+		0 <= x1 <= 1
+		0 <= x2 <= 1
+
+	The optimal solution is x1 = 0, x2 = 0 with an objective value of 0.
+*/
+func BuildOptimizationProblem() problem.OptimizationProblem {
+	// setup
+	varCount := 2
+	out := problem.NewProblem("Box LP Problem")
+
+	// Create the variables
+	x := out.AddVariableVector(varCount)
+
+	// Create the objective
+	c := getKVector.From(
+		[]float64{1, 2},
+	)
+	out.SetObjective(
+		c.Transpose().Multiply(x),
+		problem.SenseMinimize,
+	)
+
+	// Create the constraints
+	// - x >= 0
+	out.Constraints = append(
+		out.Constraints,
+		x.GreaterEq(symbolic.ZerosVector(varCount)),
+	)
+
+	// - x <= 1
+	out.Constraints = append(
+		out.Constraints,
+		x.LessEq(symbolic.OnesVector(varCount)),
+	)
+
+	return *out
+}
+
+func main() {
+	// This is just a placeholder to make the package "main" valid.
+	trickyProblem := BuildOptimizationProblem()
+
+	// Use solver to solve the problem
+	solver := simplexSolver.New("Simplex Solver Example")
+	solver.IterationLimit = 100
+
+	// Solve the problem
+	solution, err := solver.Solve(trickyProblem)
+	if err != nil {
+		panic(err)
+	}
+
+	// Print the solution
+	solutionMessage, _ := solution.Status.ToMessage()
+	println("Solution Status: ", solutionMessage)
+	println("Objective Value: ", solution.Objective)
+	println("Number of Iterations: ", solution.Iterations)
+	println("Variable Values: ")
+	for varName, varValue := range solution.VariableValues {
+		println("  ", varName, ": ", varValue)
+	}
+}

From e0f2023d03db9caf5a32bc291169de5d4d0e64d7 Mon Sep 17 00:00:00 2001
From: Kwesi Rutledge <thesolitaryecrivain@gmail.com>
Date: Wed, 15 Oct 2025 21:33:39 -0400
Subject: [PATCH 14/19] remove references to old MatProInterface.go

---
 go.sum | 2 --
 1 file changed, 2 deletions(-)

diff --git a/go.sum b/go.sum
index 48fd2a7..7e87577 100644
--- a/go.sum
+++ b/go.sum
@@ -1,5 +1,3 @@
-github.com/MatProGo-dev/MatProInterface.go v0.6.2 h1:DSHXN5OLtYUfBUx41jSkhIitZwfJ3VabmttP7eDCLQ0=
-github.com/MatProGo-dev/MatProInterface.go v0.6.2/go.mod h1:v7e1RkEpIX5F2l/AeDy04CCaVERBA7vGI8rjVItB3dc=
 github.com/MatProGo-dev/MatProInterface.go v0.6.4 h1:tjoDJMmAelPVXz7gZcdUJyLYpSd2Xb9Pbqlb5FOQmTc=
 github.com/MatProGo-dev/MatProInterface.go v0.6.4/go.mod h1:v7e1RkEpIX5F2l/AeDy04CCaVERBA7vGI8rjVItB3dc=
 github.com/MatProGo-dev/SymbolicMath.go v0.2.6 h1:0THkOKIjdjadIb9MHIUflk08U7tv17KvtQPOP3eMOfk=

From c58b3b9fef183e9fc869ef2f0bd03a665edc43ec Mon Sep 17 00:00:00 2001
From: Kwesi Rutledge <thesolitaryecrivain@gmail.com>
Date: Wed, 15 Oct 2025 21:37:05 -0400
Subject: [PATCH 15/19] Updated README.md

---
 README.md | 78 ++++++++++++++++++++++++++++++++++++++++++++++++++++++-
 1 file changed, 77 insertions(+), 1 deletion(-)

diff --git a/README.md b/README.md
index 3b7642d..5dde69e 100644
--- a/README.md
+++ b/README.md
@@ -10,4 +10,80 @@ go get github.com/MatProGo-dev/simplex
 
 # Usage
 
-TBD
\ No newline at end of file
+```
+/*
+Description:
+
+	This function builds an optimization problem where we attempt to find
+	the optimal solution to a linear programming problem that is in a feasible
+	region that is a box.
