11.9.3 GCD in ℤ/pℤ[x]
In Xcas mode, Gcd is simply the inert form of
gcd; namely, it returns the greatest common divisor of two
polynomials without evaluation. (See Section 11.2.5.)
In Maple mode, the Gcd command
can additionally be used in conjunction with mod to
compute the greatest common divisor of two polynomials with
coefficients in ℤ/pℤ.
-
In Maple mode,
Gcd takes polys, a sequence or list of polynomials with coefficients
in ℤ/pℤ.
- Gcd(polys) returns the
greatest common divisor of the polynomials in polys.
Examples
Input in Xcas mode:
Gcd(2*x^2+5%13,5*x^2+2*x-3%13) |
|
gcd | ⎛
⎝ | 2 x2+5%13,5 x2+2 x+ | ⎛
⎝ | −3 | ⎞
⎠ | %13 | ⎞
⎠ |
| | | | | | | | | | |
|
To get the actual greatest common divisor:
Input in Maple mode:
Gcd(2*x^2+5,5*x^2+2*x-3) mod 13 |
Gcd(x^2+2*x,x^2+6*x+5) mod 5 |