-- Example from "On some basic applications of Groebner bases in noncommutative polynomial rings", Patrik Nordbeck
X_1 := "abc";
R_1 := []; -- free associative algebra
X_2 := "xy";
R_2 := []; -- 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(X_1, R_1, X_2, R_2, Images);
[[[1, "ab"], [-1, "ba"], [1, "ac"], [-1, "ca"]], [[1, "aa"], [-1, "b"], [-1, "c"]]]
-------------------------------
-- Small Changes
X_1 := "abc";
R_1 := []; -- free associative algebra
X_2 := "xy";
R_2 := []; -- free associative algebra
F1 := [[1,"x"], [1,"y"]];
F2 := [[1,"xx"],[1,"xy"]];
F3 := [[1,"yy"],[1,"xy"]]; -- change here
Images := [F1, F2, F3];
NC.MRKernelOfHomomorphism(X_1, R_1, X_2, R_2, Images,12,50, True);
[[[1, "aab"], [-1, "aba"], [1, "aca"], [-1, "caa"]], [[1, "aaa"], [-1, "ab"], [-1, "ca"]], [[1, "abaa"], [-1, "aaca"], [-1, "abb"], [1, "cca"]],
[[1, "aacaa"], [-1, "abab"], [1, "abba"], [-1, "abca"], [-1, "ccaa"]]]
-------------------------------
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