+
+	The problem will be:
+
+	Minimize:  x1 + 2*x2
+	Subject to:
+		0 <= x1 <= 1
+		0 <= x2 <= 1
+
+	The optimal solution is x1 = 0, x2 = 0 with an objective value of 0.
+*/
+func BuildOptimizationProblem() problem.OptimizationProblem {
+	// setup
+	varCount := 2
+	out := problem.NewProblem("Box LP Problem")
+
+	// Create the variables
+	x := out.AddVariableVector(varCount)
+
+	// Create the objective
+	c := getKVector.From(
+		[]float64{1, 2},
+	)
+	out.SetObjective(
+		c.Transpose().Multiply(x),
+		problem.SenseMinimize,
+	)
+
+	// Create the constraints
+	// - x >= 0
+	out.Constraints = append(
+		out.Constraints,
+		x.GreaterEq(symbolic.ZerosVector(varCount)),
+	)
+
+	// - x <= 1
+	out.Constraints = append(
+		out.Constraints,
+		x.LessEq(symbolic.OnesVector(varCount)),
+	)
+
+	return *out
+}
+
+func main() {
+	// This is just a placeholder to make the package "main" valid.
+	trickyProblem := BuildOptimizationProblem()
+
+	// Use solver to solve the problem
+	solver := simplexSolver.New("Simplex Solver Example")
+	solver.IterationLimit = 100
+
+	// Solve the problem
+	solution, err := solver.Solve(trickyProblem)
+	if err != nil {
+		panic(err)
+	}
+
+	// Print the solution
+	solutionMessage, _ := solution.Status.ToMessage()
+	println("Solution Status: ", solutionMessage)
+	println("Objective Value: ", solution.Objective)
+	println("Number of Iterations: ", solution.Iterations)
+	println("Variable Values: ")
+	for varName, varValue := range solution.VariableValues {
+		println("  ", varName, ": ", varValue)
+	}
+}
+```
+
+See the examples directory for more example use cases for the library.
\ No newline at end of file

From 1882ae9d909b18608c33cbddc034577c6f6fcdea Mon Sep 17 00:00:00 2001
From: Kwesi Rutledge <thesolitaryecrivain@gmail.com>
Date: Wed, 15 Oct 2025 21:37:59 -0400
Subject: [PATCH 16/19] Updated README.md example

---
 README.md | 21 +++++++--------------
 1 file changed, 7 insertions(+), 14 deletions(-)

diff --git a/README.md b/README.md
index 5dde69e..264dec3 100644
--- a/README.md
+++ b/README.md
@@ -11,22 +11,15 @@ go get github.com/MatProGo-dev/simplex
 # Usage
 
 ```
-/*
-Description:
+package main
 
-	This function builds an optimization problem where we attempt to find
-	the optimal solution to a linear programming problem that is in a feasible
-	region that is a box.
+import (
+	"github.com/MatProGo-dev/MatProInterface.go/problem"
+	getKVector "github.com/MatProGo-dev/SymbolicMath.go/get/KVector"
+	"github.com/MatProGo-dev/SymbolicMath.go/symbolic"
+	"github.com/MatProGo-dev/simplex/simplexSolver"
+)
 
-	The problem will be:
-
-	Minimize:  x1 + 2*x2
-	Subject to:
-		0 <= x1 <= 1
-		0 <= x2 <= 1
-
-	The optimal solution is x1 = 0, x2 = 0 with an objective value of 0.
