Lists

Using curly braces you can create a list of several objects (e.g. points, segments, circles).

Example:

• L = {A, B, C} gives you a list consisting of three prior defined points A, B, and C.
• L = {(0, 0), (1, 1), (2, 2)} produces a list that consists of the entered points, as well as these nameless points.
• The short syntax .. creates a list of successive integers: e.g. -5..5 creates the list {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}.

Note: By default, the elements of this list are not shown in the Graphics View.

To access particular elements of the list you can use Element Command. Lists can also be used as arguments in list operations (mentioned further in this article) or List Commands.

Compare Lists of Objects

You can compare two lists of objects by using the following syntaxes and commands:

• List1 == List2: checks if the two lists are equal as ordered tuples, and yields true or false.
• List1 != List2: checks if the two lists are not equal as ordered tuples, and yields true or false.
• Unique[list1] == Unique[list2] or list1 \ list2 == {} : checks if the two lists are equal as sets (i.e. all repeated elements are ignored, as well as the elements order) and yields true or false.
• Sort[list1] == Sort[list2]: checks if the two lists are equal as multisets (i.e. the elements order is ignored) and yields true or false.

See also Unique and Sort commands.

List Operators

<Object> ∈ <List>: returns true if Object is an element of List

<List1> ⊆ <List2>: returns true if List1 is subset of List2

<List1> ⊂ <List2>: returns true if List1 is a strict subset of List2

<List1> \ <List2>: creates the set difference of List1 and List2

Apply Predefined Operations and Functions to Lists

If you apply Predefined Functions and Operators to lists, you will always get a new list as a result.

Addition and subtraction

• List1 + List2: adds the corresponding elements of two lists.
  Note: The two lists need to be of the same length.
• List + Number: adds Number to every element of List.
• List1 – List2: subtracts the elements of List2 from corresponding elements of List1.
  Note: The lists need to be of the same length.
• List – Number: subtracts Number from every element of List.

Multiplication and division

• List1 * List2: multiplies the corresponding elements of two lists.
  Note: The lists need to be of the same length. If the two lists are compatible matrices, matrix multiplication is used.
• List * Number: multiplies every List element by the given Number.
• List1 / List2: divides the elements of List1 by the corresponding elements of List2.
  Note: The two lists need to be of the same length.
• List / Number: divides every List element by Number.
• Number / List: divides Number by every element of List.

Note: See also Vector product.

Other examples

• List ^ 2: squares every element of List.
• 2 ^ List: creates a list of powers of two, using the List elements as exponents.
• List1 ^ List2: creates a list containing a^b, where a and b are corresponding elements of List1 and List2.
• sin(List): applies the sine function to every element of List.
  

User defined functions can be applied the same way as well.