Given the two polynomials in two variables x and y
A(y,x)=((a1)y+(a2))((a3)*x+(a4))
B(y,x)=((b4)-(b3)x)((b2)-(b1)*y)
both congruent to zero mod a semiprimal number N Using the LLL algorithm I should find m and n such that:
m(a1)(a3)+n(b1)(b3) = N*t +T
m(a1)(a4)-n(b1)(b4) = N*s + S
m(a2)(a3)-n(b2)(b3) = N*w + W
64 < T <= 64 *j
0 < S <= sqrt(N)
0 < W <= sqrt(N)
Where j is an integer greater than 1 Is anyone kind enough to show me the implementation in sagemath?