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NormalToricVarieties :: cartesianProduct(Sequence)

cartesianProduct(Sequence) -- make the Cartesian product of normal toric varieties

Synopsis

Description

The Cartesian product of varieties X0, X1, X2, …, all defined over the same ground field k, is the fiber product X0 ×k X1 ×k X2 ×k. For normal toric varieties, the fan of the product is given by the Cartesian product of the underlying fans of the factors.

i1 : X = toricProjectiveSpace 1;
i2 : Y = toricProjectiveSpace 2;
i3 : Z = toricProjectiveSpace 3;
i4 : Seq = (X, Y, Z);
i5 : P = cartesianProduct Seq;
i6 : dim P

o6 = 6
i7 : assert (dim P == 1+2+3)
i8 : factors = components P

o8 = {X, Y, Z}

o8 : List
i9 : # factors

o9 = 3
i10 : assert (factors#0 === X and factors#1 === Y and factors#2 === Z)

This general method for constructing products is invoked by all of the other product constructors.

See also