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NC.Intersection

Enumerate a (partial) Groebner basis of the intersection of two finitely generated two-sided ideals in a free monoid ring.
Syntax
          
NC.Intersection(G1:LIST, G2:LIST):LIST
NC.Intersection(G1:LIST, G2: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 fieldK, alphabet (or set of indeterminates) X and ordering via the functions NC.SetFp, NC.SetX and NC.SetOrdering, respectively, before calling the function. The default coefficient field is Q. The default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions. Since this function is based on Groebner basis computations, we refer users to NC.GB or NC.ReducedGB for information about the following three optional parameters:

Example
NC.SetFp(); -- set default Fp=F2
NC.SetX("xyz"); 
F1 := [[1,"xy"], [1,"z"]]; 
F2 := [[1,"yz"], [1, "x"]]; 
F3 := [[1,"zx"], [1,"y"]]; 
G1 := [F1, F2]; -- ideal generated by {xy+z, yz+x} 
G2 := [F2, F3]; -- ideal generated by {yz+x, zx+y}
NC.Intersection(G1, G2, 20, 25, 1);
[[[1, "yzyz"], [1, "zyzy"]], [[1, "zzyzyy"], [1, "yyzy"], [1, "zyzz"], [1, "yz"]], 
[[1, "yzzyzy"], [1, "yzyy"], [1, "zzyz"], [1, "zy"]], [[1, "x"], [1, "yz"]]]
-------------------------------
Note the following information printed by the server shows it is a partial Groebner basis. 
===== 25th Loop =====
Number of elements in (partial) Groebner basis G: 22 -- partial Groebner basis before being interreduced
Number of S-elements: 25/86 -- 25 S-elements have been check, and 61 (=86-25) unchecked S-elements


See Also