Step by Step solution about How to resolve the algorithm ISBN13 check digit step by step in the Mathematica / Wolfram Language programming language

The provided Wolfram code defines a function called ValidISBNQ to validate International Standard Book Numbers (ISBNs). An ISBN is a unique identifier assigned to books and other publications. A valid ISBN consists of 13 digits (or 10 digits for older ISBNs), and it follows specific rules to ensure its validity.

Here's a detailed explanation of the code:

1. The ClearAll[ValidISBNQ] line clears any previous definitions of the ValidISBNQ function.

2. The ValidISBNQ[iban_String] line defines the ValidISBNQ function, which takes a single argument, iban, which is expected to be a string representing an ISBN.

3. Inside the function, the first line i = StringReplace[iban, {" " -> "", "-" -> ""}] removes any spaces or dashes from the input ISBN. This step helps ensure a consistent ISBN format for validation.

4. The If statement checks whether the cleaned ISBN i matches the pattern Repeated[DigitCharacter], which means it consists of only digits repeated one after another. This pattern check is crucial because a valid ISBN should contain only numerical characters.

5. If the ISBN matches the digit-only pattern, it proceeds to the next steps:

   • i = ToExpression /@ Characters[i] converts the string i into a list of digits by using Characters to extract each character and then ToExpression to convert them into numbers.
   • i[[2 ;; ;; 2]] *= 3 multiplies every second digit in the list by 3. This multiplication is part of the ISBN validation algorithm.
   • Mod[Total[i], 10] == 0 checks if the sum of all the digits in the modified list i is divisible by 10. If the remainder is 0, it indicates a valid ISBN according to the algorithm.

6. If any of the above conditions are not met (e.g., the input ISBN has non-digit characters or fails the validation algorithm), the function returns False.

7. After defining the function, the code includes several examples of ISBNs and calls the ValidISBNQ function to check their validity:

   • ValidISBNQ["978-1734314502"] returns True because this ISBN passes the validation algorithm.
   • ValidISBNQ["978-1734314509"] returns False because the last digit does not satisfy the validation algorithm.
   • ValidISBNQ["978-1788399081"] returns True for a valid ISBN.
   • ValidISBNQ["978-1788399083"] returns False for an ISBN that fails the validation.

Overall, this Wolfram code provides a robust function to validate ISBNs based on specific rules and algorithms. The examples demonstrate how to use the function and interpret the results.

ClearAll[ValidISBNQ]
ValidISBNQ[iban_String] := Module[{i},
  i = StringReplace[iban, {" " -> "", "-" -> ""}];
  If[StringMatchQ[i, Repeated[DigitCharacter]],
   i = ToExpression /@ Characters[i];
   i[[2 ;; ;; 2]] *= 3;
   Mod[Total[i], 10] == 0
   ,
   False
   ]
  ]
ValidISBNQ["978-1734314502"]
ValidISBNQ["978-1734314509"]
ValidISBNQ["978-1788399081"]
ValidISBNQ["978-1788399083"]