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NC.MRIntersection

(Partial) Groebner basis of the intersection of two finitely generated two-sided ideals over a finitely presented monoid ring.
Syntax
          
NC.MRIntersection(X:STRING, Relations:LIST, G1:LIST, G2:LIST):LIST
NC.MRIntersection(X:STRING, Relations:LIST, 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. Since the algorithm used in this function is based on Groebner basis computation, we refer users to NC.MRGB or NC.MRReducedGB for information about the following optional parameters:

Example
X := "xyz"; 
Relations := []; -- free associative algebra
F1 := [[1,"xy"], [-1,"z"]]; 
F2 := [[1,"yz"], [-1, "x"]]; 
F3 := [[1,"zx"], [-1,"y"]]; 
G1 := [F1, F2]; -- (xy-z, yz-x)
G2 := [F2, F3]; -- (yz-x, zx-y)
NC.MRIntersection(X, Relations, G1, G2, 20, 50, 0); -- intersection of ideals (xy-z, yz-x) and (yz-x, zx-y)
[[[1, "zyzzz"], [-1, "zzzyz"], [-1, "yzz"], [1, "zzy"]], [[1, "yzyz"], [-1, "zyzy"]], 
[[1, "yyzz"], [-1, "zzyy"]], [[1, "zzyzyy"], [-1, "yyzy"], [-1, "zyzz"], [1, "yz"]], 
[[1, "zyzyyz"], [-1, "yzyy"], [-1, "zzyz"], [1, "zy"]], [[1, "yzzyzy"], [-1, "yzyy"], [-1, "zzyz"], [1, "zy"]], 
[[1, "yzzzyzy"], [-1, "yzzyy"], [-1, "zyyzy"], [1, "zzyyy"], [-1, "zzyzz"], [1, "zyz"]], 
[[1, "zyzyyyz"], [-1, "yyzyy"], [-1, "zyzzy"], [-1, "zzyyz"], [1, "zzzyy"], [1, "yzy"]],
[[1, "yyzyyyz"], [-1, "zyzyyyy"], [1, "zyzzyyz"], [-1, "zzzyyyz"], [-2, "yzyyz"], [1, "yzzyy"], [1, "zyyzy"]], 
[[1, "zyzyyyyz"], [-1, "yzyyyy"], [-1, "zzyyyz"], [1, "zyyy"]], 
[[1, "zyzyyyyyz"], [-1, "yyzyyyy"], [1, "zyyzyyz"], [-1, "zyzzyyy"], [-1, "zzyyyyz"], [-1, "zzyyzyy"], 
 [1, "zzzyyyy"], [1, "yzyyy"], [1, "zzyzzyz"], [-1, "zzzyzzy"], [-1, "zzzzyyz"], [1, "zzzzzyy"]],
[[1, "yyzyyyyyz"], [-1, "zyzyyyyyy"], [1, "zyzzyyyyz"], [-1, "zzzyyyyyz"], [1, "yyzyyzy"], [-1, "yzyyyyz"],
 [-1, "zyyzyyy"], [1, "zzyyyyy"], [-2, "zzyzzyy"], [-2, "zzzyyzy"], [2, "zzzzyyy"], [2, "zyzyy"], [2, "zzzyz"], [-2, "zzy"]], 
[[1, "x"], [-1, "yz"]]]
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Note that it is a partial Groebner basis.


See Also