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NC.MRMinimalPolynomial

Minimal polynomials of a quotient ring element over a finitely presented monoid ring.
Syntax
          
NC.MRMinimalPolynomial(X:STRING, Relations:LIST, G:LIST, P:LIST):LIST
NC.MRMinimalPolynomial(X:STRING, Relations:LIST, G:LIST, P: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. Since the algorithm used in this function is based on Groebner basis computation, we refer users to NC.MRGB or NC.MRReducedGB for information about the following optional parameters:

Example
X := "xy"; 
Relations := []; 
F1 := [[1,""], [1,"y"]]; 
F2 := [[1,"xx"],[1,"xy"],[1,""]]; 
G := [F1, F2]; 
P := [[1,"yx"],[1,""]]; 
NC.MRMinimalPolynomial(X, Relations, G, P);
[[[1, "tt"], [-1, "t"], [1, ""]]]
-------------------------------
X := "xyz";    
Ordering := "LLEX";    
Relations := [];    
F1 := [[1,"xx"], [1,""]];    
F2 := [[1,"yyy"], [1,""]];   
F3 := [[1,"zz"], [1,""]];   
F4 := [[1,"xyxyyxyxyy"], [1,""]];  
F5 := [[1,"xzxz"], [1,""]];   
F6 := [[1,"yzyz"], [1,""]];    
G := [F1, F2, F3, F4, F5, F6]; 
NC.MRMinimalPolynomial(X, Relations, G, [[1,"x"]]);
[[[1, "tt"], [1, ""]]]
-------------------------------


See Also