The solutions of a set of unital binomial equations exist in a cyclotomic field. This function will compute the variety of a unital binomial ideal and construct an appropriate cyclotomic field containing the entire variety (as a subset of the algebraic closure of QQ).
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
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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