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NC.GReducedGB

Reduced (partial) Groebner basis of a finitely generated two-sided ideal in a free group ring over F2.
Syntax
          
NC.GReducedGB(G:LIST):LIST
NC.GReducedGB(G: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.

Please set ring environment alphabet (or indeterminates) X and 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: For most cases we do not know whether there exists a finite Groebner basis. Instead of forcing computer yelling and informing nothing valuable, the function has 3 optional parameters to control the computation. Note that at the moment all of the following 3 additional optional parameters must be used at the same time.

Example
NC.SetX("ab");
NC.SetOrdering("LLEX");
F1:=["aa", ""];
F2:=["bbb", ""];
F3:=["abababbabbabababbabb", ""];
G:=[F1,F2,F3];
RGB:=NC.GReducedGB(G);

-- Done.
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RGB;

[["aa", ""], ["bbb", ""], ["abbabbabab", "bbabbababa"], 
["abbabababb", "babbabbaba"], ["ababbabbab", "bbabababba"], ["abababbabb", "bababbabba"], 
["abababbababab", "babababbababa"], ["ababababbabab", "bababbabababa"], ["abbababababbab", "babbababababba"], 
["ababbababababb", "bbababababbaba"], ["abababbababbabab", "bababbababbababa"], ["babbabbabbabbabbab", "abbababababababba"], 
["abbabbabbabbabbaba", "bbabbababababababb"], ["abbababbababbababa", "bababbabababababab"], ["abbabababababababb", "babbabababababbaba"], 
["ababbabababababbab", "bbabababababababba"], ["bbabbababbababbabab", "ababbababababababa"], ["bbabbababababababba", "abbabbabbabbabbab"], 
["bababbababbababbabb", "abababababababbaba"], ["bababbababababababa", "abbababbababbabab"], ["ababbababbababbabba", "bbabababababababbab"], 
["bbabababababababbaba", "ababbababbababbabb"], ["abbababababababababbab", "babbababababababababba"], 
["ababbababbabababababab", "bababbababbabababababa"], ["ababbababababababababb", "bbababababababababbaba"], 
["babbababbababbababbabab", "abbabababababababababa"], ["bababbababbababbababbab", "ababababababababababba"], 
["ababbababbababbababbaba", "bbababababababababababb"], ["ababbababababababababab", "babbabababababababababa"], 
["ababababababababababbab", "babababababababababbaba"], ["bbabbabababababababababa", "abbababbababbababbabab"], 
["bbababababababababababba", "ababbababbababbababbab"], ["abbababababababababababb", "babbababbababbababbaba"], 
["abababababababababababab", "babababababababababababa"],  ["abbababababababababababab", "babababababababababababba"]]
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-- Done.
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NC.GIsGB(RGB);

True
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-- Done.
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Len(RGB);

35
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-- Done.
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GB:=NC.GGB(G);

-- Done.
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Len(GB);

62
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-- Done.
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See Also