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NC.LTIdeal

Computes the (partial) two-sided leading-term ideal of a finitely generated ideal over a free associative K-algebra.
Syntax
          
NC.LTIdeal(Polynomials:LIST):LIST
NC.LTIdeal(Polynomials: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.

Before calling the function, please set ring environment coefficient field K, alphabet X and ordering through the functions NC.SetFp(Prime) (or NC.UnsetFp()), NC.SetX(X) and NC.SetOrdering(Ordering) respectively. Default coefficient field is Q. Default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions. Since the algorithm used in this function is based on Groebner basis computation, we refer users to NC.BP or NC.GB for information about the following optional parameters:

Example
NC.SetX("xyzt");  
F1 := [[1,"xx"], [-1,"yx"]];    
F2 := [[1,"xy"], [-1,"ty"]];   
F3 := [[1,"xt"], [-1, "tx"]];   
F4 := [[1,"yt"], [-1, "ty"]];   
Generators := [F1, F2,F3,F4]; -- over Q (default field), LLEX ordering (default ordering) 
NC.LTIdeal(Generators);
["yt", "xt", "xy", "xx", "tyy", "yyx"]
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NC.SetFp(); 
NC.LTIdeal(Generators); -- over F2
["yt", "xt", "xy", "xx", "tyy", "yyx"]
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NC.SetFp(3); 
NC.LTIdeal(Generators); -- over F3
["yt", "xt", "xy", "xx", "tyy", "yyx"]
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See Also