### Math-List Commands

#### MAKELIST

Creates a list based on the expression, start point, end point, and increment. The increment can be omitted. The expression can be a constant.

The increment can be negative if start point > end point.

Syntax

Input:

Home Mode - Algebraic Entry Home Mode - Textbook Entry Program Editor

MAKELIST(expression, variable, start point, end point, increment)

If increment = 1, it can be left out: MAKELIST(expression, variable, start point, end point)

Home Mode - RPN Entry

5: Expression in single quotes 4: Variable in single quotes 3: Start Point 2: End Point 1: Increment MAKELIST(5), press Enter

If increment = 1, it can be left out: 4: Expression in single quotes 3: Variable in single quotes 2: Start Point 1: End Point MAKELIST(4), press Enter

CAS Mode

Not available. Rev. 5166 Use the seq command instead. The seq command works similar to the MAKELIST command.

Output: A list.

Examples:

A list of constants: MAKELIST(4,X,1,4) returns {4, 4, 4, 4}

A sequence generated with of increment of 1: MAKELIST(X²,X,1,6) returns {1,4,9,16,25, 36}

A sequence generated with a specified increment: MAKELIST(X²,X,1,6,2) returns {1, 9, 25}

A sequence generated with a negative increment (start point > end point). MAKELIST(X²,X,6,1,-1) returns {36, 25,16,9,4,1}

Notes: Lists generated by MAKELIST must be stored to universal list variables L#, C#, and D#.

If increment is positive, the generation of the list stops when variable ≥ end point.

If increment is negative, the generation of the list stops when variable ≤ end point.

Access: Toolbox, Math, 6. List, 1. MAKELIST

#### Intersect

Returns the intersection between lists. The intersected list contains elements that the two lists have in common. The lists can be different lengths and the number of lists to be compared can vary.

Syntax

Input:

Home Mode - Algebraic Entry Home Mode - Textbook Entry Program Editor

Intersect(list 1, list 2, list 3, … , list n)

Home Mode - RPN Entry

n: list n … 2: list 2 1: list 1 Intersect(n), press Enter

CAS Mode

Intersect(list 1, list 2, list 3, … ,list n)

Output: A list. If there is no element in common, the list will be empty.

Examples:

Let L1 = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, L2 = {2, 4, 6, 8, 10}, and L3 = {1, 4, 9, 16}

Intersect(L1, L2) returns {2, 4, 6, 8, 10} Intersect(L1, L3) returns {1, 4, 9} Intersect(L1, L2, L3) returns {4}

Access: Toolbox, Math, 6. List, 2. Intersect

#### SORT

Sorts a list of numbers in ascending order. In CAS mode, you can use SORT on sequences. Complex numbers are not sorted (logically).

Syntax

Input:

Home Mode - Algebraic Entry Home Mode - Textbook Entry Program Editor

SORT(list of numbers)

Home Mode - RPN Entry

1: list of numbers SORT, press Enter

The list is sorted automatically.

CAS Mode

sort(list of numbers) or sort(sequence of numbers)

Output: A list or sequence, sorted in ascending order.

Examples:

SORT({-7,9,-11,2}) returns {-11,-7,2,9}

Notes: Attempting to use SORT on vectors will return “Error: Bad argument type”.

Access: Toolbox, Math, 6. List, 3. SORT

#### Difference

Returns all the unique elements from a set of lists. Difference can be the thought of as the inverse of Intersection.

Syntax

Input:

Home Mode - Algebraic Entry Home Mode - Textbook Entry Program Editor

Difference(list 1, list 2, list 3, … , list n)

Home Mode - RPN Entry

n: list n … 2: list 2 1: list 1 Difference(n), press Enter

CAS Mode

Difference(list 1, list 2, list 3, … ,list n)

Output: A list. If there is no unique element, the list will be empty.

Examples:

Let L1 = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, L2 = {2, 4, 6, 8, 10}, and L3 = {1, 4, 9, 16} Difference(L1, L2) returns {1,3,5,7,9} Difference(L1, L3) returns {2, 3, 5, 6, 7, 8, 10, 16} Difference(L1, L2, L3) returns {3, 5, 7, 4, 16}

Access: Toolbox, Math, 6. List, 4. Difference

#### SORT

Sorts a list of numbers in ascending order. In CAS mode, you can use SORT on sequences. Complex numbers are not sorted (logically).

Syntax

Input:

Home Mode - Algebraic Entry Home Mode - Textbook Entry Program Editor

SORT(list of numbers)

Home Mode - RPN Entry

1: list of numbers SORT, press Enter

The list is sorted automatically.

CAS Mode

sort(list of numbers) or sort(sequence of numbers)

Output: A list or sequence, sorted in ascending order.

Examples:

SORT({-7,9,-11,2}) returns {-11,-7,2,9}

Notes: Attempting to use SORT on vectors will return “Error: Bad argument type”.

Access: Toolbox, Math, 6. List, 3. SORT

#### REVERSE

Reverses the order of the list elements in the list. In CAS mode, this Reverse on sequences.

Syntax

Input:

Home Mode - Algebraic Entry Home Mode - Textbook Entry Program Editor

REVERSE(list)

Home Mode - RPN Entry

1: list REVERSE, press Enter

The order of the elements are reversed automatically.

CAS Mode

REVERSE(list) or REVERSE(sequence)

Output: A list or sequence, sorted in ascending order.

Examples:

REVERSE({8,2,3,1}) returns {1, 3, 2, 8}

Use REVERSE and SORT to sort a list of numbers in descending order: REVERSE(SORT({7, 3, 11, 14, 2})) returns {14, 11, 7, 3, 2}

Access: Toolbox, Math, 6. List, 5. REVERSE

#### CONCAT

CONCAT is the concatenate command. CONCAT joins a set of lists and numbers and puts all of its arguments into one list.

