-- Example from "On some basic applications of Groebner bases in noncommutative polynomial rings", Patrik Nordbeck
X1 := "abc";
Relations1 := []; -- free associative algebra
X2 := "xy";
Relations2 := []; -- free associative algebra
F1 := [[1,"x"], [1,"y"]];
F2 := [[1,"xx"],[1,"xy"]];
F3 := [[1,"yy"],[1,"yx"]];
Images := [F1, F2, F3]; -- k-algebra homomorphism is defined by a |->x+y, b |->xx+xy, c |->yy+yx
NC.MRKernelOfHomomorphism(X1, Relations1, X2, Relations2, Images);
[[[1, "ab"], [-1, "ba"], [1, "ac"], [-1, "ca"]], [[1, "aa"], [-1, "b"], [-1, "c"]]]
-------------------------------
-- Small Changes
F3 := [[1,"yy"],[1,"xy"]]; -- change here
Images := [F1, F2, F3];
NC.MRKernelOfHomomorphism(X1, Relations1, X2, Relations2, Images, 10, 20, 1);
[[[1, "aab"], [-1, "aba"], [1, "aca"], [-1, "caa"]], [[1, "aaa"], [-1, "ab"], [-1, "ca"]], [[1, "abaa"], [-1, "aaca"], [-1, "abb"], [1, "cca"]],
[[1, "ababa"], [-1, "abbaa"], [-1, "aacab"], [1, "abcaa"], [-1, "aacca"], [1, "ccab"], [1, "ccca"]],
[[1, "aacaa"], [-1, "abab"], [1, "abba"], [-1, "abca"], [-1, "ccaa"]]] -- it is a partical Groebner basis
-------------------------------
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