-*/
 func BuildOptimizationProblem() problem.OptimizationProblem {
 	// setup
 	varCount := 2

From ccc5f8ae3b0fe9f803b28ef606f66c18210d0645 Mon Sep 17 00:00:00 2001
From: Kwesi Rutledge <thesolitaryecrivain@gmail.com>
Date: Fri, 17 Oct 2025 00:04:14 -0400
Subject: [PATCH 17/19] upgraded MatProInterface

---
 go.mod | 4 ++--
 go.sum | 8 ++++----
 2 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/go.mod b/go.mod
index a602e97..194d383 100644
--- a/go.mod
+++ b/go.mod
@@ -5,7 +5,7 @@ go 1.23.0
 toolchain go1.23.9
 
 require (
-	github.com/MatProGo-dev/MatProInterface.go v0.6.4
-	github.com/MatProGo-dev/SymbolicMath.go v0.2.6
+	github.com/MatProGo-dev/MatProInterface.go v0.6.5-1
+	github.com/MatProGo-dev/SymbolicMath.go v0.3.2-0.20251017032605-a7dee10c22bf
 	gonum.org/v1/gonum v0.16.0
 )
diff --git a/go.sum b/go.sum
index 7e87577..2c52a4f 100644
--- a/go.sum
+++ b/go.sum
@@ -1,6 +1,6 @@
-github.com/MatProGo-dev/MatProInterface.go v0.6.4 h1:tjoDJMmAelPVXz7gZcdUJyLYpSd2Xb9Pbqlb5FOQmTc=
-github.com/MatProGo-dev/MatProInterface.go v0.6.4/go.mod h1:v7e1RkEpIX5F2l/AeDy04CCaVERBA7vGI8rjVItB3dc=
-github.com/MatProGo-dev/SymbolicMath.go v0.2.6 h1:0THkOKIjdjadIb9MHIUflk08U7tv17KvtQPOP3eMOfk=
-github.com/MatProGo-dev/SymbolicMath.go v0.2.6/go.mod h1:tW8thj4pkaTV9lFNU3OCKmwQ3mZ2Eim6S4JpHRDfRvU=
+github.com/MatProGo-dev/MatProInterface.go v0.6.5-1 h1:dOpwi8mQiHSkA2oXY1B2v/uOM/3ZvZSwbmMomsMLakY=
+github.com/MatProGo-dev/MatProInterface.go v0.6.5-1/go.mod h1:Ip6cN6/uT39LSc6XCqIPnwXLq9N+T/4nLtDPPmHYwhA=
+github.com/MatProGo-dev/SymbolicMath.go v0.3.2-0.20251017032605-a7dee10c22bf h1:fvHlqO39XHb/TfMm979zsnrcvZDSAFU7PW61g1UQCW8=
+github.com/MatProGo-dev/SymbolicMath.go v0.3.2-0.20251017032605-a7dee10c22bf/go.mod h1:tW8thj4pkaTV9lFNU3OCKmwQ3mZ2Eim6S4JpHRDfRvU=
 gonum.org/v1/gonum v0.16.0 h1:5+ul4Swaf3ESvrOnidPp4GZbzf0mxVQpDCYUQE7OJfk=
 gonum.org/v1/gonum v0.16.0/go.mod h1:fef3am4MQ93R2HHpKnLk4/Tbh/s0+wqD5nfa6Pnwy4E=

From 5919a5edb74f5659f16c0c36533b6117976555fe Mon Sep 17 00:00:00 2001
From: Kwesi Rutledge <thesolitaryecrivain@gmail.com>
Date: Fri, 17 Oct 2025 00:18:48 -0400
Subject: [PATCH 18/19] With the introduction of improved termination detection
 + better exiting variable selection, it looks like we've come up with a
 better solution

---
 algorithms/tableau/errors.go                | 18 +++++
 algorithms/tableau/selection/blands_rule.go |  5 +-
 algorithms/tableau/state.go                 |  2 +-
 examples/box2/box.go                        | 83 +++++++++++++++++++++
 utils/tableau.go                            | 22 ++++++
 5 files changed, 127 insertions(+), 3 deletions(-)
 create mode 100644 algorithms/tableau/errors.go
 create mode 100644 examples/box2/box.go

diff --git a/algorithms/tableau/errors.go b/algorithms/tableau/errors.go
new file mode 100644
index 0000000..ff38335
--- /dev/null
+++ b/algorithms/tableau/errors.go
@@ -0,0 +1,18 @@
+package tableau_algorithm1
+
+type VariableSelectionError struct {
+	EnteringVarIndex int
+	ExitingVarIndex  int
+}
+
+func (e VariableSelectionError) Error() string {
+	if e.ExitingVarIndex == -1 {
+		return "VariableSelectionError: No exiting variable found, problem can not be improved."
