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NormalToricVarieties :: normalToricVariety(Ring)

normalToricVariety(Ring) -- get the associated normal toric variety

Synopsis

Description

If a polynomial ring is constructed as the total coordinate ring of normal toric variety, then this method returns the associated variety.

i1 : PP3 = toricProjectiveSpace 3;
i2 : S = ring PP3

o2 = S

o2 : PolynomialRing
i3 : gens S

o3 = {x , x , x , x }
       0   1   2   3

o3 : List
i4 : degrees S

o4 = {{1}, {1}, {1}, {1}}

o4 : List
i5 : normalToricVariety S

o5 = PP3

o5 : NormalToricVariety
i6 : assert (PP3 === normalToricVariety S)
i7 : variety S

o7 = PP3

o7 : NormalToricVariety
i8 : assert (PP3 === variety S)

If the polynomial ring is not constructed from a variety, then this method produces an error: "no variety associated with ring".

i9 : S = QQ[x_0..x_2];
i10 : gens S

o10 = {x , x , x }
        0   1   2

o10 : List
i11 : degrees S

o11 = {{1}, {1}, {1}}

o11 : List
i12 : assert (try (normalToricVariety S; false) else true)
i13 : assert (try (variety S; false) else true)

Caveat

This methods does not determine if a ring could be realized as the total coordinate ring of a normal toric variety.

See also