Galois Field Arithmetic Calculator
Galois Field Arithmetic Calculator performs arithmetic operations (addition, subtraction, multiplication, division) in a Galois field GF(p). Input two polynomials as coefficient arrays, select the prime modulus and operation, and calculate the result.
Enter Parameters
How to Use Galois Field Arithmetic Calculator:
- Enter the coefficients of two polynomials (e.g., “1,2,3” for \\( 1 + 2x + 3x^2 \\)) using the keypad or direct input; use “Next” to switch fields.
- Select the prime modulus (e.g., 2, 3, 5, 7, 11).
- Choose the operation (add, subtract, multiply, divide).
- Click “Calculate” to see step-by-step results.
- Use “Share Result” to get shareable text or “Copy Result” to copy to clipboard.
Formulas:
Addition/Subtraction: Coefficients are added/subtracted modulo p.
Multiplication: Polynomial multiplication with coefficients modulo p.
Division: Polynomial division with modular arithmetic, using the extended Euclidean algorithm for inverses.
Important Notes:
- Polynomial coefficients must be integers, entered as comma-separated values (e.g., “1,2,3”).
- For division, the second polynomial must be non-zero, and an inverse must exist in GF(p).
- Calculations are performed modulo the selected prime to ensure results stay within the field.
- Clipboard access requires a secure context (HTTPS). If copying fails, try accessing over HTTPS or copy manually.