# quarticSurfaceRational -- creates a QuarticSurfaceRational

## 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

 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