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2.2.22 Ring Mapping Example
If R is the current ring and E is an object in another ring, then the function Image may be used to map E into R by substituting polynomials from R for the indeterminates in E. (Also: see the command BringIn for a shortcut in certain cases.)

  Use S ::= QQ[a,b,c];
  I := Ideal(a^2+b^2,ab-c^2);
  Use R ::= QQ[x,y];  -- the current ring is R
  F := RMap(x+y,x-y,y^2); -- define a map F:S --> R sending a to x+y,
                          -- b to x-y, and c to y^2
  Image(I, F); -- the image of I under F
Ideal(2x^2 + 2y^2, -y^4 + x^2 - y^2)