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intersectionRing(AbstractVariety) -- get the intersection ring of an abstract variety

Synopsis

Function: intersectionRing
Usage:

intersectionRing X
Inputs:
- X, an abstract variety,
Outputs:
- a ring, the intersection ring of $X$

Description

i1 : intersectionRing abstractProjectiveSpace' 3

                      QQ[][H   ..H   , h]
                            1,1   1,3
o1 = ----------------------------------------------------
     (- H    - h, - H    - H   h, - H    - H   h, -H   h)
         1,1         1,2    1,1      1,3    1,2     1,3

o1 : QuotientRing

The variables may not have been assigned their values in the intersection ring yet:

i2 : H_(1,1)

o2 = -h

                      QQ[][H   ..H   , h]
                            1,1   1,3
o2 : ----------------------------------------------------
     (- H    - h, - H    - H   h, - H    - H   h, -H   h)
         1,1         1,2    1,1      1,3    1,2     1,3

The function use will arrange for the assignment of values:

i3 : use ooo

                      QQ[][H   ..H   , h]
                            1,1   1,3
o3 = ----------------------------------------------------
     (- H    - h, - H    - H   h, - H    - H   h, -H   h)
         1,1         1,2    1,1      1,3    1,2     1,3

o3 : QuotientRing

i4 : H_(1,1), H_(1,2), H_(1,3)

           2    3
o4 = (-h, h , -h )

o4 : Sequence

See also

abstractProjectiveSpace' -- make a projective space
IntersectionRing -- a key used for storing the intersection ring in an abstract variety

Ways to use this method:

intersectionRing(AbstractVariety) -- get the intersection ring of an abstract variety