makeProductRing -- Makes the coordinate ring of a product of projective spaces.

• Usage:

  makeProductRing(n)

  makeProductRing(kk,n)

• Inputs:
  • n, a list, a list {n_1,...,n_m} of the dimensions of the m projective spaces in the product \PP^{n_1}x...x\PP^{n_m}.
  • kk, a ring, the coefficient ring to be used
• Outputs:
  • a ring, the graded coordinate ring of \PP^{n_1}x...x\PP^{n_m}.

i1 : R = makeProductRing(QQ,{3,4})

o1 = R

o1 : PolynomialRing

i2 : R = makeProductRing({3,4})

o2 = R

o2 : PolynomialRing

i3 : degrees R

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

o3 : List

i4 : gens R

o4 = {a, b, c, d, e, f, g, h, i}

o4 : List