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gcd

  

greatest common divisor of polynomials

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

gcd(A, B)

gcd(A, B, x)

[g, s, t] = gcd(A, B)

[g, s, t] = gcd(A, B, x)

Parameters

A

-

array or expression

B

-

array or expression

x

-

variable

Description

• 

The gcd function computes the greatest common divisor of two polynomials A and B.

• 

The optional argument x specifies the dependant variable.  If unspecified, findsym(A,1) or findsym(B,1) is used (whichever returns a non-NULL result first).  Note that if the input polynomials are multivariate then, in general, s and t will be rational functions in variables other than x.

• 

The extended Euclidean algorithm is applied by gcd to compute unique polynomials s, t and g in x such that s*A + t*B = g where g is the monic greatest common divisor of A and B. The results computed satisfy degree(s) < degree(B/g) and degree(t) < degree(A/g). The greatest common divisor g is returned as the function value.

• 

If A and B are arrays, the gcd(A,B) function computes the element-wise greatest common divisor of A and B.

• 

If A is a scalar and B is an array then gcd computes the greatest common divisor of A and each element of B.

• 

Arrays A and B must be the same size.

Examples

withMTM&colon;

AMatrix2&comma;3&comma;fill=12x&colon;

BMatrix2&comma;3&comma;fill=27xy&colon;

gcdA&comma;B

xxxxxx

(1)

g,c,dgcdx310x2+31x30&comma;x21&comma;x312x2+41x42&comma;x2+2x+1

g,c,dx25x+6x+1,1212,1212

(2)

See Also

gcd

MTM[lcm]