- Usage:
`X ^** i`

- Operator: ^**
- Inputs:
`X`, a normal toric variety`i`, an integer

- Outputs:
- a normal toric variety, the
`i`-ary Cartesian product of`X`with itself

- a normal toric variety, the

The *i*-ary Cartesian product of the variety *X*, defined over the ground field *k*, is the *i*-ary fiber product of *X* with itself over *k*. For a normal toric variety, the fan of the *i*-ary Cartesian product is given by the *i*-ary Cartesian product of the cones.

i1 : PP2 = toricProjectiveSpace 2; |

i2 : X = PP2 ^** 4; |

i3 : fromWDivToCl X o3 = | 1 1 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 1 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 1 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 1 1 | 4 12 o3 : Matrix ZZ <--- ZZ |

i4 : FF2 = hirzebruchSurface (2); |

i5 : Y = FF2 ^** 3; |

i6 : fromWDivToCl Y o6 = | 1 -2 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 -2 1 0 0 0 0 0 | | 0 0 0 0 0 1 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 -2 1 0 | | 0 0 0 0 0 0 0 0 0 1 0 1 | 6 12 o6 : Matrix ZZ <--- ZZ |

i7 : X' = PP2 ** PP2; |

i8 : X'' = PP2 ^** 2; |

i9 : assert (rays X' == rays X'' and max X' == max X'') |

- Making normal toric varieties
- NormalToricVariety ** NormalToricVariety -- make the Cartesian product of normal toric varieties
- normalToricVariety -- make a normal toric variety