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==== CAS-Integer Commands ====

Return to the Prime Programming Page:  
[[Prime:Programming|Prime Programming Language (PPL)]]

This section will cover the Integer commands of the HP Prime.  Unless noted, the commands are practically useful //only// in CAS Mode and in CAS programs.  

Examples given in this section is with the CAS Simplify setting set to Maximum.  The "Include complex results in variables" option is turned off.
 
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=== idivis ===

Returns a sequence (vector) of an integer's divisors.  

** Syntax **

** Input: **

** CAS Mode ** \\
** Program Editor - CAS Programs **

idivis(//integer//)

** Home Mode- Algebraic or Textbook Entry: ** \\
** Normal Program Editor**

CAS.idivis(//integer//)

**Home Mode - RPN Entry:**

1:  //integer//
CAS.idivis(1) press Enter

** Examples: **

CAS Mode \\
idivis(36) returns [1 2 4 3 6 12 9 18 36]

** Access: **  
Toolbox, CAS, 5.  Integers, 1. idivis

** See Also: ** ifactor, lcm, gcd
 
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=== ifactor ===

Returns the prime factorization of an integer.  The output is a textbook representation of an integer's factorization.  

** Syntax **

** Input: **

** CAS Mode ** \\
** Program Editor - CAS Programs **

ifactor(//integer//)

** Home Mode- Algebraic or Textbook Entry: ** \\
** Normal Program Editor**

CAS.ifactor(//integer//)

**Home Mode - RPN Entry:**

1:  //integer//
CAS.ifactor(1) press Enter

** Examples: **

CAS Mode \\
ifactor(36) returns 2^2*3^2

** Access: **  
Toolbox, CAS, 5.  Integers, 2.  ifactor

** Note: ** Be careful because the commands ifactor and ifactors do different things (one little "s").

** See Also: ** idivis, ifactors
 
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=== ifactor ===

Returns the prime factorization of an integer.  The output is a sequence of pairs:  prime divisor followed by its multiplicity. 

** Syntax **

** Input: **

** CAS Mode ** \\
** Program Editor - CAS Programs **

ifactors(//integer//)

** Home Mode- Algebraic or Textbook Entry: ** \\
** Normal Program Editor**

CAS.ifactors(//integer//)

**Home Mode - RPN Entry:**

1:  //integer//
CAS.ifactors(1) press Enter

** Examples: **

CAS Mode \\
ifactors(36) returns [2 2 3 2]

** Access: **  
Toolbox, CAS, 5.  Integers, 3.  ifactors

** Note: ** Be careful because the commands ifactor and ifactors do different things (one little "s").

** See Also: ** ifactor, isprime
 
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=== gcd  ===

Greatest common divisor of two polynomials or integers.

** Syntax **

** Input: **

** CAS Mode ** \\
** Program Editor - CAS Programs **

Greatest Common Divisor of Polynomials: \\
gcd(//polynomial//, //polynomial//)

Greatest Common Divisor of Integers: \\
gcd(//integer//, //integer//)

** Home Mode- Algebraic or Textbook Entry: ** \\
** Normal Program Editor**

CAS.gcd(//integer//, //integer//)

**Home Mode - RPN Entry:**

2:   //integer// \\
1:   //integer// \\
CAS.gcd(2)

** Examples: **

CAS Mode \\

Polynomials: \\
gcd(2x^2+4x, 4x) returns 2x

gcd(2x^3+2, 3x^5+3) returns x+1

Integers: \\
gcd(175, 225) returns 25

** Access: **  
Toolbox, CAS, 6.  Polynomial, 5. gcd   OR \\
Toolbox, CAS, 5.  Integers, 5. gcd

** See Also:  **  lcm, euler

 
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=== lcm  ===

Least common multiple of two polynomials or integers.   

