up previous next
NC.GTruncatedGB

Compute a degree truncated Groebner basis of a finitely generated homogenous two-sided ideal in a free monoid ring over F2.
Syntax
          
NC.GTruncatedGB(G:LIST, D:INT):LIST
NC.GTruncatedGB(G:LIST, D: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 alphabet (or set of indeterminates) X and admissible ordering via the functions NC.SetX and NC.SetOrdering, respectively, before calling the function. The 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 too large for our applications. Thus instead of computing the whole D-truncated Groebner basis, the function has two optional parameters to interrupt the enumerating procedure. Note that at the moment all of the following two 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"]]
-------------------------------


See Also