Mastering Mathematica Functions: Recursive Vector Squaring & List Sorting

[Physics_rocks]

Hi guys ,

I'm a little new with Mathematica and I'm trying to write down some functions.
the first one is writing a functions that square the elements in a vector , recursively ,
using patterns .

so , I tried this one :
x = Range[1, 10];
sq[0,list_]=list^2;
sq[sum_,list_] := Sum[sum*sq[sum, list[n - 1]], _list]

but it isn't working . what's the problem ? 2. The second function is writing a function that sorts a list of numbers , by checking each time two numbers that are adjacent .

if I write this : sort[list_] :=
how can I tell mathematica that I want to use an actual list of numbers ? can I say list ?

thank you

 

[CompuChip]

There seem to be multiple problems.
First of all, the assignment in the second line should probably be delayed (:= instead of =) because you want to substitute "list" for whatever value is passed. Also, list[n - 1] is a function call, you meant list[[n - 1]]? Anyway, what is n in that expression? Finally, what are you doing with the "Sum" expression? Sum[f[x], {x, a, b}] sums the values of f[x] for a <= x <= b.

Can you maybe explain more clearly what you want the function to do (e.g. if you input x = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, do you want it to output {1, 4, 9, 16, 25, 36, 49, 64, 81, 100} ?)

2) How do you mean: "use an actual list of numbers"? You can call sort[x] (where x is defined as in your first example). In the expression after ":=", the expression "list" will contain whatever list you input (so if you call sort[x], then the definition is executed where list = x).

 

[oswaler]

Hi there,

Great to hear that you are learning Mathematica and working on writing functions! I can see that you are trying to use recursive functions to square the elements in a vector and sort a list of numbers. Let me provide some feedback on your code and suggestions for improvement.

Firstly, for your recursive vector squaring function, I see that you have defined two patterns - one for the base case (when sum is 0) and one for the recursive step. However, your recursive step is not quite correct. Instead of using the Sum function, you should use a product operation, like Times. Also, you should specify the index of the list element you want to square, rather than using a general list[n-1]. Here's a possible correction for your code:

sq[0, list_] := list^2;
sq[sum_, list_] := sum * sq[sum, list[[1]]] * sq[sum, Rest

• ]
  
  Note that I am using the Rest function to get the remaining elements of the list after the first one. This way, the recursive step will continue until the list is empty.
  
  As for your second function for sorting a list of numbers, you can indeed use list to specify a specific element in the list. However, you should also specify the range of i, such as i=1 to Length
  • . Additionally, you need to define a condition for when the two adjacent numbers need to be swapped. Here's a possible correction for your code:
    
    sort[list_] := Module[{i, temp},
    For[i = 1, i < Length
    • , i++,
      If[list > list[i + 1],
      temp = list;
      list = list[i + 1];
      list[i + 1] = temp;
      ]
      ];
      list
      ]
      
      In this code, I am using a For loop to iterate through the list and check if the current element is larger than the next one. If it is, then I swap them using a temporary variable.
      
      I hope this helps and good luck with your function writing! Mathematica has a lot of powerful built-in functions that can help you achieve your goals, so don't hesitate to explore and experiment.