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TriangularSets :: saturate(TriaSystem)

saturate(TriaSystem) -- saturated ideal of a triangular system

Synopsis

Description

Returns the saturated ideal of a triangular system.

Let T = (F,H) be a triangular system. Denoting J=ideal(F), the saturated ideal of T is

sat(T) = J : h = {f: hk f ∈J for some h∈H, k∈ℕ }

i1 : R = QQ[a,b,c,d,e,f,g,h, MonomialOrder=>Lex];
i2 : F = {a*d - b*c, c*f - d*e, e*h - f*g};
i3 : H = {d, f, h};
i4 : T = triaSystem(R,F,H)

o4 = {a*d - b*c, c*f - d*e, e*h - f*g} / {d, f, h}

o4 : TriaSystem
i5 : saturate T

o5 = ideal (e*h - f*g, c*h - d*g, c*f - d*e, a*h - b*g, a*f - b*e, a*d - b*c)

o5 : Ideal of R

See also