Given f : X →Y ⊂PN, this returns the defining ideal of f(x) ⊆PN. It should be noted for inputs that all rings are quotients of polynomial rings, and all ideals and ring maps are of these. In particular, this function returns an ideal defining a subset of the the ambient projective space of the image. In the following example we consider the image of P1 inside P1 ×P1.
i1 : S = QQ[x,y,z,w]; |
i2 : b = ideal(x*y-z*w); o2 : Ideal of S |
i3 : R = QQ[u,v]; |
i4 : a = ideal(sub(0,R)); o4 : Ideal of R |
i5 : f = matrix {{u,0,v,0}}; 1 4 o5 : Matrix R <--- R |
i6 : idealOfImageOfMap(a,b,f) o6 = ideal (w, y) o6 : Ideal of S |