// Function to find the LCM of two polynomials
 function lcm_poly = poly_lcm(poly1, poly2)
  // Find the GCD using the 'gcd' function in Scilab
  gcd_poly = gcd(poly1, poly2);
 

  // Calculate the LCM: LCM(a, b) = (a * b) / GCD(a, b)
  lcm_poly = clean(poly1 * poly2 / gcd_poly); 
 endfunction
 

 // Example Usage:
 

 // Define polynomial variable
 s = poly(0, 's');
 

 // Define the polynomials
 poly1 = s^2 + 5*s + 6;  // Example: (s+2)(s+3)
 poly2 = s^2 + 6*s + 8;  // Example: (s+2)(s+4)
 

 // Calculate the LCM
 lcm_result = poly_lcm(poly1, poly2);
 

 // Display the results
 disp("Polynomial 1: " + string(poly1));
 disp("Polynomial 2: " + string(poly2));
 disp("LCM: " + string(lcm_result));
 

 //Another Example
 

 poly3 = s^3 + 6*s^2 + 11*s + 6;  //(s+1)(s+2)(s+3)
 poly4 = s^2 + s;  //s(s+1)
 

 lcm_result2 = poly_lcm(poly3, poly4);
 disp("Polynomial 3: " + string(poly3));
 disp("Polynomial 4: " + string(poly4));
 disp("LCM: " + string(lcm_result2));
 

 

 

 

• `poly_lcm(poly1, poly2)` function: This function takes two polynomial inputs, `poly1` and `poly2`, and calculates their LCM.
• `gcd_poly = gcd(poly1, poly2)`: This line uses Scilab's built-in `gcd()` function to find the Greatest Common Divisor (GCD) of the two polynomials. The GCD is the largest polynomial that divides both input polynomials without leaving a remainder.
• `lcm_poly = clean(poly1 * poly2 ./ gcd_poly)`: This is the core of the LCM calculation. It uses the relationship: LCM(a, b) = (a * b) / GCD(a, b) It multiplies the two polynomials and then divides the result by their GCD. The `clean()` function is important for simplifying the polynomial expression and removing very small (essentially zero) coefficients that might arise from numerical inaccuracies during the division. The `/.` operator is used for element-by-element division of polynomial coefficients.
• Example Usage:
  • `s = poly(0, 's')`: This defines the polynomial variable 's'. It's crucial to define the variable before creating polynomials with it.
  • `poly1 = s^2 + 5*s + 6;` and `poly2 = s^2 + 6*s + 8;`: These lines define two example polynomials.
  • `lcm_result = poly_lcm(poly1, poly2);`: This calls the `poly_lcm` function to calculate the LCM of the example polynomials.
  • `disp(...)`: These lines display the original polynomials and the calculated LCM to the Scilab console.
• `clean()` function: As noted, `clean()` is crucial. Without it, you might see very small coefficients (e.g., 1.0D-16) in the LCM due to numerical rounding errors during the division. `clean()` removes terms with negligible coefficients, giving you a cleaner, more mathematically correct result.

1. Open Scilab.
2. Copy and paste the code into the Scilab editor.
3. Save the file (e.g., `lcm_polynomials.sce`).
4. Execute the script by typing `exec("lcm_polynomials.sce")` in the Scilab console or by clicking the "Execute" button in the editor.

• Error Handling: The code doesn't include explicit error handling (e.g., checking if the inputs are indeed polynomials). You could add checks using `typeof()` to make it more robust.
• `clean()` Threshold: The `clean()` function has an optional tolerance argument. The default tolerance is usually sufficient, but if you encounter issues with very complex polynomials, you might need to adjust it. Refer to the Scilab documentation for `clean()` for details.
• Scilab Version: The code is compatible with recent versions of Scilab. If you're using a very old version, there might be minor syntax differences (though unlikely).