🧮 FormulaValider - Σ/Δ Formula Validation System 🎯 What is FormulaValider? FormulaValider is a system that automatically checks the correctness of mathematical and physical formulas on many levels.

It's not an ordinary calculator - it's an intelligent validator that "understands" the structure of formulas and can detect errors before you use them!

🔬 Why is it important? Imagine that:

You are writing a scientific paper and you want to check if the formulas are written correctly You are learning physics and you are not sure about the mathematical syntax You are creating a scientific program and you need to validate formulas You want to automatically check hundreds of formulas in a database FormulaValider solves these problems! 🚀

🏗️ Σ/Δ (Sigma/Delta) Architecture The system works in two layers of validation:

🔤 [Σ] SIGMA - Mathematical Syntax ✅ Correct: ❌ Incorrect: F = m * a F = m * E = m * c**2 E == m * c² v = s / t v s / t P = U * I P = U * (I + R

What it checks:

Does the formula contain the equal sign =? Are the left and right sides mathematically correct? Are there no syntactic errors (unclosed brackets, incorrect operators)? ⚖️ [Δ] DELTA - Unit Consistency ✅ Correct units: F = m * a → [N] = [kg] × [m/s²] ✓

❌ Incorrect units: F = m * v → [N] ≠ [kg] × [m/s] ✗

What it checks:

Do all symbols have defined units? Are the units on both sides of the equation consistent?

Basis for future full dimensional analysis 🚀 Future extensions (planned): 🧠 [Λ] LAMBDA - Symbol Semantics Meaning of symbols (mass, energy, force...) Type of quantity (scalar, vector, tensor) Context of the scientific field 🌍 [Π] PI - Conformity with Reality Verification with the physical knowledge base Checking the limits of applicability of the formula Integration with AI/AGI systems 💻 How to use the program?

1. Run the program: python formulavalider.py

2. Select an option from menu: ╔════════════════════════════════════════════════════════════════════╗ ║ FORMULAVALIDER ║ ║ Validation System Σ/Δ ║ ╠══════════════════════════════════════════════════════════════════╣ ║ 1. Check your own pattern ║ ║ 2. Select a pattern from the ready list ║ ║ 3. System information Σ/Δ ║ ║ 4. Create sample formulas.json ║ ║ 5. Output ║ ╚══════════════════════════════════════════════════════════════╝

3. Example of checking the formula: Enter the formula: F = m * a Do you want to add units? (y/n): t

Symbol and unit: F N Symbol and unit: m kg Symbol and unit: a m/s**2 Symbol and unit: [Enter]

===================================================== FORMULA VALIDATION: F = m * a Description: Newton's Second Law of Motion = ... [N]

────────────────────────────────── 🎉 CORRECT PATTERN! ───────────────────────────────────

📚 Examples of patterns to test: ✅ Patterns correct: E = m * c2 # Einstein F = m * a # Newton P = U * I # Ohm's Law v = s / t # Velocity Ek = (1/2) * m * v2 # Kinetic energy p = m * v # Momentum W = F * s # Work

❌ Incorrect formulas (for testing): F = m * # Incomplete E == m * c**2 # Double equal sign F m * a # No equal sign lambda = h / p # 'lambda' is a Python keyword F = m * (a + b # Unclosed parenthesis

⚠️ Important restrictions: 🚫 Avoid Python keywords: ❌ Incorrect: ✅ Use instead: lambda = h / p → L = h / p if = m * a → force = m * a for = F * r → torque = F * r class = C → capacitance = C

📝 Formula format: Use ** for exponentiation (not ^) Use * for multiplication (don't skip) Use sqrt() for square root Functions: sin(), cos(), log(), exp() 🎯 Who is this program for?

👨‍🎓 Students and pupils: Checking formulas before exams Learning correct mathematical notation Verifying physical units 👨‍🔬 Scientists and engineers: Validating formulas in publications Validating formulas in programs Automating quality control 👨‍💻 Programmers: Validating formulas in scientific applications Creating computational systems Integrating with formula databases 🤖 AI enthusiasts: Exploring representations of mathematical knowledge Preparation for AGI systems Experimenting with symbolic validation 🔧 Installation and compilation: Requirements: pip install sympy

Compiling to .exe: pip install pyinstaller pyinstaller --onefile formulavalider.py

🌟 Why is FormulaValider a breakthrough?

The first formula validation system - nothing like it existed before Modular architecture - easily extendable with new layers Practical use - from education to research Preparing for the future - a foundation for AI/AGI systems Open source - anyone can develop and customize 🚀 Vision of the future:

FormulaValider is just the beginning! Imagine a system that:

Automatically checks all