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# super(RationalMap) -- get the rational map whose target is a projective space

- Function: super
- Usage:
    `super phi`
    `rationalMap(phi,Dominant=>null)`
    `rationalMap phi`
- Inputs:
  - phi, a rational map, whose target is a subvariety $Y\subset\mathbb{P}^n$
- Outputs:
  - a rational map, the composition of phi with the inclusion of $Y$ into $\mathbb{P}^n$

## Description

So that, for instance, if phi is a dominant map, then the code rationalMap(super phi,Dominant=>true) yields a map isomorphic to phi.

    i1 : phi = specialQuadraticTransformation 7;

    o1 : RationalMap (quadratic birational map from PP^8 to 8-dimensional subvariety of PP^10)

    i2 : phi' = super phi;

    o2 : RationalMap (quadratic rational map from PP^8 to PP^10)

    i3 : describe phi

    o3 = rational map defined by forms of degree 2
         source variety: PP^8
         target variety: complete intersection of type (2,2) in PP^10
         dominance: true
         birationality: true
         projective degrees: {1, 2, 4, 8, 16, 22, 20, 12, 4}
         number of minimal representatives: 1
         dimension base locus: 3
         degree base locus: 10
         coefficient ring: QQ

    i4 : describe phi'

    o4 = rational map defined by forms of degree 2
         source variety: PP^8
         target variety: PP^10
         image: complete intersection of type (2,2) in PP^10
         dominance: false
         birationality: false
         degree of map: 1
         projective degrees: {1, 2, 4, 8, 16, 22, 20, 12, 4}
         number of minimal representatives: 1
         dimension base locus: 3
         degree base locus: 10
         coefficient ring: QQ

    i5 : describe rationalMap(phi',Dominant=>true)

    o5 = rational map defined by forms of degree 2
         source variety: PP^8
         target variety: complete intersection of type (2,2) in PP^10
         dominance: true
         birationality: true
         projective degrees: {1, 2, 4, 8, 16, 22, 20, 12, 4}
         number of minimal representatives: 1
         dimension base locus: 3
         degree base locus: 10
         coefficient ring: QQ

## See also

- target(RationalMap) -- coordinate ring of the target for a rational map
- ambient -- ambient free module of a subquotient, or ambient ring
- super -- get the ambient module

## Ways to use this method:

- super(RationalMap) -- get the rational map whose target is a projective space

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Cremona/documentation.m2:590:0.