iscoprime

Check coprime relation

Syntax

iscp = iscoprime(x)

[iscp,ispcp,pidx,pgcd] = iscoprime(x)

Description

iscp = iscoprime(x) returns true if all elements of x are coprime and false if two or more elements of x have a greatest common divisor (gcd) greater than 1.

[iscp,ispcp,pidx,pgcd] = iscoprime(x) checks if pairs of elements of x have a greatest common divisor greater than 1. This syntax also returns the indices of all pairs of elements of x and the greatest common divisor of each pair.

Examples

Coprime Array Elements

Create an array x whose elements are $$9=3\times 3$$, $$15=3\times 5$$, and $$25=5\times 5$$. Verify that all elements of x are coprime.

x = [9 15 25];

iscp = iscoprime(x)

iscp = logical
   1

Verify that at least one pair of elements of x has a greatest common divisor greater than 1. Output the pairs and their greatest common divisors.

[~,ispcp,pidx,pgcd] = iscoprime(x)

ispcp = logical
   0

pidx = 2×3

     1     1     2
     2     3     3

pgcd = 1×3

     3     1     5

Input Arguments

x — Input array

row vector of positive integers

Input array, specified as a row vector of positive integers.

Example: [21 36 49]

Data Types: single | double

Output Arguments

iscp — True if all elements are coprime

logical scalar

True if all elements are coprime, returned as a logical scalar.

ispcp — True if elements are pairwise coprime

logical scalar

True if all elements are pairwise coprime, returned as a logical scalar. ispcp is true if x has no two elements whose greatest common divisor is greater than 1. ispcp is false if any two elements of x have as greatest common divisor a number greater than 1.

pidx — Array pair indices

two-row matrix

Array pair indices, returned as a two-row matrix. pidx has $$\left(\begin{array}{c}n\\ 2\end{array}\right)=\frac{1}{2}n\left(n-1\right)$$ columns. Each column of pidx specifies the indices of a pair of elements in x.

pgcd — Pair greatest common divisors

row vector

Pair greatest common divisors, returned as a row vector with a number of elements equal to the number of columns of pidx. Each element of pgcd is the greatest common divisor of the two elements of x identified by the indices in the corresponding column of pidx.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2021a