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# projections -- projections of a multi-projective variety

- Usage:
    `projections X`
- Inputs:
  - X, a multi-projective variety, a subvariety of $\mathbb{P}^{k_1}\times\mathbb{P}^{k_2}\times\cdots\times\mathbb{P}^{k_n}$
- Outputs:
  - the list of the projections $X\to \mathbb{P}^{k_i}$, for $i=1,\ldots,n$

## Description

This function is intended for internal use. Use the projectionMaps function instead.

    i1 : X = projectiveVariety(ZZ/101[x_0..x_3]) ** projectiveVariety(ZZ/101[y_0..y_2]);

    o1 : ProjectiveVariety, PP^3 x PP^2

    i2 : projections X

    o2 = {-- rational map --                                              ,
                        ZZ                              ZZ
          source: Proj(---[x0 , x0 , x0 , x0 ]) x Proj(---[x1 , x1 , x1 ])
                       101   0    1    2    3          101   0    1    2
                        ZZ
          target: Proj(---[x , x , x , x ])
                       101  0   1   2   3
          defining forms: {
                           x0 ,
                             0

                           x0 ,
                             1

                           x0 ,
                             2

                           x0
                             3
                          }
         ------------------------------------------------------------------------
         -- rational map --                                              }
                       ZZ                              ZZ
         source: Proj(---[x0 , x0 , x0 , x0 ]) x Proj(---[x1 , x1 , x1 ])
                      101   0    1    2    3          101   0    1    2
                       ZZ
         target: Proj(---[y , y , y ])
                      101  0   1   2
         defining forms: {
                          x1 ,
                            0

                          x1 ,
                            1

                          x1
                            2
                         }

    o2 : List

## See also

- projectionMaps -- projections of a multi-projective variety

## Ways to use projections:

- `projections(MultiprojectiveVariety)`

## For the programmer

The object projections is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/MultiprojectiveVarieties.m2:2596:0.