 
 
 
11.2.8  Bézout’s identity
Bézout’s Identity (also known as Extended Greatest Common Divisor)
states that for two polynomials A(x),B(x) with greatest common
divisor D(x), there exist polynomials U(x) and V(x) such that
| U(x) A(x)+V(x) B(x)=D(x). | 
The egcd or
gcdex command
computes the greatest common divisor of two polynomials
as well as the polynomials U(x) and V(x) in the above identity.
- 
egcd takes two mandatory
arguments and one optional argument:
- 
A and B, polynomials given as expressions or lists of
coefficients in decreasing order.
- Optionally, if the polynomials are expressions, x, the
variable (which defaults to x).
 
- egcd(A,B  ⟨,x⟩)
returns a list [U,V,D], where D is the greatest common divisor
of A and B, and U and V are the polynomials from
Bézout’s identity.
Examples
|  | | |  | ⎡ ⎣
 | ⎡ ⎣
 | 1 | ⎤ ⎦
 | , | ⎡ ⎣
 | −1 | ⎤ ⎦
 | , | ⎡ ⎣
 | 2,2 | ⎤ ⎦
 | ⎤ ⎦
 | 
 |  |  |  |  |  |  |  |  |  |  | 
 | 
| egcd(y^2-2*y+1,y^2-y+2,y) | 
|  | | |  | ⎡ ⎣
 | ⎡ ⎣
 | 1,−2 | ⎤ ⎦
 | , | ⎡ ⎣
 | −1,3 | ⎤ ⎦
 | , | ⎡ ⎣
 | 4 | ⎤ ⎦
 | ⎤ ⎦
 | 
 |  |  |  |  |  |  |  |  |  |  | 
 | 
 
 
