GCD and types

Types help to make it clear where the computation happens.

Let's first start with a few abbreviations.

P(R,x)==>UnivariatePolynomial(x,R);

Z==>Integer;

Q==>Fraction Z;

Now we compute the gcd in

p11: P(P(Z, x), y) := 12*x^2*y;

p12: P(P(Z, x), y) := 18*x*y^2;

gcd(p11, p12)

(1)

Now in

p21: P(P(Q, x), y) := 12*x^2*y;

p22: P(P(Q, x), y) := 18*x*y^2;

gcd(p21, p22)

(2)

In

p31: P(Fraction P(Q, x), y) := 12*x^2*y;

p32: P(Fraction P(Q, x), y) := 18*x*y^2;

gcd(p31, p32)

(3)

And finally in the field

p41: Fraction P(P(Q, x), y) := 12*x^2*y;

p42: Fraction P(P(Q, x), y) := 18*x*y^2;

gcd(p41, p42)

(4)