linearlyNormalEmbedding -- get the linearly normal embedding

i1 : K = ZZ/333331;

i2 : X = PP_K^(1,7); -- rational normal curve of degree 7

o2 : ProjectiveVariety, curve in PP^7

i3 : time f = linearlyNormalEmbedding X;
 -- used 0.00799977s (cpu); 0.00776204s (thread); 0s (gc)

o3 : MultirationalMap (automorphism of X)

i4 : Y = (rationalMap {for i to 3 list random(1,ring ambient X)}) X; -- an isomorphic projection of X in PP^3

o4 : ProjectiveVariety, curve in PP^3

i5 : time g = linearlyNormalEmbedding Y;
 -- used 0.404337s (cpu); 0.319185s (thread); 0s (gc)

o5 : MultirationalMap (birational map from Y to curve in PP^7)

i6 : assert(isIsomorphism g)

i7 : describe g

o7 = multi-rational map consisting of one single rational map
     source variety: curve in PP^3 cut out by 6 hypersurfaces of degree 4
     target variety: curve in PP^7 cut out by 21 hypersurfaces of degree 2
     base locus: empty subscheme of PP^3
     dominance: true
     multidegree: {7, 7}
     degree: 1
     degree sequence (map 1/1): [3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]
     coefficient ring: K