+	}
+
+	if e.EnteringVarIndex == -1 {
+		return "VariableSelectionError: No entering variable found, current solution is optimal."
+	}
+
+	return "VariableSelectionError: Unknown variable selection error."
+}
diff --git a/algorithms/tableau/selection/blands_rule.go b/algorithms/tableau/selection/blands_rule.go
index 0aaa3cc..f0e4670 100644
--- a/algorithms/tableau/selection/blands_rule.go
+++ b/algorithms/tableau/selection/blands_rule.go
@@ -2,6 +2,7 @@ package selection
 
 import (
 	"fmt"
+	"math"
 
 	"github.com/MatProGo-dev/SymbolicMath.go/symbolic"
 	"github.com/MatProGo-dev/simplex/utils"
@@ -65,7 +66,7 @@ func (br BlandsRule) SelectExitingVariable(tableau utils.Tableau, enteringVarIdx
 	// Create the vector of ratios
 	ratios := make([]float64, tableau.NumberOfConstraints())
 	for i := 0; i < tableau.NumberOfConstraints(); i++ {
-		if A.At(i, enteringVarIdx) > 0 {
+		if math.Abs(A.At(i, enteringVarIdx)) > 1e-12 {
 			ratios[i] = b.AtVec(i) / A.At(i, enteringVarIdx)
 		} else {
 			ratios[i] = -1.0 // Indicate that this variable cannot be used
@@ -104,7 +105,7 @@ func (br BlandsRule) SelectEnteringAndExitingVariables(tableau utils.Tableau) (i
 	// Select the exiting variable
 	exitingVarIdx := br.SelectExitingVariable(tableau, enteringVarIdx)
 	if exitingVarIdx == -1 {
-		return enteringVarIdx, -1, fmt.Errorf("BlandsRule: No exiting variable found, problem is unbounded (?)")
+		return enteringVarIdx, -1, fmt.Errorf("BlandsRule: No exiting variable found, problem can not be improved.")
 	}
 
 	return enteringVarIdx, exitingVarIdx, nil
diff --git a/algorithms/tableau/state.go b/algorithms/tableau/state.go
index fe9a0e5..dde90f7 100644
--- a/algorithms/tableau/state.go
+++ b/algorithms/tableau/state.go
@@ -250,7 +250,7 @@ func (state *TableauAlgorithmState) CalculateNextState() (TableauAlgorithmState,
 	selectionRule := selection.BlandsRule{}
 	enteringVarIdx, exitingVarIdx, err := selectionRule.SelectEnteringAndExitingVariables(*state.Tableau)
 	if err != nil {
-		return TableauAlgorithmState{}, fmt.Errorf("TableauAlgorithmState: Failed to select entering and exiting variables (%v)", err)
+		return TableauAlgorithmState{}, VariableSelectionError{EnteringVarIndex: enteringVarIdx, ExitingVarIndex: exitingVarIdx}
 	}
 
 	// fmt.Println("Entering variable index: ", enteringVarIdx, " (", state.Tableau.Variables[enteringVarIdx], ")")
diff --git a/examples/box2/box.go b/examples/box2/box.go
new file mode 100644
index 0000000..6ddd8e8
--- /dev/null
+++ b/examples/box2/box.go
@@ -0,0 +1,83 @@
+package main
+
+import (
+	"github.com/MatProGo-dev/MatProInterface.go/problem"
+	getKVector "github.com/MatProGo-dev/SymbolicMath.go/get/KVector"
+	"github.com/MatProGo-dev/SymbolicMath.go/symbolic"
+	"github.com/MatProGo-dev/simplex/simplexSolver"
+	"gonum.org/v1/gonum/mat"
+)
+
+/*
+Description:
+
+	This function builds an optimization problem where we attempt to find
+	the optimal solution to a linear programming problem that is in a feasible
+	region that is a box.
