Complete group law for genus 2 Jacobians on Jacobian coordinates

This manuscript provides complete, inversion-free, and explicit group law formulas in Jacobian coordinates for the genus 2 hyperelliptic curves of the form \(y^2 = x^5+a_3 x^3+a_2 x^2+a_1 x+a_0\) $y^2=x^5+a_3{x}^3+a_2{x}^2+a_{1}x+a_0$ over a field K with \(\textrm{char}(K) \ne 2\) $\text{char}(K)\ne 2$ . The formulas do not require the use of polynomial arithmetic operations such as resultant, mod, or gcd computations but only operations in K.