Figure Properties - SERC

2gcd
Purpose Greatest common divisor
Syntax G = gcd(A,B)
[G,C,D] = gcd(A,B)
Description G = gcd(A,B) returns an array containing the greatest common divisors of the
corresponding elements of integer arrays A and B. By convention, gcd(0,0)
returns a value of 0; all other inputs return positive integers for G.
[G,C,D] = gcd(A,B) returns both the greatest common divisor array G, and
the arrays C and D, which satisfy the equation: A(i).*C(i) + B(i).*D(i) =
G(i). These are useful for solving Diophantine equations and computing
elementary Hermite transformations.
Examples The first example involves elementary Hermite transformations.
For any two integers a and b there is a 2-by-2 matrix E with integer entries and
determinant = 1 (a unimodular matrix) such that:
E * [a;b] = [g,0],
where g is the greatest common divisor of a and b as returned by the command
[g,c,d] = gcd(a,b).
The matrix E equals:
c d
-b/g a/g
In the case where a = 2 and b = 4:
[g,c,d] = gcd(2,4)
g =
2
c =
1
d =
0
gcd
2-955