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

- Function: components
- Usage:
    `components X`
- Inputs:
  - X, a normal toric variety,
- 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)

## See also

- cartesianProduct(Sequence) -- make the Cartesian product of normal toric varieties
- NormalToricVariety ** NormalToricVariety -- make the Cartesian product of two normal toric varieties
- components -- list the components of a direct sum

## Ways to use this method:

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

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/NormalToricVarieties/ToricVarietiesDocumentation.m2:959:0.