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NCo.BMB

Enumerate a Macauley's basis of a finitely generated algebra over the binary field F_{2}={0,1}.
Syntax
          
NCo.BMB(Gb:LIST[, DB:INT]):LIST

          

Description
Given a two-sided ideal I in a free monoid ring F_{2}, we can consider the F_{2}-algebra F_{2}/I as a F_{2}-vector space. Moreover, let G be a Groebner basis of I, and let B be the set of all words which are not a multiple of any word in the leading word set BLW{G}. Then the residue class of the words in B form a F_{2}-basis, called a Macaulay's basis, of F_{2}/I. For the sake of computing the values of the Hilbert function (see NCo.BHF) of F_{2}/I, in this function we require that G has to be a Groebner basis with respect to a length compatible word ordering (see NCo.SetOrdering).

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 word ordering via the functions NCo.SetX and NCo.SetOrdering, respectively, before calling this function. The default ordering is the length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions. Optional parameter:

Example
NCo.SetX("xyzt");
NCo.SetOrdering("LLEX");
GB:= [["yt", "ty"], ["xt", "tx"], ["xy", "ty"], [ "xx", "yx"], 
["tyy", "tty"], ["yyx", "tyx"]];
NCo.BMB(GB,3);
[[""], ["t", "z", "y", "x"], ["tt", "tz", "ty", "tx", "zt", "zz", "zy", "zx", "yz", "yy", "yx", "xz"], 
["ttt", "ttz", "tty", "ttx", "tzt", "tzz", "tzy", "tzx", "tyz", "tyx", "txz", "ztt", "ztz", "zty", "ztx", 
"zzt", "zzz", "zzy", "zzx", "zyz", "zyy", "zyx", "zxz", "yzt", "yzz", "yzy", "yzx", "yyz", "yyy", "yxz", 
"xzt", "xzz", "xzy", "xzx"]]
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See Also