ApCoCoA-1:NC.TruncatedGB
NC.TruncatedGB
DegreeBound-truncated Groebner basis of a finitely generated two-sided ideal over a free associative K-algebra.
Syntax
NC.TruncatedGB(G:LIST, DegreeBound:INT):LIST NC.TruncatedGB(G:LIST, DegreeBound:INT, LoopBound:INT, Flag:INT):LIST
Description
Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.
Please set ring environment coefficient field K, alphabet (or indeterminates) X and ordering through the functions NC.SetFp(Prime), NC.SetX(X) and NC.SetOrdering(Ordering), respectively, before calling the function. Default coefficient field is Q. Default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.
@param G: a LIST of non-zero homogeneous polynomials generating a two-sided ideal in K<X>. Each polynomial is represented as a LIST of LISTs, which are pairs of form [C, W] where C is a coefficient and W is a word (or term). Each term is represented as a STRING. For example, xy^2x is represented as "xyyx", unit is represented as an empty string "". Then, polynomial F=xy-yx is represented as F:=[[1,"xy"], [-1, "yx"]]. 0 polynomial is represented as an empty LIST [].
@param DegreeBound: a positive integer which is the truncated degree of Groebner basis.
About the optional parameters: For most cases we do not know whether there exists a finite Groebner basis. Instead of forcing computer yelling and informing nothing valuable, the function has 2 optional parameters to control the computation. Note that at the moment all of the following 2 additional optional parameters must be used at the same time.
@param LoopBound: a positive integer which gives a bound for the main loop of Groebner basis computation. When it runs through the main loop LoopBound times, the function stops the loop and returns a partial Groebner basis.
@param Flag: a non-negative integer which is a multi-switch for the output of ApCoCoAServer. If Flag=0, the server prints nothing on the screen. If Flag=1, the server prints basic information about computing procedure, such as number of S-elements has been checked and to be checked. If Flag=2, the server additionally prints current partial Groebner basis before each loop as well as the information when Flag=1. Note that the initial idea of Flag is to use it as a tool for debugging and tracing the computing process.
@return: a LIST of polynomials, which is a DegreeBound-truncated Groebner basis if (1)finite Groebner basis of degree no more than DegreeBound exists or (2)the computation reach the DegreeBound, and which and is a partial Groebner basis otherwise.
Example
See also
