linearizable_p_q.sagews

def get_var(i):
    return var("x"+str(i));

p=1;
q=1;
k=p+q;
l=p*q;
m=3*l+2;
x=[0]*m;
for i in range(k):
    x[i]=get_var(i);
for i in range(k,m):
#    x[i]=factor((x[i-p]*x[i-q]+1)/x[i-k]);
    x[i]=factor((x[i-p]*x[i-q]+x[i-k/2])/x[i-k]);
print(x);

#for i in range(m-2*l):
#    print(expand(factor(x[i]+x[i+2*l])/x[i+l]));

for j in range(1,l):
    first=expand(factor(x[3*j]-x[0])/(x[2*j]-x[j]));
    second=expand(factor(x[1+3*j]-x[1])/(x[1+2*l]-x[i+l]))
    for i in range(m-3*j):
        print(expand(factor(x[i+3*l]-x[i])/(x[i+2*l]-x[i+l])));

[x0, x1, (x1 + 1)*x1/x0, (x1^2 + x0 + x1)*(x1 + 1)/x0^2, (x1^3 + x0^2 + x0*x1 + 2*x1^2 + x0 + x1)*(x1^2 + x0 + x1)/(x0^3*x1)] x0/(x1 - x1^2/x0 - x1/x0) - x1^3/(x0^2*(x1 - x1^2/x0 - x1/x0)) - x1/(x0*(x1 - x1^2/x0 - x1/x0)) - 2*x1^2/(x0^2*(x1 - x1^2/x0 - x1/x0)) - 1/(x0*(x1 - x1^2/x0 - x1/x0)) - x1/(x0^2*(x1 - x1^2/x0 - x1/x0)) x1/(x1^2/x0 - x1^3/x0^2 - 2*x1^2/x0^2 - 1/x0 - x1/x0^2) - x1^4/(x0^3*(x1^2/x0 - x1^3/x0^2 - 2*x1^2/x0^2 - 1/x0 - x1/x0^2)) - x1/(x0*(x1^2/x0 - x1^3/x0^2 - 2*x1^2/x0^2 - 1/x0 - x1/x0^2)) - 2*x1^2/(x0^2*(x1^2/x0 - x1^3/x0^2 - 2*x1^2/x0^2 - 1/x0 - x1/x0^2)) - 3*x1^3/(x0^3*(x1^2/x0 - x1^3/x0^2 - 2*x1^2/x0^2 - 1/x0 - x1/x0^2)) - 2/(x0*(x1^2/x0 - x1^3/x0^2 - 2*x1^2/x0^2 - 1/x0 - x1/x0^2)) - 1/(x1*(x1^2/x0 - x1^3/x0^2 - 2*x1^2/x0^2 - 1/x0 - x1/x0^2)) - 4*x1/(x0^2*(x1^2/x0 - x1^3/x0^2 - 2*x1^2/x0^2 - 1/x0 - x1/x0^2)) - 3*x1^2/(x0^3*(x1^2/x0 - x1^3/x0^2 - 2*x1^2/x0^2 - 1/x0 - x1/x0^2)) - 2/(x0^2*(x1^2/x0 - x1^3/x0^2 - 2*x1^2/x0^2 - 1/x0 - x1/x0^2)) - 1/(x0*x1*(x1^2/x0 - x1^3/x0^2 - 2*x1^2/x0^2 - 1/x0 - x1/x0^2)) - x1/(x0^3*(x1^2/x0 - x1^3/x0^2 - 2*x1^2/x0^2 - 1/x0 - x1/x0^2))