+
+	The problem will be:
+
+	Minimize:  x1 - 2*x2
+	Subject to:
+		-1 <= x1 <= 1
+		-1 <= x2 <= 1
+
+	The optimal solution is x1 = -1, x2 = 1 with an objective value of -3.
+*/
+func BuildOptimizationProblem() problem.OptimizationProblem {
+	// setup
+	varCount := 2
+	out := problem.NewProblem("Box LP Problem")
+
+	// Create the variables
+	x := out.AddVariableVector(varCount)
+
+	// Create the objective
+	c := getKVector.From(
+		[]float64{1, -2},
+	)
+	out.SetObjective(
+		c.Transpose().Multiply(x),
+		problem.SenseMinimize,
+	)
+
+	// Create the constraints
+	// - x >= -1
+	out.Constraints = append(
+		out.Constraints,
+		x.GreaterEq(mat.NewVecDense(varCount, []float64{-1, -1})),
+	)
+
+	// - x <= 1
+	out.Constraints = append(
+		out.Constraints,
+		x.LessEq(symbolic.OnesVector(varCount)),
+	)
+
+	return *out
+}
+
+func main() {
+	// This is just a placeholder to make the package "main" valid.
+	trickyProblem := BuildOptimizationProblem()
+
+	// Use solver to solve the problem
+	solver := simplexSolver.New("Simplex Solver Example")
+	solver.IterationLimit = 100
+
+	// Solve the problem
+	solution, err := solver.Solve(trickyProblem)
+	if err != nil {
+		panic(err)
+	}
+
+	// Print the solution
+	solutionMessage, _ := solution.Status.ToMessage()
+	println("Solution Status: ", solutionMessage)
+	println("Objective Value: ", solution.Objective)
+	println("Number of Iterations: ", solution.Iterations)
+	println("Variable Values: ")
+	for varName, varValue := range solution.VariableValues {
+		println("  ", varName, ": ", varValue)
+	}
+}
diff --git a/utils/tableau.go b/utils/tableau.go
index b3188ea..3ae4fb1 100644
--- a/utils/tableau.go
+++ b/utils/tableau.go
@@ -457,6 +457,28 @@ func (tableau *Tableau) CanNotBeImproved() bool {
 		}
 	}
 
+	// For each coefficient that is negative, check if there is a corresponding
+	// row in the Tableau matrix that has a positive ratio (i.e., b[i] / A[i, enteringVarIdx] > 0).
+	// If there is no such row for any entering variable, then the problem can not be improved.
