6.40.25  Sum of list (or matrix) elements transformed by a function: count

The count command adds the values of a function applied to the elements of a list or matrix.

• count takes two arguments:
  • f, a real-valued or boolean-valued function.
  • L, a list or a matrix.
• count(f,L) returns the sum of f(x) for all elements x in L.
  If f is a boolean-valued function, this is just the number of elements for which the boolean is true.

Examples.

• Input:
  count((x)->x,[2,12,45,3,7,78])
  Output:

  147

  because: 2+12+45+3+7+78=147.
• Input:
  count((x)->x<12,[2,12,45,3,7,78])
  Output:

  3

• Input:
  count((x)->x==12,[2,12,45,3,7,78])
  Output:

  1

• Input:
  count((x)->x>12,[2,12,45,3,7,78])
  Output:

  2

• Input:
  count(x->x^2,[3,5,1])
  Output:

  35

  Indeed 3²+5²+1¹=35.
• Input:
  count(id,[3,5,1])
  Output:

  9

  Indeed, id is the identity functions and 3+5+1=9.
• Input:
  count(1,[3,5,1])
  Output:

  3

  Indeed, 1 is the constant function equal to 1 and 1+1+1=3.