Syntax

Input:

Home Mode - Algebraic Entry Home Mode - Textbook Entry Program Editor

CONCAT(list or number, list or number, …)

Home Mode - RPN Entry

n: list or number … 2: list or number 1: list or number CONCAT(n), press Enter

CAS Mode

CONCAT(list or number or algebraic expression, list or number or algebraic expression, …)

Output: In Home Mode, a combined list of elements. In CAS Mode, a sequence of combined elements.

Examples:

Let L1 = {-1 , 0 , 1}. CONCAT(-2, L1) returns {-2, -1, 0, 1} CONCAT(L1, 2) returns {-1, 0, 1, 2} CONCAT(-2, L1, 2) returns {-2, -1, 0, 1, 2}

Combining lists: CONCAT({1, 3}, {6, 7}) returns {1, 3, 6, 7}

Access: Toolbox, Math, 6. List, 6. CONCAT

#### POS

List Position: Returns the first position of which an element's list occurs. If the desired element is not in the left, POS returns 0.

Syntax

Input:

Home Mode - Algebraic Entry Home Mode - Textbook Entry Program Editor

POS(list, desired element)

Home Mode - RPN Entry

2: list 1: desired element POS, press Enter

CAS Mode

POS(list, desired element)

Output: see description above

Examples:

Let L1 = {-1 , 0 , 1, 2, -1}. POS(L1, 1) returns 3. 1 is in position #3. POS(L1, 3) returns 0. 3 is not in L1. POS(L1, -1) returns 1. -1 occurs twice, positions #1 and #5. POS returns the first position the element is encountered.

Access: Toolbox, Math, 6. List, 7. POS

#### SIZE

Size command: Returns the number of elements of a list.

Syntax

Input:

Home Mode - Algebraic Entry Home Mode - Textbook Entry Program Editor

SIZE(list)

Home Mode - RPN Entry

1: list SIZE, press ENTER

CAS Mode

SIZE(list)

Output: see description above

Examples:

SIZE({7,9,6}) returns 3

Access: Toolbox, Math, 6. List, 8. SIZE

#### ∆LIST

Calculates the difference between sequential elements. The resulting list will have one less element than the original list.

Syntax

Input:

Home Mode - Algebraic Entry Home Mode - Textbook Entry Program Editor

∆LIST(list)

Home Mode - RPN Entry

1: list ∆LIST, press ENTER

CAS Mode

∆LIST(list of numbers and/or algebraic expressions)

Output: see description above

Examples:

∆LIST({8,9,5,6}) returns {1, -4, 1}

In CAS Mode: ∆LIST({8,9*x,5,6*x²}) returns {9*x-8, 5-9*x, 6*x²-5}

Access: Toolbox, Math, 6. List, 9. ∆LIST

#### ΣLIST

Calculates the sum of all the list's elements.

Syntax

Input:

Home Mode - Algebraic Entry Home Mode - Textbook Entry Program Editor

ΣLIST(list)

Home - RPN Entry

1: list ΣLIST, press ENTER

CAS Mode

ΣLIST(list of numbers and/or algebraic expressions)

Output: see description above

Examples:

ΣLIST({8,9,2}) returns 19

In CAS Mode: ΣLIST({1,x,x²}) returns 1+x+x²

Access: Toolbox, Math, 6. List, A. ΣLIST [press the Vars key]

#### ΠLIST

Calculates the product of all the list's elements.

Syntax

Input:

Home Mode - Algebraic Entry Home Mode - Textbook Entry Program Editor

ΠLIST(list)

Home Mode - RPN Entry

1: list ΠLIST, press ENTER

CAS Mode

ΠLIST(list of numbers and/or algebraic expressions)

Output: see description above

Examples:

ΠLIST({8,9,2}) returns 144

In CAS Mode: ΠLIST({1,x,x²}) returns x*x^2 or x^3 when CAS is set to Maximum Simplification

Access: Toolbox, Math, 6. List, B. ΠLIST [press the Template key]

#### seq

Creates a sequence based on the expression, start point, end point, and increment. The increment can be omitted. The expression can be a constant.

The increment can be negative if start point > end point.

seq can create a sequence of constants, and is more flexible than MAKELIST.

Syntax

Input:

Home Mode - Algebraic Entry Home Mode - Textbook Entry CAS Mode Program Editor

seq(expression, variable, start point, end point, increment)

If increment = 1, it can be left out: seq(expression, variable, start point, end point) OR seq(expression, x =start point..end point) (CAS Mode only)

If you want a vector with a copy of expression, such as a vector filled with the same constant: seq(expression, number of copies)

Home Mode - RPN Entry

5: Expression in single quotes 4: Variable in single quotes 3: Start Point 2: End Point 1: Increment seq(5), press Enter

If increment = 1, it can be left out: 4: Expression in single quotes 3: Variable in single quotes 2: Start Point 1: End Point seq(4), press Enter

Generate a vector of constants: 2: constant 1: number of copies seq(2), press Enter

Output: A vector.

Examples:

A list of constants: seq(4,4) returns [4, 4, 4, 4]

A sequence generated with of increment of 1: seq(X!, X, 1, 6) returns [1, 2, 6, 24, 120, 720]

A sequence generated with a specified increment: seq(X!, X, 1, 6, 2) returns [1, 6, 120]

A sequence generated with a negative increment (start point > end point). seq(X!, X, 6, 1, -1) returns [720, 120, 24, 6, 2, 1]

Notes: If increment is positive, the generation of the sequence stops when variable ≥ end point.

If increment is negative, the generation of the sequence stops when variable ≤ end point.

Access: Catalog: Toolbox, Ctlg