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NC.MinimalPolynomial

Compute a minimal polynomial of an element over the quotient of a free monoid ring if it exists.
Syntax
          
NC.MinimalPolynomial(G:LIST, P:LIST):LIST
NC.MinimalPolynomial(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.

Please set ring environment coefficient fieldK and alphabet (or set of indeterminates) X via the functions NC.SetFp and NC.SetX, respectively, before calling the function. The default coefficient field is Q. For more information, please check the relevant functions. Since this function is based on Groebner basis computations, we refer users to NC.MRGB or NC.MRReducedGB for information about the following three optional parameters:

Example
NC.SetX("xy"); 
NC.SetFp(); -- default Fp=F2
F1 := [[1,""], [1,"y"]];
F2 := [[1,"xx"],[1,"xy"],[1,""]];
G := [F1, F2]; 
P := [[1,"yx"],[1,""]];
NC.MinimalPolynomial(G, P); -- mimnimal polynomial of P over Z/(2)/(F1, F2) 
[[[1, "tt"], [1, "t"], [1, ""]]]
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See Also