`igcd`

Greatest common divisor of integers and complex numbers with integer real and imaginary parts

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Syntax

igcd(i1, i2, …)

Description

igcd(i1, i2, ...) computes the greatest common divisor of the integers i₁, i₂, …

igcd computes the greatest common nonnegative divisor of a sequence of integers. If an argument of igcd is a single integer number, the function returns the absolute value of that argument.

igcd also computes the greatest common divisor of a sequence of complex numbers of the domain DOM_COMPLEX. Both the real and the imaginary parts of all complex numbers in a sequence must be integers. The greatest common divisor is a complex number with a positive real part and a nonnegative imaginary part.

If all arguments are 0, igcd returns 0.

If there are no arguments, igcd also returns 0.

If one argument is a number, but is neither an integer nor a complex number with integer real and imaginary parts, then igcd returns an error message.

If at least one of the arguments is 1 or -1, igcd returns 1. Otherwise, if one argument is not a number, the igcd function returns a symbolic igcd call.

Examples

Example 1

Compute the greatest common divisor of the following integers:

igcd(-10, 6), igcd(6, 10, 15)

a := 4420, 128, 8984, 488:
igcd(a), igcd(a, 64)

Example 2

Compute the greatest common divisor of the following complex numbers:

igcd(-10*I, 6), igcd(10 - 5*I, 20 - 10*I, 30 - 15*I)

Example 3

The following example shows some special cases:

igcd(), igcd(0), igcd(1), igcd(-1), igcd(2)

Example 4

If one argument is not a number, then the result is a symbolic igcd call. However, if at least one of the arguments is 1 or -1, the greatest common divisor is always 1:

delete x:
igcd(a, x), igcd(1, x), igcd(-1, x)

type(igcd(a, x))

Parameters

i1, i2, …

arithmetical expressions representing integers or arithmetical expressions representing complex numbers of the domain DOM_COMPLEX, of which both the real part and the imaginary part are integers.