# 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, , 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