# Difference between revisions of "Lists"

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− | <noinclude>{{Manual Page|version= | + | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{objects|general}} |

− | {{objects|general}} | + | Using curly braces you can create a ''list'' of several objects (e.g. points, segments, circles). |

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

{{Example|1=<br> | {{Example|1=<br> | ||

− | * <code>L = {A, B, C}</code> gives you a list consisting of three prior defined points A, B, and C. | + | * <code>L = {A, B, C}</code> gives you a list consisting of three prior defined points ''A'', ''B'', and ''C''. |

− | * <code>L = {(0, 0), (1, 1), (2, 2)}</code> produces a list that consists of the entered points | + | * <code>L = {(0, 0), (1, 1), (2, 2)}</code> produces a list that consists of the entered points and also creates these nameless points. |

− | {{ | + | * The short syntax <code>..</code> creates a list of successive integers: e.g. <code>-5..5</code> creates the list {''-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5''}. }} |

+ | {{Notes|1=<div> | ||

+ | *By default, the elements of this list are not shown in the [[File:Menu view graphics.svg|link=|16px]] [[Graphics View]]. | ||

+ | *Lists can also be used as arguments in list operations (mentioned further in this article) or [[List Commands]].</div>}} | ||

− | To access particular elements of | + | ==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|1=Let <code>list = {1, 2, 3, 4, 5}</code>, then:<div> | ||

+ | *<code>list(1)</code> returns the first element of the list: ''1'' | ||

+ | *<code>list(2)</code> returns the second element of the list: ''2'' | ||

+ | *.../... | ||

+ | *<code>list(-1)</code> returns the last element of the list: ''5'' | ||

+ | *<code>list(-5)</code> returns the first element of the list: ''1'' | ||

+ | *<code>list(0)</code> returns ''undefined'', as well as <code>list(k)</code> for k > 5 or k < -5</div>}} | ||

− | == | + | ==Comparing Lists of Objects== |

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

− | * List1 == List2: | + | * <code>List1 == List2</code>: checks if the two lists are equal as ordered [[w:Tuple|tuples]], and yields ''true'' or ''false''. |

− | *List1 != List2: | + | * <code>List1 != List2</code>: checks if the two lists are not equal as ordered tuples, and yields ''true'' or ''false''. |

+ | * <code>Unique[list1] == Unique[list2]</code> or <code>list1 \ list2 == {}</code> : 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''. | ||

+ | * <code>Sort[list1] == Sort[list2]</code>: checks if the two lists are equal as [[w:Multiset|multisets]] (i.e. the elements order is ignored) and yields ''true'' or ''false''. | ||

+ | |||

+ | See also [[Unique Command|Unique]] and [[Sort Command|Sort]] commands. | ||

+ | |||

+ | ==List Operators== | ||

+ | |||

+ | <code><Object> ∈ <List></code>: returns ''true'' if ''Object'' is an element of ''List'' | ||

+ | |||

+ | <code><List1> ⊆ <List2></code>: returns ''true'' if ''List1'' is subset of ''List2'' | ||

+ | |||

+ | <code><List1> ⊂ <List2></code>: returns ''true'' if ''List1'' is a strict subset of ''List2'' | ||

+ | |||

+ | <code><List1> \ <List2></code>: creates the set difference of ''List1'' and ''List2'' | ||

==Apply Predefined Operations and Functions to Lists== | ==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. | If you apply [[Predefined Functions and Operators]] to lists, you will always get a new list as a result. | ||

===Addition and subtraction=== | ===Addition and subtraction=== | ||

− | * List1 + List2: | + | * <code>List1 + List2</code>: adds the corresponding elements of two lists. {{Note|The two lists need to be of the same length.}} |

− | * List + Number: | + | * <code>List + Number</code>: adds ''Number'' to every element of ''List''. |

− | * List1 – List2: | + | * <code>List1 – List2</code>: subtracts the elements of ''List2'' from corresponding elements of ''List1''. {{Note|The lists need to be of the same length.}} |

− | * List – Number: | + | * <code>List – Number</code>: subtracts ''Number'' from every element of ''List''. |

===Multiplication and division=== | ===Multiplication and division=== | ||

− | * List1 * List2: | + | * <code>List1 * List2</code>: 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: | + | * <code>List * Number</code>: multiplies every ''List'' element by the given ''Number''. |

− | * List1 / List2: | + | * <code>List1 / List2</code>: divides the elements of ''List1'' by the corresponding elements of ''List2''. {{Note|The two lists need to be of the same length.}} |

− | * List / Number: | + | * <code>List / Number</code>: divides every ''List'' element by ''Number''. |

− | * Number / List: | + | * <code>Number / List</code>: divides ''Number'' by every element of ''List''. |

− | + | {{Note|See also [[Points and Vectors#Vector Product|Vector product]].}} | |

===Other examples=== | ===Other examples=== | ||

− | * List^2: | + | * <code>List ^ 2</code>: squares every element of ''List''. |

− | * 2^List: | + | * <code>2 ^ List</code>: creates a list of powers of two, using the ''List'' elements as exponents. |

− | * List1^List2: | + | * <code>List1 ^ List2</code>: creates a list containing ''a^b'', where ''a'' and ''b'' are corresponding elements of ''List1'' and ''List2''. |

− | * sin(List): | + | * <code>sin(List)</code>: applies the sine function to every element of ''List''. <br> |

+ | User defined [[Functions|functions]] can be applied the same way as well. |

## Latest revision as of 15:17, 30 October 2015

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.