Given a (graded) ideal I in a (graded-)local ring (R,m), this function computes the bi-graded ring Gr_m(Gr_I(R)), presented as a quotient of a bigraded polynomial ring with variables names u and v. After being computed once, this ring is stored in the cache of I. This function is based on the method normalCone.
i1 : R = QQ[x,y] o1 = R o1 : PolynomialRing |
i2 : I = ideal"x2,xy"
2
o2 = ideal (x , x*y)
o2 : Ideal of R
|
i3 : A = grGr I o3 = A o3 : QuotientRing |
i4 : describe A
QQ[u ..v ]
0 1
o4 = -----------------------
2
(u v - u v , u , u u )
0 1 1 0 1 0 1
|
i5 : hilbertSeries A
2 3 2
1 - 2T - T T + T + T T
0 0 1 0 0 1
o5 = --------------------------
2 2
(1 - T ) (1 - T )
1 0
o5 : Expression of class Divide
|
The object grGr is a method function.