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Schubert2 :: intersectionRing(AbstractVariety)

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

Synopsis

Description

i1 : intersectionRing PP'^3

               QQ[][H   , H   , H   , h]
                     1,1   1,2   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   , h]
                     1,1   1,2   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   , h]
                     1,1   1,2   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