+	A := tableau.A()
+	nRowsA, _ := A.Dims()
+	b := tableau.B()
+	for enteringVarIdx := 0; enteringVarIdx < c.Len(); enteringVarIdx++ {
+		if c.AtVec(enteringVarIdx) < 0 {
+			// Check for positive ratios
+			hasPositiveRatio := false
+			for rowIdx := 0; rowIdx < nRowsA; rowIdx++ {
+				if b.AtVec(rowIdx)/A.At(rowIdx, enteringVarIdx) > 0 {
+					hasPositiveRatio = true
+					break
+				}
+			}
+			if hasPositiveRatio {
+				return false
+			}
+		}
+	}
+
 	return true
 }
 

From 05e617923ec61c2d5a9dabf3bb174d60611af1bf Mon Sep 17 00:00:00 2001
From: Kwesi Rutledge <thesolitaryecrivain@gmail.com>
Date: Fri, 17 Oct 2025 00:29:40 -0400
Subject: [PATCH 19/19] Fixed issues with the unused exported member Objective
 in SimplexSolution

---
 algorithms/stanford/stanford.go                 |  6 ++----
 algorithms/tableau/state.go                     | 11 -----------
 examples/box1/box.go                            | 17 ++++++++++++-----
 examples/box2/box.go                            | 15 ++++++++++-----
 examples/gonum_bug1/try_bug.go                  | 15 ++++++++++-----
 .../the_simplex_method_part_ii.go               | 12 +++++++-----
 solution/simplex_solution.go                    | 10 +++++++---
 7 files changed, 48 insertions(+), 38 deletions(-)

diff --git a/algorithms/stanford/stanford.go b/algorithms/stanford/stanford.go
index 089192f..984cd5d 100644
--- a/algorithms/stanford/stanford.go
+++ b/algorithms/stanford/stanford.go
@@ -194,11 +194,10 @@ func (algo *StanfordAlgorithm) ComputeSolutionFromState(state StanfordAlgorithmS
 	}
 
 	// Compute the value of the objective function
-	objValue, err := algo.ComputeObjectiveFunctionValueWithFeasibleBasicSolution(state, xBasic)
+	_, err = algo.ComputeObjectiveFunctionValueWithFeasibleBasicSolution(state, xBasic)
 	if err != nil {
 		return solution, fmt.Errorf("StanfordAlgorithm: Failed to compute objective function value (%v)", err)
 	}
-	solution.Objective = objValue
 
 	// Set the values of the basic variables
 	for ii, bv := range state.BasicVariables {
@@ -293,8 +292,7 @@ func (algo *StanfordAlgorithm) Solve(initialState StanfordAlgorithmState) (simpl
 
 		if iter == algo.IterationLimit {
 			return simplex_solution.SimplexSolution{
-				Objective: objII,
-				Status:    solution_status.ITERATION_LIMIT,
+				Status: solution_status.ITERATION_LIMIT,
 			}, nil
 		}
 
diff --git a/algorithms/tableau/state.go b/algorithms/tableau/state.go
index dde90f7..ae187ab 100644
--- a/algorithms/tableau/state.go
+++ b/algorithms/tableau/state.go
@@ -4,7 +4,6 @@ import (
 	"fmt"
 
 	"github.com/MatProGo-dev/MatProInterface.go/problem"
-	"github.com/MatProGo-dev/MatProInterface.go/solution"
 	"github.com/MatProGo-dev/SymbolicMath.go/symbolic"
 	"github.com/MatProGo-dev/simplex/algorithms"
 	"github.com/MatProGo-dev/simplex/algorithms/tableau/selection"
@@ -377,16 +376,6 @@ func (state *TableauAlgorithmState) ToSolution(
 			)
 	}
 
-	// Construct Objective Value
-	sol.Objective, err = solution.GetOptimalObjectiveValue(&sol)
-	if err != nil {
-		return sol,
-			fmt.Errorf(
-				"There was an issue getting the objective value at termination: %v",
-				err,
-			)
-	}
-
 	// Assemble Solution Output
 	return sol, nil
 }
diff --git a/examples/box1/box.go b/examples/box1/box.go
index 9780d98..ba50c25 100644
