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RationalMaps :: idealOfImageOfMap

idealOfImageOfMap -- Finds defining equations for the image of a rational map between varieties or schemes

Synopsis

Description

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

Ways to use idealOfImageOfMap :