This method converts a NormalToricVariety into an AbstractVariety, as defined in the Schubert2 package.
Since many routines from the Schubert2 package have been overloaded so that they apply directly to normal toric varieties, this method is primarily of interest to developers.
Projective space can be constructed as an AbstractVariety in a few equivalent, but not identical, ways.
i1 : tPP2 = toricProjectiveSpace 2; |
i2 : aPP2 = abstractVariety tPP2 o2 = aPP2 o2 : an abstract variety of dimension 2 |
i3 : assert (dim tPP2 === dim aPP2) |
i4 : intersectionRing aPP2
QQ[][t ..t ]
0 2
o4 = ------------------------------
(t t t , - t + t , - t + t )
0 1 2 0 1 0 2
o4 : QuotientRing
|
i5 : intersectionRing tPP2
QQ[][t ..t ]
0 2
o5 = ------------------------------
(t t t , - t + t , - t + t )
0 1 2 0 1 0 2
o5 : QuotientRing
|
i6 : intersectionRing abstractVariety (tPP2, base())
QQ[][t ..t ]
0 2
o6 = ------------------------------
(t t t , - t + t , - t + t )
0 1 2 0 1 0 2
o6 : QuotientRing
|
i7 : intersectionRing abstractVariety (tPP2, base(a))
QQ[a][t ..t ]
0 2
o7 = ------------------------------
(t t t , - t + t , - t + t )
0 1 2 0 1 0 2
o7 : QuotientRing
|
i8 : PP2 = toricProjectiveSpace 2 o8 = PP2 o8 : NormalToricVariety |
i9 : intersectionRing PP2
QQ[][t ..t ]
0 2
o9 = ------------------------------
(t t t , - t + t , - t + t )
0 1 2 0 1 0 2
o9 : QuotientRing
|
i10 : minimalPresentation intersectionRing PP2
QQ[t ]
2
o10 = ------
3
t
2
o10 : QuotientRing
|
i11 : minimalPresentation intersectionRing tPP2
QQ[t ]
2
o11 = ------
3
t
2
o11 : QuotientRing
|