grGr -- the bigraded ring Gr_m(Gr_I(R))

Synopsis

Usage:

grGr(I)
Inputs:
- m, an ideal, (assumed to be the irrelevant ideal of R, if not specified)
- I, an ideal,
Outputs:
- a ring, the bigraded ring Gr_m(Gr_I(R))

Description

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

Ways to use grGr :

grGr(Ideal)
grGr(Ideal,Ideal)

For the programmer

The object grGr is a method function.

grGr -- the bigraded ring Gr_m(Gr_I(R))

Synopsis

Description

See also

Ways to use grGr :

For the programmer