** Syntax **

** Input: **

** CAS Mode ** \\
** Program Editor - CAS Programs **

Least Common Multiple of Polynomials: \\
lcm(//polynomial//, //polynomial//)

Least Common Multiple of Integers: \\
lcm(//integer//, //integer//)

** Home Mode- Algebraic or Textbook Entry: ** \\
** Normal Program Editor**

CAS.lcm(//integer//, //integer//)

**Home Mode - RPN Entry:**

2:   //integer// \\
1:   //integer// \\
CAS.lcm(2)

** Examples: **

CAS Mode \\

Polynomials: \\
lcm(x+1, x^2-1) returns x^2-1

lcm(x^2+1, x^3-1) returns x^5+x^3-x^2-1

Integers: \\
lcm(175, 225) returns 1575 

** Access: **  
Toolbox, CAS, 6.  Polynomial, 6. lcm   OR \\
Toolbox, CAS, 5.  Integers, 6. lcm

** See Also:  **  gcd 
 
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==== Prime Number Commands ====

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=== isprime ===

Tests to see if an integer is a prime number.  The number is prime if the integer's divisors are only itself and 1.  

** Syntax **

** Input: **

** CAS Mode ** \\
** Program Editor - CAS Programs **

isprime(//integer//)

** Home Mode- Algebraic or Textbook Entry: ** \\
** Normal Program Editor**

CAS.isprime(//integer//)

**Home Mode - RPN Entry:**

1:  //integer//
CAS.isprime(1), press Enter

** Output: **

In CAS mode, isprime returns true and false.

In all other modes, CAS.isprime returns 1 (representing true) and 0 (representing false).

** Examples: **

CAS Mode \\

isprime(36) returns false

isprime(47) returns true

Home Mode \\

CAS.isprime(36) returns 0

CAS.isprime(47) returns 1

** Access: **  
Toolbox, CAS, 5.  Integer, 6.  Prime, 1.  isprime

** See Also:  ** ifactor, ifactors

 
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=== ithprime ===

Returns the nth prime number.  Example, ithprime(25) returns the 25th prime number, which is 97.  The sequence of primes is: 2, 3, 5, 7, etc.

** Syntax **

** Input: **

** CAS Mode ** \\
** Program Editor - CAS Programs **

ithprime(//integer//)

** Home Mode- Algebraic or Textbook Entry: ** \\
** Normal Program Editor**

CAS.ithprime(//integer//)

**Home Mode - RPN Entry:**

1:  //integer//
CAS.ithprime(1), press Enter

** Note: **  If the argument for ithprime is not an integer, it returns an "Error: Bad Argument Type" .  

** Examples: **

CAS Mode \\

ithprime(25) returns 97.

ithprime(36) returns 149.

** Access: **  
Toolbox, CAS, 5.  Integer, 6.  Prime, 2. ithprime

** See Also:  ** isprime, nextprime, prevprime


 
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=== nextprime ===

Returns the next prime number //greater than// n.  

** Syntax **

** Input: **

** CAS Mode ** \\
** Program Editor - CAS Programs **

nextprime(//integer//)

** Home Mode- Algebraic or Textbook Entry: ** \\
** Normal Program Editor**

CAS.nextprime(//integer//)

**Home Mode - RPN Entry:**

1:  //integer//
CAS.nextprime(1), press Enter

** Note: **  If the argument for nextprime is not an integer, it returns an "Error: Bad Argument Type" .  

** Examples: **

CAS Mode \\

nextprime(33) returns 37

nextprime(37) returns 41

** Access: **  
Toolbox, CAS, 5.  Integer, 6.  Prime, 3.  nextprime

** See Also:  ** isprime, ithprime, prevprime

 
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=== prevprime ===

Returns the next prime number //less than// n.  

** Syntax **

** Input: **

** CAS Mode ** \\
** Program Editor - CAS Programs **

prevprime(//integer//)

** Home Mode- Algebraic or Textbook Entry: ** \\
** Normal Program Editor**

CAS.prevprime(//integer//)

**Home Mode - RPN Entry:**

1:  //integer//
CAS.prevprime(1), press Enter

** Note: **  If the argument for prevprime is not an integer, it returns an "Error: Bad Argument Type" .  

** Examples: **

CAS Mode \\

prevprime(33) returns 31

prevprime(31) returns 29

** Access: **  
Toolbox, CAS, 5.  Integer, 6.  Prime, 5.  prevprime

** See Also:  ** isprime, ithprime, nextprime

 
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=== euler ===

Euler's phi function, also known as the totient function.  Φ(n).  The function returns the number of positive integers less than or equal to n which are coprime to n.  An integer is coprime to n if their greatest common divisor (gcd) is 1.  

