# components(NormalToricVariety) -- list the factors in a product

## Synopsis

• Function: components
• Usage:
components X
• Inputs:
• Outputs:
• a list, of the factors from which the product was form or just \{X\} if X was not formed by a Cartesian product

## Description

The Cartesian product of varieties $X_0, X_1, X_2, ...$, all defined over the same ground field $k$, is the fiber product $X_0 \times_k X_1 \times_k X_2 \times_k ...$. 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)

The factors are cached and can be accessed with components.

 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)