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NC.GTruncatedGB

Degree truncated Groebner basis of a finitely generated two-sided ideal in a free group ring over F2.
Syntax
          
NC.GTruncatedGB(G:LIST, D:INT):LIST
NC.GTruncatedGB(G:LIST, D:INT, LoopBound:INT, IFlag: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 alphabet (or indeterminates) X and ordering Ordering through the functions NC.SetX(X) and NC.SetOrdering(Ordering), respectively, before calling the function. Default ordering is length-lexicographic ordering "LLEX". For more information, please check the relevant functions. About the optional parameters: in some situations, D-truncated Groebner basis is huge. Thus instead of computing the whole D-truncated Groebner basis, 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.

Example
NC.SetX("xyz");
F1:=["yxy","zyz"];
F2:=["xyx","zxy"];
F3:=["zxz","yzx"];
F4:=["xxx","yyy","zzz","xyz"];
G:=[F1,F2,F3,F4];
NC.GTruncatedGB(G,6);

[["yzx", "zxz"], ["yxy", "zyz"], ["xyx", "zxy"], ["xxx", "xyz", "yyy", "zzz"], 
["zxzy", "zzxz"], ["xzyz", "zxyy"], ["xxyz", "xyyy", "xzxz", "xzzz", "yyyx", "zzzx"], 
["zzxyy", "zzxzz"], ["yzzxz", "zxzzy"], ["yzzxy", "zzxzx"], ["yzyyy", "yzzzz", "zxzxx", "zzxzz"], 
["yxzxz", "zyzzx"], ["xzzxz", "zxyyx"], ["xyyyy", "xyzzz", "zxyyz", "zzzxy"], 
["xxzxz", "xyyyx", "xzxzx", "xzzzx", "yyyxx", "zzzxx"], ["xxzxy", "xyzyx", "yyyyx", "zzzyx"], 
["xxyyy", "xxzzz", "xyzyz", "xzxzx", "yyyxx", "yyyyz", "zzzxx", "zzzyz"], 
["zxzzyz", "zzxzxy"], ["yzzzxz", "zxzzyy"], ["yzzzxy", "zzxzxx"], ["xzzzxz", "zxyzyz"], 
["xyyzyz", "xzxyyx", "xzxzxy", "xzzzxy", "yyyxxy", "zzzxxy"], 
["xxzzzy", "xyyyzz", "xyzyzy", "xzxyyz", "xzxzxy", "xzxzzz", "xzzzxy", 
"xzzzzz", "yyyxxy", "yyyxzz", "yyyyzy", "zzzxxy", "zzzxzz", "zzzyzy"], 
["xxzzxy", "xyzyxx", "yyyyxx", "zzzyxx"]]
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See Also