Scilab 5.5.2
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See the recommended documentation of this function
bezout
Bezout equation for polynomials or integers
Calling Sequence
[thegcd,U]=bezout(p1,p2)
Arguments
- p1, p2
two real polynomials or two integer scalars (type equal to 1, 2 or 8)
- thegcd
scalar of the same type as
p1
andp2
- U
2x2
matrix of the same type asp1
andp2
Description
[thegcd, U] = bezout(p1, p2)
computes the GCD thegcd
of p1
and p2
, and in addition a (2x2)
unimodular matrix U
such that:
[p1 p2]*U = [thegcd 0]
The lcm of p1
and p2
is given by:
p1*U(1,2)
(or -p2*U(2,2)
)
If p1
or p2
are given as doubles (type 1), then they are treated as
null degree polynomials.
Examples
// Polynomial case x = poly(0, 'x'); p1 = (x+1)*(x-3)^5; p2 = (x-2)*(x-3)^3; [thegcd,U] = bezout(p1, p2) det(U) clean([p1 p2]*U) thelcm = p1*U(1,2) lcm([p1 p2]) // Double case i1 = 2*3^5; i2 = 2^3*3^2; [thegcd,U] = bezout(i1, i2) V = [2^2*3^5 2^3*3^2 2^2*3^4*5]; [thegcd,U] = gcd(V) V*U lcm(V) // Integer case i1 = int32(2*3^5); i2 = int32(2^3*3^2); [thegcd,U] = bezout(i1, i2) V = int32([2^2*3^5 2^3*3^2 2^2*3^4*5]); [thegcd,U] = gcd(V) V*U lcm(V)
See Also
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