AffineVariety ** AffineVariety -- Cartesian product of two affine varieties

Synopsis

• Usage:

  X ** Y

• Inputs:
  • X, an affine variety,
  • Y, an affine variety,
• Outputs:
  • an affine variety, the Cartesian product $X \times Y$

i1 : X = Spec QQ[x,y]

o1 = X

o1 : AffineVariety

i2 : Y = X ** X

o2 = Y

o2 : AffineVariety

i3 : describe Y

o3 = Spec(QQ[x , y , x , y ])
              0   0   1   1

Synopsis

• Usage:

  X ** R

• Inputs:
  • X, an affine variety,
  • R, a ring,
• Outputs:
  • an affine variety, the Cartesian product $X \times \mathrm{Spec} R$

i4 : Z = X ** QQ[t]

o4 = Z

o4 : AffineVariety

i5 : describe Z

o5 = Spec(QQ[x..y, t])

Cartesian products of non-affine varieties are not yet implemented in this package, but see cartesianProduct(NormalToricVariety) for another implementation.