Polynomial Root Finder 🧮⚙️

An interactive Windows Forms app to compute polynomial roots and critical points using numeric methods.
Designed for fast experimentation with cubic polynomials in a custom interval. 🔬📈

Table of Contents 🗂️

• Overview
• Key Features
• Tech Stack
• Project Structure
• How It Works
• Run the Project
• Usage Guide
• Notes

Overview 🚀

This project solves polynomial-related tasks through a desktop UI:

• Finds zeros of a polynomial in a given interval using a Bisection-based search 🔍
• Finds critical points by analyzing the first derivative 📐
• Classifies critical points as Max / Min / Const 🧭

The app currently works with 4 coefficients, which corresponds to a cubic polynomial:

$$ P(x) = ax^3 + bx^2 + cx + d $$

Key Features 🧩

• Numeric polynomial evaluation engine (Evaluate) 🧠
• Root detection with interval validation (Bolzano) ✅
• Recursive bisection search (Bisection) ♻️
• Input validation and visual error feedback in the UI 🎛️
• Automatic derivative generation for first-order analysis (GetFirstOrder) 🧪

Tech Stack 🛠️

• Language: C# 💻
• Framework: .NET 8 (net8.0-windows) 🧱
• UI: Windows Forms 🪟
• Solution Type: Desktop app (WinExe) 📦

Project Structure 🗃️

.
├── Ceros Polinomios.sln
├── Ceros Polinomios/
│   ├── Ceros Polinomios.csproj
│   ├── Program.cs
│   ├── Form1.cs
│   ├── Form1.Designer.cs
│   ├── Form1.resx
│   ├── Properties/
│   │   ├── Resources.Designer.cs
│   │   └── Resources.resx
│   ├── Resources/
│   ├── bin/
│   └── obj/
└── .vs/ (ignored)

Main Files 🔧

• Program.cs: Application entry point and form bootstrap (Application.Run(new Form1())).
• Form1.cs: Core logic for polynomial evaluation, bisection, validation, and UI event handling.
• Form1.Designer.cs: Auto-generated layout and control definitions.
• Ceros Polinomios.csproj: Project configuration, target framework, WinForms activation.

How It Works ⚡

1. User enters polynomial coefficients and an interval. 🧾
2. App validates all fields before running calculations. 🛡️
3. Bisection process searches for sign changes to detect roots. 📉
4. First derivative is computed and analyzed to get critical points. 📊
5. Results are printed in the interface labels. 🖥️

Run the Project ▶️

Requirements 📌

• Windows 10/11
• .NET 8 SDK
• Optional: Visual Studio 2022 (for GUI development)

Option 1: Run with Visual Studio 🧰

1. Open the solution file: Ceros Polinomios.sln
2. Set startup project to Ceros Polinomios
3. Press F5 (or click Start) to run

Option 2: Run from Terminal 🖥️

From the repository root:

dotnet restore "Ceros Polinomios.sln"
dotnet build "Ceros Polinomios.sln" -c Debug
dotnet run --project "Ceros Polinomios/Ceros Polinomios.csproj"

Usage Guide 🧭

1. Enter the 4 polynomial coefficients.
2. Enter interval start and end values.
3. Click the calculate button.
4. Check:
   • Polynomial roots
   • Derivative critical points
   • Max/Min classification

Notes 📝

• This is a numerical approach, so precision depends on interval width and tolerance. 🎯
• Inputs are integer-like in current validation logic (digits and optional -).
• Auto-generated folders (bin, obj) are build artifacts. 🧪

---

Built with C#, numerical methods, and a lot of math energy. ⚙️📐🔥