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NC.FindPolynomials

Find polynomials with specified alphabet (set of indeterminates) from a list of polynomials in monoid rings.
Syntax
          
NC.FindPolynomials(Alphabet:STRING, Polynomials:LIST):LIST

          

Description


Example
Polynomials:=[[[1,"a"], [1,"b"], [1,"c"]], [[1,"b"]]];
NC.FindPolynomials("abc", Polynomials);

[[[1, "a"], [1, "b"], [1, "c"]], [[1, "b"]]]
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NC.FindPolynomials("a", Polynomials);

[ ]
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NC.FindPolynomials("b", Polynomials);

[[[1, "b"]]]
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NC.FindPolynomials("ab", Polynomials);

[[[1, "b"]]]
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NC.SetX("txyz"); 
NC.SetOrdering("ELIM"); -- ELIM will eliminate t, x, y, z one after another
F1 := [[1,"xx"], [-1,"yx"]];
F2 := [[1,"xy"], [-1,"ty"]];
F3 := [[1,"xt"], [-1, "tx"]];
F4 := [[1,"yt"], [-1, "ty"]];
G := [F1, F2,F3,F4]; 
Gb := NC.GB(G); -- compute Groebner basis of  w.r.t. ELIM
Gb;
NC.FindPolynomials("xyz",Gb); -- compute Groebner basis of the intersection of  and K w.r.t. ELIM

[[[1, "xx"], [2, "yx"]], [[1, "ty"], [2, "xy"]], [[1, "yt"], [2, "xy"]], [[1, "tx"], [2, "xt"]], 
[[1, "xyx"], [2, "yyx"]], [[1, "xyy"], [2, "yxy"]], [[1, "yxt"], [2, "yyx"]]]
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[[[1, "xx"], [2, "yx"]], [[1, "xyx"], [2, "yyx"]], [[1, "xyy"], [2, "yxy"]]]
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See Also