smallDiagonal -- Ideal of the small diagonal in (P^1)^n

Synopsis

• Usage:

  I = smallDiagonal n

  I = smallDiagonal S

• Inputs:
  • n, an integer, number of factors of P^1
  • S, a ring, ring with 2n vars, corresponding to (P^1)^n for some n
• Outputs:
  • I, an ideal, ideal of the small diagonal

Description

i1 : smallDiagonal 3

o1 = ideal (- x   x    + x   x   , - x   x    + x   x   , - x   x    + x   x   )
               0,1 1,0    0,0 1,1     0,1 2,0    0,0 2,1     1,1 2,0    1,0 2,1

                ZZ
o1 : Ideal of -----[x   ..x   ]
              32003  0,0   2,1

i2 : S = productOfProjectiveSpaces 3

o2 = S

o2 : PolynomialRing

i3 : smallDiagonal S

o3 = ideal (- x   x    + x   x   , - x   x    + x   x   , - x   x    + x   x   )
               0,1 1,0    0,0 1,1     0,1 2,0    0,0 2,1     1,1 2,0    1,0 2,1

o3 : Ideal of S

See also

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