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iscoprime

Check coprime relation

Since R2021a

Description

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

example

[iscp,ispcp] = iscoprime(x) also returns ispcp as true to indicate if any of the elements in x are pairwise coprime.

[iscp,ispcp,pidx] = iscoprime(x) also returns the indices of all pairs of elements of x. pidx is a 2-row matrix whose number of columns equals to M choose 2. Each column of pidx specifies the indices of a pair of elements in x.

example

[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. Each element in pgcd is the greatest common divisor of the two elements in x identified by the indices in the corresponding column of pidx.

Examples

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

x = [9 15 25];

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.

[iscp,ispcp,pidx,pgcd] = iscoprime(x)
iscp = logical
   1

ispcp = logical
   0

pidx = 2×3

     1     1     2
     2     3     3

pgcd = 1×3

     3     1     5

Create an array of integers; 9=3×3, 15=3×5, and 25=5×5.

x = [9 15 25];

Show that the integers form a coprime set.

iscp = iscoprime(x)
iscp = logical
   1

Verify that at least one of the three possible pairs of integers form a coprime pair.

[icsp,ispcp] = iscoprime(x)
icsp = logical
   1

ispcp = logical
   0

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

x = [9 15 25];

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

[~,ispcp,pidx] = iscoprime(x);
disp(pidx)
     1     1     2
     2     3     3

Input Arguments

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

Example: [21 36 49]

Data Types: single | double

Output Arguments

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Returns true if all elements of x are coprimes.

Returns true If any two elements of x are pairwise coprime. Returns false if no elements of x are pairwise coprime.

Array pair indices, returned as a two-row integer-valued matrix. pidx has N-choose-2 (N2)=12N(N1) columns. Each column of pidx specifies the indices of a pair of elements in x.

Greatest common divisors of element pairs, 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.

More About

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Extended Capabilities

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

Version History

Introduced in R2021a

See Also

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