Projective $d$-space is a smooth complete normal toric variety. The rays are generated by the standard basis $e_1, e_2, \dots,e_d$ of $\ZZ^d$ together with vector $-e_1-e_2-\dots-e_d$. The maximal cones in the fan correspond to the $d$-element subsets of $\{ 0,1, \dots,d\}$.
The examples illustrate the projective line and projective $3$-space.
i1 : PP1 = toricProjectiveSpace 1; |
i2 : rays PP1
o2 = {{-1}, {1}}
o2 : List
|
i3 : max PP1
o3 = {{0}, {1}}
o3 : List
|
i4 : dim PP1 o4 = 1 |
i5 : ring PP1
o5 = QQ[x ..x ]
0 1
o5 : PolynomialRing
|
i6 : ideal PP1
o6 = ideal (x , x )
1 0
o6 : Ideal of QQ[x ..x ]
0 1
|
i7 : assert (isWellDefined PP1 and isSmooth PP1 and isComplete PP1) |
i8 : PP3 = toricProjectiveSpace (3, CoefficientRing => ZZ/32003, Variable => y); |
i9 : rays PP3
o9 = {{-1, -1, -1}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
o9 : List
|
i10 : max PP3
o10 = {{0, 1, 2}, {0, 1, 3}, {0, 2, 3}, {1, 2, 3}}
o10 : List
|
i11 : dim PP3 o11 = 3 |
i12 : ring PP3
ZZ
o12 = -----[y ..y ]
32003 0 3
o12 : PolynomialRing
|
i13 : ideal PP3
o13 = ideal (y , y , y , y )
3 2 1 0
ZZ
o13 : Ideal of -----[y ..y ]
32003 0 3
|
i14 : assert (isWellDefined PP3 and isSmooth PP3 and isComplete PP3) |