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NormalToricVarieties :: affineSpace

affineSpace -- make an affine space

Synopsis

Description

Affine d-space is a smooth normal toric variety. The rays are generated by the standard basis e1,…,ed of d and the maximal cone in the fan correspond to the d-element subset of {0,...,d-1}.

The examples illustrate the affine line and projective 3-space.

i1 : AA1 = affineSpace 1;
i2 : rays AA1

o2 = {{1}}

o2 : List
i3 : max AA1

o3 = {{0}}

o3 : List
i4 : dim AA1

o4 = 1
i5 : isComplete AA1

o5 = false
i6 : isSmooth AA1    

o6 = true
i7 : AA3 = affineSpace 3;
i8 : rays AA3

o8 = {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}

o8 : List
i9 : max AA3

o9 = {{0, 1, 2}}

o9 : List
i10 : dim AA3

o10 = 3
i11 : isComplete AA3    

o11 = false
i12 : isSmooth AA3    

o12 = true

See also

Ways to use affineSpace :