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 computes the greatest common
divisor of two polynomials as well as the polynomials U(x) and
V(x) in the above identity.
gcdex is a synonym for egcd.
Examples.
⎡ ⎣ | 1,−1,2 x+2 | ⎤ ⎦ |
⎡ ⎣ | ⎡ ⎣ | 1 | ⎤ ⎦ | , | ⎡ ⎣ | −1 | ⎤ ⎦ | , | ⎡ ⎣ | 2,2 | ⎤ ⎦ | ⎤ ⎦ |
⎡ ⎣ | y−2,−y+3,4 | ⎤ ⎦ |
⎡ ⎣ | ⎡ ⎣ | 1,−2 | ⎤ ⎦ | , | ⎡ ⎣ | −1,3 | ⎤ ⎦ | , | ⎡ ⎣ | 4 | ⎤ ⎦ | ⎤ ⎦ |