@Markiyan Hirnyk Its just a name appended by some developer to categorize procedures. probably it means Triangular decomposition. Start reading and it will come slowly. :)

@Markiyan Hirnyk You can start with https://en.wikipedia.org/wiki/Polynomial_ring

And if you want to work on softwares that help in such computations, either you can use maple's RegularChains package or other softwares like

"Singular", https://www.singular.uni-kl.de/ or

"Macaulay2", http://www.math.uiuc.edu/Macaulay2/.

They are dedicated softwares for polynomials and related branches of mathematics.

@Markiyan Hirnyk I would suggest you should study Polynomial rings from any website. There is plenty of information on internet with examples and repeating it will do not much. Just google it.

@Markiyan Hirnyk If you asking about meaning of this code then its kind of data structure that keeps reference of various properties of polynomial rings that represents properties of that polynomial. In Maple they have used Table, in C it could be a structure, in OOPS may be a class with some data members.

@Carl Love Yes that correctly answers my problem. How to accept this as correct answer?

@Markiyan Hirnyk It is a function called in RegularChains:-PolynomialRing() method.