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 and also creates 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}.

Notes:

• By default, the elements of this list are not shown in the Graphics View.
• Lists can also be used as arguments in list operations (mentioned further in this article) or List Commands.

Accessing Elements of Lists

To access particular elements of a list you can use the Element Command or the simplified syntax shown in the example below:

Example: Let list = {1, 2, 3, 4, 5}, then:

• list(1) returns the first element of the list: 1
• list(2) returns the second element of the list: 2
• .../...
• list(-1) returns the last element of the list: 5
• list(-5) returns the first element of the list: 1
• list(0) returns undefined, as well as list(k) for k > 5 or k < -5

Comparing 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.