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# multirationalMap(MultiprojectiveVariety,MultiprojectiveVariety) -- get the natural inclusion

- Function: multirationalMap
- Usage:
    `rationalMap(X,Y)`
    `multirationalMap(X,Y)`
- Inputs:
  - X, a multi-projective variety
  - Y, a multi-projective variety, with $X\subseteq Y$ (after identifying the ambient spaces)
- Outputs:
  - a multi-rational map, the natural inclusion of $X$ into $Y$

## Description

    i1 : R = ZZ/101[a_0,a_1,b_0..b_2,Degrees=>{2:{1,0},3:{0,1}}], S = ZZ/101[c_0,c_1,d_0..d_2,Degrees=>{2:{1,0},3:{0,1}}]

    o1 = (R, S)

    o1 : Sequence

    i2 : I = ideal (random({0,1},R),random({1,1},R)), J = sub(I,vars S)

    o2 = (ideal (24b  - 36b  - 30b , - 29a b  - 10a b  + 19a b  - 29a b  + 19a b
                    0      1      2       0 0      1 0      0 1      1 1      0 2
         ------------------------------------------------------------------------
         - 8a b ), ideal (24d  - 36d  - 30d , - 29c d  - 10c d  + 19c d  - 29c d
             1 2             0      1      2       0 0      1 0      0 1      1 1
         ------------------------------------------------------------------------
         + 19c d  - 8c d ))
              0 2     1 2

    o2 : Sequence

    i3 : X = projectiveVariety I, Y = projectiveVariety J

    o3 = (X, Y)

    o3 : Sequence

    i4 : rationalMap(X,ambient X);

    o4 : MultirationalMap (morphism from X to PP^1 x PP^2)

    i5 : rationalMap(X,Y);

    o5 : MultirationalMap (morphism from X to Y)

    i6 : stopIfError = false;

    i7 : rationalMap(ambient X,X)
    stdio:7:11:(3): error: not able to define a natural map between the two varieties

## See also

- ZZ _ MultiprojectiveVariety -- identity map

## Ways to use this method:

- multirationalMap(MultiprojectiveVariety,MultiprojectiveVariety) -- get the natural inclusion

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/MultiprojectiveVarieties.m2:3299:0.