schemeInProduct -- multi-graded Ideal of the image of a map to a product of projective spaces

Synopsis

• Usage:

  J = schemeInProduct(I,maps,PP)

  J = schemeInProduct(I,maps,X)

• Inputs:
  • I, an ideal, defining the source scheme
  • maps, a list, list of sequences of polynomials each of a single degree, in I
  • PP, a ring, multigraded ring of the product of projective spaces
  • X, a symbol, name of variable to use in constructing a ring PP if none is given
• Outputs:
  • J, an ideal, multi-graded ideal of the image

Description

i1 : S = ZZ/101[a,b]

o1 = S

o1 : PolynomialRing

i2 : I = ideal 0_S

o2 = ideal 0

o2 : Ideal of S

i3 : f0 = matrix"a,b"

o3 = | a b |

             1       2
o3 : Matrix S  <--- S

i4 : f1 = matrix"a,b"

o4 = | a b |

             1       2
o4 : Matrix S  <--- S

i5 : maps = {f0,f1}

o5 = {| a b |, | a b |}

o5 : List

i6 : schemeInProduct(I, maps, Y)
warning: clearing value of symbol X to allow access to subscripted variables based on it
       : debug with expression   debug 1308   or with command line option   --debug 1308

o6 = ideal(X   X    - X   X   )
            1,0 0,1    0,0 1,1

               ZZ
o6 : Ideal of ---[X   , X   , X   , X   , a..b]
              101  0,0   1,0   0,1   1,1

See also

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