productOfProjectiveSpaces -- Constructs the multi-graded ring of a product of copies of P^1 (pp is a synonym)

Synopsis

• Usage:

  R = productOfProjectiveSpaces L

  R = productOfProjectiveSpaces n

• Inputs:
  • L, a list, of positive integers, the dimensions of the projective spaces
  • n, an integer, positive integer, number of P¹ factors
• Optional inputs:
  • CoefficientField => a ring, default value ZZ/32003, the ground field
  • VariableName => a string, default value x, name of variable to use.
• Outputs:
  • R, a ring, ZZⁿ - graded

Description

i1 : R = productOfProjectiveSpaces{1,3}

o1 = R

o1 : PolynomialRing

i2 : v = gens R

o2 = {x   , x   , x   , x   , x   , x   }
       0,0   0,1   1,0   1,1   1,2   1,3

o2 : List

i3 : v/degree

o3 = {{1, 0}, {1, 0}, {0, 1}, {0, 1}, {0, 1}, {0, 1}}

o3 : List

i4 : gens productOfProjectiveSpaces({1,1}, VariableName => "y")

o4 = {y   , y   , y   , y   }
       0,0   0,1   1,0   1,1

o4 : List

i5 : gens productOfProjectiveSpaces 2

o5 = {x   , x   , x   , x   }
       0,0   0,1   1,0   1,1

o5 : List