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K3Carpets :: productOfProjectiveSpaces

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

Synopsis

Description

The variables are in 1+L_i -tuples, x_(0,i).. x_(L_i,i) with degree {0..0,1,0..0}, the 1 being in the i-th place.

i1 : R = productOfProjectiveSpaces{1,3}

o1 = R

o1 : PolynomialRing
i2 : v = gens R

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

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},symbol y)

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

o4 : List
i5 : gens productOfProjectiveSpaces 2

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

o5 : List

Ways to use productOfProjectiveSpaces :

For the programmer

The object productOfProjectiveSpaces is a method function with options.