# abstractVariety(NormalToricVariety,AbstractVariety) -- make the corresponding abstract variety

## Description

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