** Syntax **

** Input: **

** CAS Mode ** \\
** Program Editor - CAS Programs **

euler(//integer//)

** Home Mode- Algebraic or Textbook Entry: ** \\
** Normal Program Editor**

CAS.euler(//integer//)

**Home Mode - RPN Entry:**

1:  //integer//
CAS.euler(1), press Enter

** Note: **  If the argument for euler is not an integer, it returns an "Error: Bad Argument Type" .  

** Examples: **

CAS Mode \\

euler(25) returns 20

euler(36) returns 12

** Access: **  
Toolbox, CAS, 5.  Integer, 6.  Prime, 5.  euler

** See Also:  ** gcd

 
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==== Integer Divsion Commands ====

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=== iquo ===

Returns the quotient portion of the division //m// ÷ //n//, where //m// and //n// are integers.

** Syntax **

** Input: **

** CAS Mode ** \\
** Program Editor - CAS Programs **

iquo(//dividend or numerator//, //divisor or denominator//)

** Home Mode- Algebraic or Textbook Entry: ** \\
** Normal Program Editor**

CAS.iquo(//dividend or numerator//, //divisor or denominator//)

**Home Mode - RPN Entry:**

2:  //dividend or numerator //
1: //divisor or denominator //
CAS.iquo(2), press Enter

** Examples: **

CAS Mode \\

iquo(96, 85) returns 1

iquo(96, 6) returns 16

** Access: **  
Toolbox, CAS, 5.  Integer, 7.  Division, 1.  iquo

** See Also:  ** ÷, irem
 
 
=== irem ===

Returns the remainder portion of the division //m// ÷ //n//, where //m// and //n// are integers.

** Syntax **

** Input: **

** CAS Mode ** \\
** Program Editor - CAS Programs **

irem(//dividend or numerator//, //divisor or denominator//)

** Home Mode- Algebraic or Textbook Entry: ** \\
** Normal Program Editor**

CAS.irem(//dividend or numerator//, //divisor or denominator//)

**Home Mode - RPN Entry:**

2:  //dividend or numerator //
1: //divisor or denominator //
CAS.irem(2), press Enter

** Examples: **

CAS Mode \\

irem(96, 85) returns 11

irem(96, 6) returns 0

** Access: **  
Toolbox, CAS, 5.  Integer, 7.  Division, 2. irem

** See Also:  ** ÷, iquo
 
=== ichinrem ===


Integer Chinese Remainder Theorem for two equations.  Takes two lists [a, p] and [b, q] and returns a list of two integers [r, n] such that x Ξ r mod n.  In this case, x Ξ a mod p, x Ξ b mod q, and n Ξ p * q.

Source:  HP Prime help screen for ichinrem 

** Syntax **

** Input: **

** CAS Mode ** \\
** Program Editor - CAS Programs **

ichinrem([a,p],[b,q])

** Home Mode- Algebraic or Textbook Entry: ** \\
** Normal Program Editor**

CAS.inchinrem([a,p],[b,q])

**Home Mode - RPN Entry:**

2:  [a, p] \\
1:  [b, q] \\
CAS.inchinrem(2), press Enter

** Examples: **

CAS Mode \\

ichinrem([2,7],[3,5]) returns [-12, 35]   meaning: \\

** Access: **  
Toolbox, CAS, 5.  Integer, 7.  Division, 3.  inchinrem

** See Also:  ** ÷, irem

 
 
=== powmod ===

Power and modulo function.  powmod takes three integers: a, n, and p and returns a^n mod p.

Source:  HP Prime help screen for powmod 

** Syntax **

** Input: **

** CAS Mode ** \\
** Program Editor - CAS Programs **

powmod(a,n,p)

** Home Mode- Algebraic or Textbook Entry: ** \\
** Normal Program Editor**

CAS.powmod(a,n,p)

**Home Mode - RPN Entry:**

3:  a \\
2:  n \\
1:  p \\
CAS.powmod(3), press Enter

** Examples: **

CAS Mode \\

powmod(4,8,6) returns 4  (4^8 MOD 6)

powmod(8, 2,3)  returns 1    (8^2 MOD 3)

** Access: **  
Toolbox, CAS, 5.  Integer, 7.  Division, 4.  powmod

** See Also:  ** mod

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[[Prime:Programming|Prime Programming Language (PPL)]]
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