The solutions of a pure difference binomial ideal exist in a cyclotomic field. This function will solve the ideal and construct an apropriate cyclotomic field such that the solutions are contained. If no extension is needed then the symbol that was given will remain untouched
i1 : R = QQ[x,y,z,w]
o1 = R
o1 : PolynomialRing
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i2 : I = ideal (x-y,y-z,z*w-1*w,w^2-x)
2
o2 = ideal (x - y, y - z, z*w - w, w - x)
o2 : Ideal of R
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i3 : dim I
o3 = 0
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i4 : binomialSolve I
o4 = {{1, 1, 1, 1}, {1, 1, 1, -1}, {0, 0, 0, 0}}
o4 : List
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i5 : J = ideal (x^3-1,y-x,z-1,w-1)
3
o5 = ideal (x - 1, - x + y, z - 1, w - 1)
o5 : Ideal of R
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i6 : binomialSolve J
BinomialSolve created a cyclotomic field of order 3
o6 = {{1, 1, 1, 1}, {ww , ww , 1, 1}, {- ww - 1, - ww - 1, 1, 1}}
3 3 3 3
o6 : List
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