--- a/examples/box1/box.go
+++ b/examples/box1/box.go
@@ -2,6 +2,7 @@ package main
 
 import (
 	"github.com/MatProGo-dev/MatProInterface.go/problem"
+	"github.com/MatProGo-dev/MatProInterface.go/solution"
 	getKVector "github.com/MatProGo-dev/SymbolicMath.go/get/KVector"
 	"github.com/MatProGo-dev/SymbolicMath.go/symbolic"
 	"github.com/MatProGo-dev/simplex/simplexSolver"
@@ -65,18 +66,24 @@ func main() {
 	solver.IterationLimit = 100
 
 	// Solve the problem
-	solution, err := solver.Solve(trickyProblem)
+	sol, err := solver.Solve(trickyProblem)
 	if err != nil {
 		panic(err)
 	}
 
 	// Print the solution
-	solutionMessage, _ := solution.Status.ToMessage()
+	solutionMessage, _ := sol.Status.ToMessage()
 	println("Solution Status: ", solutionMessage)
-	println("Objective Value: ", solution.Objective)
-	println("Number of Iterations: ", solution.Iterations)
+
+	optObj, err := solution.GetOptimalObjectiveValue(&sol)
+	if err != nil {
+		panic(err)
+	}
+	println("Objective Value: ", optObj)
+
+	println("Number of Iterations: ", sol.Iterations)
 	println("Variable Values: ")
-	for varName, varValue := range solution.VariableValues {
+	for varName, varValue := range sol.VariableValues {
 		println("  ", varName, ": ", varValue)
 	}
 }
diff --git a/examples/box2/box.go b/examples/box2/box.go
index 6ddd8e8..efb14ff 100644
--- a/examples/box2/box.go
+++ b/examples/box2/box.go
@@ -2,6 +2,7 @@ package main
 
 import (
 	"github.com/MatProGo-dev/MatProInterface.go/problem"
+	"github.com/MatProGo-dev/MatProInterface.go/solution"
 	getKVector "github.com/MatProGo-dev/SymbolicMath.go/get/KVector"
 	"github.com/MatProGo-dev/SymbolicMath.go/symbolic"
 	"github.com/MatProGo-dev/simplex/simplexSolver"
@@ -66,18 +67,22 @@ func main() {
 	solver.IterationLimit = 100
 
 	// Solve the problem
-	solution, err := solver.Solve(trickyProblem)
+	sol, err := solver.Solve(trickyProblem)
 	if err != nil {
 		panic(err)
 	}
 
 	// Print the solution
-	solutionMessage, _ := solution.Status.ToMessage()
+	solutionMessage, _ := sol.Status.ToMessage()
 	println("Solution Status: ", solutionMessage)
-	println("Objective Value: ", solution.Objective)
-	println("Number of Iterations: ", solution.Iterations)
+	optObj, err := solution.GetOptimalObjectiveValue(&sol)
+	if err != nil {
+		panic(err)
+	}
+	println("Objective Value: ", optObj)
+	println("Number of Iterations: ", sol.Iterations)
 	println("Variable Values: ")
-	for varName, varValue := range solution.VariableValues {
+	for varName, varValue := range sol.VariableValues {
 		println("  ", varName, ": ", varValue)
 	}
 }
diff --git a/examples/gonum_bug1/try_bug.go b/examples/gonum_bug1/try_bug.go
index 6545d10..a16bd6d 100644
--- a/examples/gonum_bug1/try_bug.go
+++ b/examples/gonum_bug1/try_bug.go
@@ -2,6 +2,7 @@ package main
 
 import (
 	"github.com/MatProGo-dev/MatProInterface.go/problem"
+	"github.com/MatProGo-dev/MatProInterface.go/solution"
 	getKMatrix "github.com/MatProGo-dev/SymbolicMath.go/get/KMatrix"
 	getKVector "github.com/MatProGo-dev/SymbolicMath.go/get/KVector"
 	"github.com/MatProGo-dev/simplex/simplexSolver"
@@ -76,18 +77,22 @@ func main() {
 	solver.IterationLimit = 100
 
 	// Solve the problem
-	solution, err := solver.Solve(trickyProblem)
+	sol, err := solver.Solve(trickyProblem)
 	if err != nil {
 		panic(err)
