[SPACECADET3D]

These polynomials appear when computing Feynman diagrams, which are used to make predictions for the Large Hadron Collider. The collider can measure collisions with such astonishing precision (<1% error) that predictions of the same order are also needed. The more precise you want to be, the more terms in a series approximation of the mathematical description of the collision you need to compute. For example, I computed the fifth-order approximation of the QCD beta function, which governs how intense the strong force affects matter. This takes 5 days of symbolic manipulations (pattern matching, substitutions, rational polynomial arithmetic, etc) on 32 cores.

The large polynomials appear in the middle of the computation, often referred to as intermediate expression swell. This also happens when you do a Gaussian elimination or compute greatest common divisors: the final result will be small, but intermediately, the expressions can get large.

[eh_why_not]

Is there a document/book you can recommend that includes a simplified example/tutorial of this computation process from beginning to end? (Or, what are the right keywords to search for such a thing?)

I'm looking for something like: here's the particle interaction we will work on, this is a very simple Feynman diagram, and here's the simplified data the LHC gave us about it, here's the resulting equation from which we'll derive a series, etc.

Not looking for how to program it, but actually for seeing the problem structure, and the solution design from beginning to end. (Familiar with high level physics concepts, and comfortable with any math).

[Y_Y]

I like Peskin's Introduction to QFT, but Zee's QFT in a Nutshell is also good.