The ΔList( Command

Command Summary

Calculates the differences between consecutive terms of a list.

Command Syntax


Menu Location


  1. 2nd LIST to access the list menu.
  2. RIGHT to access the OPS submenu.
  3. 7 to select ΔList(, or use arrows.

Calculator Compatibility


Token Size

2 bytes

ΔList( calculates the differences between consecutive terms of a list, and returns them in a new list.

    {1 3 5 7 9 11}

Advanced Uses

The ΔList( command is very nearly the inverse of the cumSum( command, which calculates the cumulative sums of a list. For any list, ΔList(cumSum(list)) will return the same list, but without its first element:

    {2 3 4 5 6 7}

Removing the first element would otherwise be a difficult procedure involving the seq( command, so this is a useful trick to know.

If a list is sorted in ascending order, min(ΔList(list)) will return 0 (false) if there are repeating values in the list, and a value corresponding to true if they are all distinct. The number of repeating elements can be determined similarly via 1+sum(0≠ΔList(list)) (again, so long as the list is sorted).

Error Conditions

Related Commands


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