🧮 ComputorV1 — Advanced Polynomial Equation Solver (42 Project)

A complete polynomial equation solver written in Python.
Handles equations up to degree 2, including real and complex solutions.
Fully compliant with the 42 subject — including mandatory and bonus parts.

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📌 Project Overview

ComputorV1 parses, reduces, and solves polynomial equations of the form:

a * X^0 + b * X^1 + c * X^2 = d * X^0 + ...

It supports:

• Reduction to canonical form
• Degree detection
• Degree 0 resolution
• Degree 1 resolution
• Degree 2 resolution
• Real solutions
• Complex solutions
• Fraction input (bonus)
• Natural input format (bonus)
• Irreducible fraction output (bonus)
• Error handling
• Intermediate step display (bonus)

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📂 Project Architecture

ComputorV1/
│
├── mandatory/
│   ├── main.py
│   ├── parser.py
│   ├── reducer.py
│   ├── solver.py
│   └── math_utils.py
│
├── bonus/
│   ├── main.py
│   ├── parser.py
│   ├── reducer.py
│   ├── solver.py
│   └── math_utils.py
│
└── README.md

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✅ Mandatory Part

✔ What It Must Do

• Accept one equation as argument
• Display reduced form
• Display polynomial degree
• Solve degree 0, 1, 2
• Refuse degree > 2
• Handle negative numbers
• Handle decimals
• Handle fractions (if implemented in mandatory)
• Never crash
• Never infinite loop

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▶️ Run Mandatory

cd mandatory
python3 main.py "5 * X^0 + 4 * X^1 - 9.3 * X^2 = 1 * X^0"

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🧪 Mandatory Test Cases

Degree 0 — Infinite Solutions

python3 main.py "42 * X^0 = 42 * X^0"

Expected:

Any real number is a solution.

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Degree 0 — No Solution

python3 main.py "4 * X^0 = 8 * X^0"

Expected:

No solution.

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Degree 1

python3 main.py "2 * X^1 = 4 * X^0"

Expected:

2

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Degree 2 — Real Solutions

python3 main.py "1 * X^2 - 5 * X^1 + 6 * X^0 = 0"

Roots:

2
3

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Degree 2 — Complex Solutions

python3 main.py "1 * X^2 + 1 * X^0 = 0"

Expected:

-0 + 1i
-0 - 1i

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Degree > 2

python3 main.py "1 * X^3 + 1 * X^0 = 0"

Expected:

The polynomial degree is strictly greater than 2, I can't solve.

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⭐ Bonus Part

The bonus extends the solver significantly.

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✔ Natural Input Support

Accepts:

X = 0
4X = 8
2X + 1 = 0
5 + X^2 = X^2

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✔ Fraction Input

5/2 * X^0 = 1

Interpreted as:

2.5 * X^0 = 1

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✔ Irreducible Fraction Output

2X = 1

Outputs:

1/2

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✔ Complex Solutions With Rational Parts

5 * X^0 + 3 * X^1 + 3 * X^2 = 1 * X^0

Output:

-1/2 + 1.040833i
-1/2 - 1.040833i

Rational parts simplified. Irrational parts kept as clean decimals.

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✔ Error Handling

Detects:

• Missing '='
• Invalid characters
• Invalid variable names
• Invalid power syntax
• Division by zero in fractions
• Malformed equations

Never prints Python traceback.

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✔ Intermediate Steps (Bonus)

Displays:

• Parsing phase
• Reduction phase
• Discriminant value
• Solution type decision

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🧠 Mathematical Concepts

1️⃣ Polynomial

A polynomial is an expression of the form:

[ P(X) = a_0 + a_1X + a_2X^2 + ... ]

The degree is the highest exponent.

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2️⃣ Discriminant

[ Delta = b^2 - 4ac ]

• Δ > 0 → Two real roots
• Δ = 0 → One real root
• Δ < 0 → Two complex roots

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3️⃣ Complex Solutions

When Δ < 0:

[ X = \frac{-b \pm i\sqrt{-\Delta}}{2a} ]

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4️⃣ Euclidean Algorithm

Used to simplify fractions:

gcd(a, b)

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5️⃣ Newton’s Method

Custom square root implementation:

sqrt_newton(n)

Avoids forbidden math functions.

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🔒 Stability & Safety

The program guarantees:

• No infinite loops
• No division by zero
• No float explosion
• Safe epsilon comparisons
• Clean error reporting
• Controlled fraction denominator growth

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🏁 Conclusion

ComputorV1 is not just a formula implementation.

It demonstrates:

• Algebra mastery
• Numerical reasoning
• Robust parsing
• Defensive programming
• Modular architecture
• Clean CLI design
• Mathematical rigor

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42 Network — ComputorV1 Project