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NC.KernelOfHomomorphism

Computes a (partial) Groebner basis of the kernel of a K-algebra homomorphism.
Syntax
          
NC.KernelOfHomomorphism(X_1:STRING, X_2:STRING, Images:LIST):LIST
NC.KernelOfHomomorphism(X_1:STRING, X_2: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.

Before calling the function, please set coefficient field K through the functions NC.SetFp(Prime) (or NC.UnsetFp()). Default coefficient field is Q. 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
X_1 := "abc"; 
X_2 := "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(X_1, X_2, Images);
[[[1, "ab"], [-1, "ba"], [1, "ac"], [-1, "ca"]], [[1, "aa"], [-1, "b"], [-1, "c"]]]
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See Also