Step by Step solution about How to resolve the algorithm Number names step by step in the Mathematica/Wolfram Language programming language

This Wolfram code defines a function name that converts a given integer n into its English name representation. The code handles both positive and negative integers, and it covers numbers up to the order of "decillion." Here's a step-by-step explanation of how it works:

1. Handling Negative Numbers: If the input n is a negative integer, the code converts it to a positive number and adds the prefix "negative" to the resulting name.

2. Numbers Less Than 20: For integers between 0 and 19 (inclusive), the small list is used to directly map the number to its corresponding name.

3. Tens: For integers between 10 and 99, the tens list is used. The tens digit is used to select the appropriate name from the list (e.g., "thirty" for 30). If the ones digit is non-zero, the corresponding name from the small list is appended with a hyphen.

4. Hundreds: For integers between 100 and 999, the small list is used to get the name of the hundreds digit. Then, the code concatenates " hundred and " and the name of the remaining two digits (obtained using the name function recursively).

5. Thousands and Beyond: For integers greater than 999, the code uses the big list to handle the thousands, millions, billions, and so on. It recursively applies the name function to each group of three digits (starting from the rightmost group) and then joins these names together with the appropriate unit (e.g., "thousand", "million") from the big list.

6. Formatting and Cleanup: The final name is trimmed to remove any extra spaces and the word "zero" if it appears at the end.

Overall, this code provides a concise and efficient way to convert an integer into its English name representation, handling both positive and negative numbers and numbers up to the order of "decillion."

small = "zero"["one", "two", "three", "four", "five", "six", "seven", 
  "eight", "nine", "ten", "eleven", "twelve", "thirteen", "fourteen", 
  "fifteen", "sixteen", "seventeen", "eighteen", 
  "nineteen"]; tens = # <> "-" & /@ {"twenty", "thirty", "forty", 
   "fifty", "sixty", "seventy", "eighty", "ninety"};
big = Prepend[
   " " <> # & /@ {"thousand", "million", "billion", "trillion", 
     "quadrillion", "quintillion", "sextillion", "septillion", 
     "octillion", "nonillion", "decillion", "undecillion", 
     "duodecillion", "tredecillion"}, ""];
name[n_Integer] := "negative " <> name[-n] /; n < 0;
name[n_Integer] := small[[n]] /; 0 <= n < 20;
name[n_Integer] := 
  StringTrim[tens[[#1 - 1]] <> small[[#2]] & @@ IntegerDigits[n], 
    "-zero"] /; 10 <= n < 100;
name[n_Integer] := 
 StringTrim[
   small[[#1]] <> " hundred and " <> name@#2 & @@ 
    IntegerDigits[n, 100], " and zero"] /; 100 <= n < 1000; 
name[n_Integer] := 
 StringJoin@
  Riffle[Select[
    MapThread[StringJoin, {name /@ #, Reverse@big[[;; Length@#]]}] &@
     IntegerDigits[n, 1000], StringFreeQ[#, "zero"] &], ","];