The increased capacity of elementary particle accelerators raises the demand for the simulation data of the experiments. One of the bottlenecks in the simulations is the QCD color structure calculation, which is usually treated using non-orthogonal and overcomplete sets of bases. The computational cost could be decreased significantly if orthogonal bases, such as the multiplet bases, were used instead. However, no computation tool performing calculations using these bases is available yet. In this thesis, we present a Mathematica program as proof-of-principle demonstrating the color structure decomposition into the multiplet bases. For a given amplitude, the corresponding multiplet basis states can be created and the scalar product between the amplitude and each of the basis states can be evaluated whenever the required Wigner 6j coefficients are available. The program offers tools for visualization of the tensor expressions in the birdtrack notation as well as a syntax similar to how the tensor expressions would be defined on paper. The available functions and replacement rules allow performing operations on SU(Nc) tensor expressions including index contraction, tensor conjugation, and scalar product of tensors.It might be stunning to realize that researching the smallest constituents of the world we see requires building the largest constructions people have created. On the border of Switzerland and France one can find the greatest of the examples, the Large Hadron Collider, a more than eight kilometers in diameter large ring filled with a vacuum where scientists let bunches of around 100 million protons collide almost 40 million times per second. Despite all the great discoveries (you might have heard of the Higgs boson found in 2012, for example), particle physicists often claim that further explorations of the fundamentals of the Universe require building even larger colliders and increasing the number of collisions even more. However, something is often left out in this demand for faster, bigger, and stronger. In order to find new unknown physics, we must obtain just as much data from the computer simulations as we get from the experiments. Like with two fingerprints, we analyze all the different curves and shapes in the graphs obtained from these two data sets. Any discrepancy found in them would give a clue on where to search for discoveries such as new types of elementary particles, or even change our view on how our Universe works. My contribution to particle physics is connected to speeding up the methods of mathematical simulations of the collision data. A calculation of each clash of particles, like a collision of two asteroids, involves keeping track of a tremendous mess of collision products --- where they fly, how fast and how they interact with each other. What is even more complicated to calculate are predictions about what kind of particles get to be created in each of these collisions. This is determined by the laws of \textit{Quantum Field Theory}, a theory stating that all particles can be viewed as energetic bumps in some invisible fields spanning the whole Universe. The theory predicts how particles get created and destroyed in the interaction points like waves on a drum membrane when it is hit. %Some of the particles created in these tiny interaction points attract each other so strongly that they combine long before hitting the detectors. These particles are called quarks and gluons and this immensely strong force is called, well, the strong force. An even more peculiar feature of this force is that unlike the electromagnetic charge, the strong force charge comes in three types. Gluons and quarks interact differently depending on what charge they possess. Even though simplified methods to simulate particle collisions approximately exist, for exact calculations, all of the possible color charge combinations have to be considered. This makes one of the greatest bottlenecks of the whole simulation process and is a challenge that this thesis offers a possible solution to. Some of the particles created in these tiny interaction points attract each other so strongly that they combine long before hitting the detectors. These particles are called quarks and gluons and the force that creates these immensely strong bounds is called, well, the strong force. An even more peculiar feature of this force is that unlike the electromagnetic charge, the strong force charge comes in three types. Gluons and quarks interact differently depending on what charge they possess. Even though simplified methods to simulate particle collisions approximately exist, for exact calculations, all of the possible color charge combinations have to be considered. This makes one of the greatest bottlenecks of the whole simulation process and is a challenge that this thesis offers a possible solution to. In my thesis, I computationally implemented a new technique that uses abstract mathematical objects called multiplet bases that could potentially speed up the strong force calculations. We have already validated our method for the simplest collisions. However, the highest hope is to update the multiplet bases method to be able to calculate collisions where eight or more gluons and quarks appear and where the speed differences would become more significant. When this is achieved, it should immensely increase the capacity of simulating particle collisions. In this way, physicists would be able to search for even more complicated processes and in this complexity maybe some great discoveries hide
