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NC.KernelOfHomomorphism

(Partial) (two-sided) leading-term ideal of the kernel of a K-algebra homomorphism.
Syntax
          
NC.KernelOfHomomorphism(X1:STRING, X2:STRING, Images:LIST):LIST
NC.KernelOfHomomorphism(X1:STRING, X2:STRING, Images: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 coefficient field K and alphabet (or indeterminates) X through the functions NC.SetFp(Prime) and NC.SetX(X), respectively, before calling the function. 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.GB or NC.ReducedGB for information about the following optional parameters:

Example
X1 := "abc"; 
X2 := "xy"; 
F1 := [[1,"x"], [1,"y"]]; 
F2 := [[1,"xx"],[1,"xy"]]; 
F3 := [[1,"yy"],[1,"yx"]]; 
Images :=[F1, F2, F3]; -- a |-> F1; b |-> F2; c |-> F3 
NC.KernelOfHomomorphism(X1, X2, Images);
[[[1, "ab"], [-1, "ba"], [1, "ac"], [-1, "ca"]], [[1, "aa"], [-1, "b"], [-1, "c"]]]
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See Also