map(RationalMap) -- get the ring map defining a rational map

Synopsis

Function: map
Usage:

map Phi
Inputs:
- Phi, a rational map
Optional inputs:
- Degree => ..., default value null,
- DegreeLift => ..., default value null,
- DegreeMap => ..., default value null,
Outputs:
- a ring map, the ring map from which the rational map Phi was defined

Description

i1 : QQ[t_0..t_3]

o1 = QQ[t ..t ]
         0   3

o1 : PolynomialRing

i2 : Phi = rationalMap {t_1^2+t_2^2+t_3^2,t_0*t_1,t_0*t_2,t_0*t_3}

o2 = -- rational map --
     source: Proj(QQ[t , t , t , t ])
                      0   1   2   3
     target: Proj(QQ[t , t , t , t ])
                      0   1   2   3
     defining forms: {
                       2    2    2
                      t  + t  + t ,
                       1    2    3
                      
                      t t ,
                       0 1
                      
                      t t ,
                       0 2
                      
                      t t
                       0 3
                     }

o2 : RationalMap (quadratic rational map from PP^3 to PP^3)

i3 : map Phi

                                    2    2    2
o3 = map (QQ[t ..t ], QQ[t ..t ], {t  + t  + t , t t , t t , t t })
              0   3       0   3     1    2    3   0 1   0 2   0 3

o3 : RingMap QQ[t ..t ] <-- QQ[t ..t ]
                 0   3          0   3

The command map Phi is equivalent to map(0,Phi). More generally, the command map(i,Phi) returns the i-th representative of the map Phi.

Ways to use this method: