Singular

D.15.6.9 linearlyEquivalent

Usage:

linearlyEquivalent(A,B); A = divisor, B = divisor.

Assume:

A and B are divisors on X.

Return:

list if A and B a linearly equivalent and int 0 otherwise.

Theory:

Checks whether A-B is principle. If yes, returns a list L=(f,g) where A - B = (f/g).

LIB "divisors.lib";
ring r=31991,(x,y,z),dp;
ideal I = y^2*z - x*(x-z)*(x+3*z);
qring Q = std(I);
divisor A = makeDivisor(ideal(x,z),ideal(1));
divisor B = makeDivisor(ideal(x,y),ideal(1));
linearlyEquivalent(A,B);
linearlyEquivalent(multdivisor(2,A),multdivisor(2,B));