Description
This function takes a polynomial ring in 4 variables over a field as the coordinate ring of P3 and creates a rational quartic surface with a double line as a
QuarticSurfaceRational in this ring. To do this We blow up P2 at 10 points, listed in BlowUpPoints, and map the blownup surface to P3. The map is specified as a rational map P2>P3 given in MapToP3.
Synopsis

 Usage:
X = quadricSurface(R)

Inputs:

Outputs:
i1 : X = quarticSurfaceRational(ZZ/32003[x,y,z,w])
4 3 2 2 3 4 3 2 2 3 2 2 2 2 2 3 3 3 2 2 3 2 2 2 2 2 2 2 2 2 2 2 3
o1 = ideal(x + 9724x y  14728x y + 4857x*y  3225y + 5278x z + 1636x y*z  5528x*y z + 1012y z  7898x z + 2192x*y*z + 8097y z  13288x*z  914y*z  813x w  12824x y*w  6277x*y w + 1492y w + 13647x z*w + 1491x*y*z*w + 12452y z*w  914x*z w + 9994y*z w  14516x w + 10106x*y*w + 14105y w  7003x*z*w + 6180y*z*w  6180x*w )
o1 : QuarticSurfaceRational