 	}
 
 	// Print the solution
-	solutionMessage, _ := solution.Status.ToMessage()
+	solutionMessage, _ := sol.Status.ToMessage()
 	println("Solution Status: ", solutionMessage)
-	println("Objective Value: ", solution.Objective)
-	println("Number of Iterations: ", solution.Iterations)
+	optObj, err := solution.GetOptimalObjectiveValue(&sol)
+	if err != nil {
+		panic(err)
+	}
+	println("Objective Value: ", optObj)
+	println("Number of Iterations: ", sol.Iterations)
 	println("Variable Values: ")
-	for varName, varValue := range solution.VariableValues {
+	for varName, varValue := range sol.VariableValues {
 		println("  ", varName, ": ", varValue)
 	}
 }
diff --git a/examples/sergiy_butenko1/the_simplex_method_part_ii.go b/examples/sergiy_butenko1/the_simplex_method_part_ii.go
index d9eed9d..6d8a9eb 100644
--- a/examples/sergiy_butenko1/the_simplex_method_part_ii.go
+++ b/examples/sergiy_butenko1/the_simplex_method_part_ii.go
@@ -1,6 +1,7 @@
 package main
 
 import (
+	"github.com/MatProGo-dev/MatProInterface.go/solution"
 	"github.com/MatProGo-dev/simplex/simplexSolver"
 	"github.com/MatProGo-dev/simplex/utils/examples"
 )
@@ -17,18 +18,19 @@ func main() {
 	solver.IterationLimit = 100
 
 	// Solve the problem
-	solution, err := solver.Solve(*problem5)
+	sol, err := solver.Solve(*problem5)
 	if err != nil {
 		panic(err)
 	}
 
 	// Print the solution
-	solutionMessage, _ := solution.Status.ToMessage()
+	solutionMessage, _ := sol.Status.ToMessage()
 	println("Solution Status: ", solutionMessage)
-	println("Objective Value: ", solution.Objective)
-	println("Number of Iterations: ", solution.Iterations)
+	optVal, _ := solution.GetOptimalObjectiveValue(&sol)
+	println("Objective Value: ", optVal)
+	println("Number of Iterations: ", sol.Iterations)
 	println("Variable Values: ")
-	for varName, varValue := range solution.VariableValues {
+	for varName, varValue := range sol.VariableValues {
 		println("  ", varName, ": ", varValue)
 	}
 }
diff --git a/solution/simplex_solution.go b/solution/simplex_solution.go
index 403b5d6..def27e0 100644
--- a/solution/simplex_solution.go
+++ b/solution/simplex_solution.go
@@ -2,6 +2,7 @@ package simplex_solution
 
 import (
 	"github.com/MatProGo-dev/MatProInterface.go/problem"
+	"github.com/MatProGo-dev/MatProInterface.go/solution"
 	solution_status "github.com/MatProGo-dev/MatProInterface.go/solution/status"
 )
 
@@ -11,8 +12,6 @@ type SimplexSolution struct {
 	// VariableValues maps variable IDs (as uint64) to their solution values.
 	// The uint64 key typically represents the unique identifier or index of a variable in the model.
 	VariableValues map[uint64]float64
-	// Objective is the value of the objective function at the solution.
-	Objective float64
 	// Status indicates the status of the solution (e.g., optimal, infeasible).
 	Status     solution_status.SolutionStatus
 	Iterations int
@@ -26,7 +25,12 @@ func (sol *SimplexSolution) GetValueMap() map[uint64]float64 {
 }
 
 func (sol *SimplexSolution) GetOptimalValue() float64 {
-	return sol.Objective
+	// Use the symbolic.Solution interface to compute the optimal value
+	optVal, err := solution.GetOptimalObjectiveValue(sol)
+	if err != nil {
+		return 0.0
+	}
+	return optVal
 }
 
 func (sol *SimplexSolution) GetStatus() solution_status.SolutionStatus {