# flatten(RationalMap) -- write source and target as nondegenerate varieties

## Synopsis

• Function: flatten
• Usage:
flatten phi
• Inputs:
• phi,
• Outputs:
• , a rational map isomorphic to the original map, flattened in the sense that the ideals of source and target contain no linear forms

## Description

 i1 : P5 = QQ[t_0..t_5]; phi = rationalMap(P5/(35*t_1+45*t_2+21*t_3+525*t_4+1365*t_5,1575*t_0*t_2-3250*t_2^2+735*t_0*t_3-1890*t_2*t_3-1666*t_3^2+17150*t_0*t_4-47250*t_2*t_4-22050*t_3*t_4-276850*t_4^2+46550*t_0*t_5-122850*t_2*t_5-57330*t_3*t_5-1433250*t_4*t_5-1864450*t_5^2),P5/(315*t_0+280*t_1+45*t_2+21*t_3+210*t_4+1050*t_5),{-45*t_2-21*t_3-490*t_4-1330*t_5, 45*t_2+21*t_3+525*t_4+1365*t_5, 35*t_2, 35*t_3, 35*t_4, 35*t_5}); o2 : RationalMap (linear rational map from threefold in PP^5 to hypersurface in PP^5) i3 : describe phi o3 = rational map defined by forms of degree 1 source variety: smooth complete intersection of type (1,2) in PP^5 target variety: hyperplane in PP^5 coefficient ring: QQ i4 : psi = flatten phi; o4 : RationalMap (linear rational map from hypersurface in PP^4 to PP^4) i5 : describe psi o5 = rational map defined by forms of degree 1 source variety: smooth quadric hypersurface in PP^4 target variety: PP^4 coefficient ring: QQ