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NCo.MRMB

Enumerate a Macaulay's basis of a finitely generated K-algebra.
Syntax
          
NCo.MRMB(X:STRING, Ordering:STRING, Relations:LIST, G:LIST[, DB:INT]):LIST

          

Description
Given a two-sided ideal I in a finitely generated monoid ring P=K, we can consider the K-algebra P/I as a K-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 MRLW{G}. Then the residue class of the words in B form a K-basis, called a Macaulay's basis, of P/I. For the sake of computing the values of the Hilbert function (see NCo.MRHF) of P/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 coefficient field via the function NCo.SetFp (or NCo.UnsetFp) before calling this function. The default coefficient field is the field of rational numbers, i.e. RAT in CoCoAL. For more information, please check the relevant functions. Optional parameter:

Example
X :=  "xyzt";
Ordering := "LLEX";
Relations := [];
G:= [[[1, "yt"], [-1, "ty"]], [[1, "xt"], [-1, "tx"]], [[1, "xy"], [-1, "ty"]], [[1, "xx"], [-1, "yx"]], 
[[1, "tyy"], [-1, "tty"]], [[1, "yyx"], [-1, "tyx"]]];
NCo.MRMB(X, Ordering, Relations, G, 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