11.2.5 GCD of two polynomials with the Euclidean algorithm
The gcd command computes the gcd
(greatest common divisor) of polynomials.
(See also Section 7.1.1 for GCD of integers.)
-
gcd takes an arbitrary number or arguments:
polys, a sequence or list of polynomials.
- gcd(polys) returns the greatest
common divisor of the polynomials in polys.
Gcd is the inert form of gcd;
namely, it evaluates to gcd for later evaluation.
It is used when Xcas is in
Maple mode (see Section 2.5.2) to compute the gcd of
polynomials with coefficients in ℤ/pℤ using
Maple-like syntax.
Examples
| gcd(x^2-2*x+1,x^3-1,x^2-1,x^2+x-2) |
or:
| gcd([x^2-2*x+1,x^3-1,x^2-1,x^2+x-2]) |
For polynomials with modular coefficients:
| gcd((x^2+2*x+1) mod 5,(x^2-1) mod 5) |
Input in Xcas mode:
Input in Maple mode:
| Gcd(x^2+2*x,x^2+6*x+5) mod 5 |