The function computes the defining ideal of the multi-Rees algebra of a set of ideals over a polynomial ring by computing the saturation of a binomial ideal with respect to a polynomial. The technique is a generalization of a result of D. Cox, K.-i. Lin and G. Sosa for monomial ideals over a polynomial ring.
i1 : S = QQ[x_0..x_3] o1 = S o1 : PolynomialRing |
i2 : C = trim monomialCurveIdeal(S,{2,3,5}) 3 2 3 2 o2 = ideal (x x - x x , x - x x , x - x x ) 1 2 0 3 2 1 3 1 0 2 o2 : Ideal of S |
i3 : multiReesIdeal {C} 2 2 3 2 3 2 o3 = ideal (x X - x X - x X , x X - x X - x X , (x - x x )X + (- x + x x )X ) 2 1 1 2 3 3 1 1 0 2 2 3 1 0 2 2 2 1 3 3 o3 : Ideal of S[X ..X ] 1 3 |
i4 : multiReesIdeal {C,C} 2 2 2 2 o4 = ideal (X X - X X , X X - X X , X X - X X , x X - x X - x X , x X - x X - x X , x X - x X - x X , x X - x X - 3 5 2 6 3 4 1 6 2 4 1 5 2 4 1 5 3 6 1 4 0 5 2 6 2 1 1 2 3 3 1 1 0 2 ---------------------------------------------------------------------------------------------------------------------------- 3 2 3 2 3 2 3 2 x X , (x - x x )X + (- x + x x )X , (x - x x )X + (- x + x x )X ) 2 3 1 0 2 5 2 1 3 6 1 0 2 2 2 1 3 3 o4 : Ideal of S[X ..X ] 1 6 |
The object multiReesIdeal is a method function with options.