DifferenceI

DifferenceI

DifferenceI[ list1, list2 ] returns the indices of the elements of the first list that remain when the elements of the second list are removed.

Usages

DifferenceI[ list1, list2 ]

DifferenceI[ list1, list2 ] returns the positions (starting at 1) of the elements of list1 that are left after each element of list2 has removed one matching element. These are the positions of the elements that Difference would keep. Use it when you need to know where the remaining elements are, for example to select the matching elements of another list.

Example in out
g and the first a are removed; b (position 2) and the second a (position 4) remain. DifferenceI[ {a,b,g,a}, {g,a} ] {2, 4}
Only g (position 3) remains. DifferenceI[ {a,b,g,a}, {a,b,c,d,e,a} ] {3}
Use the indices to look up the remaining elements. L := {3, 8, 5, 8}
I := DifferenceI[L, {8}]
E := Map[i -> L[[i]], I]		 I = {1, 3, 4}
E = {3, 5, 8}
Options

Method

Method sets when two elements are considered equal.

  • Not set (default): elements must be the same expression, regardless of the order of terms or factors. 2.4 and 12/5 are different.
  • numerical: elements with the same numerical value are equal, such as 2.4 and 12/5, or Sqrt[4] and 2.
  • accuracy: like the default, but numbers with a limited precision, such as PrecisionConstant[3.14,2], are equal to a value within that precision. This is the same rule that Difference uses.
Syntax Example out
DifferenceI[ list1, list2, Method=>numerical ] DifferenceI[ {2.4, 12/5, 3}, {12/5}, Method=>numerical ] {2, 3}
DifferenceI[ list1, list2, Method=>accuracy ] DifferenceI[ {1+PrecisionConstant[3.14,2], 5}, {1+3.1415}, Method=>accuracy ] {2}
Details
  • Duplicates are counted separately: an element of list2 removes only one matching element of list1, working from left to right.
  • Empty lists: DifferenceI[ {1,2,3}, {} ] returns {1, 2, 3} and DifferenceI[ {}, {1} ] returns {}.
  • Exactly two lists: unlike Difference, DifferenceI does not accept more than two lists.
Example in out
Without Method, 12/5 does not match 2.4. DifferenceI[ {2.4, 12/5, 3}, {12/5} ] {1, 3}
Invalid input Result
DifferenceI[ {a,b}, a ] Left unevaluated: the result is DifferenceI[ {a,b}, a ] itself. Both arguments must be lists.
DifferenceI[ {1,2,3,4,5,6}, {2,4}, {5} ] Left unevaluated: only two lists are allowed.
DifferenceI[ {1,2}, {1}, Foo=>True ] Error: Invalid associative argument for DifferenceI: Foo
Warning
  • Without the Method option, DifferenceI compares numbers with a limited precision differently from Difference. Use Method=>accuracy if the indices must correspond exactly to the result of Difference.
  • With a single list, DifferenceI[ {a,b} ] returns the list {a, b} itself, not a list of indices.
  • An unknown value for Method (such as a typo) is ignored without an error, and the default comparison is used.

See also: Difference, IntersectI, RemoveI, Map