What are the algorithms for the series, sums, and/or triple integrals for the structure of quarks and their probable location relative to one another?

 

Because the QCD Lagrangian is so complicated and so highly non-linear, most calculations in QCD cannot be performed in closed analytical form (i.e. with pen and paper, in principle). Numerical methods need to be employed, using powerful computers. And even then, obtaining exact results is often very difficult, because it is simply too computationally resource-intensive. For that reason, various approximation (i.e. non-perturbative) methods have been developed to enable us to run numerical computations in QCD, the most common one probably being a model called “Lattice QCD”:

https://en.m.wikipedia.org/wiki/Lattice_QCD