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# forceImage(MultirationalMap,MultiprojectiveVariety) -- declare which is the image of a multi-rational map

- Function: forceImage
- Usage:
    `forceImage(Phi,Y)`
- Inputs:
  - Phi, a multi-rational map
  - Y, a multi-projective variety
- Outputs:
  - null

## Description

This method allows to inform the system about the image of a given multi-rational map without performing any computation. In particular, this can be used to declare that a rational map is dominant.

    i1 : Phi = rationalMap {minors(3,(PP_(ZZ/65521)([6],2)).matrix)};

    o1 : MultirationalMap (rational map from PP^6 to PP^9)

    i2 : Y = image(Phi,2)

    o2 = Y

    o2 : ProjectiveVariety, 6-dimensional subvariety of PP^9

    i3 : forceImage(Phi,Y)

    i4 : image Phi

    o4 = Y

    o4 : ProjectiveVariety, 6-dimensional subvariety of PP^9

    i5 : Psi = rationalMap({minors(3,(PP_(ZZ/65521)([6],2)).matrix)},Dominant=>2);

    o5 : MultirationalMap (rational map from PP^6 to 6-dimensional subvariety of PP^9)

    i6 : forceImage(Psi,target Psi)

    i7 : Psi;

    o7 : MultirationalMap (dominant rational map from PP^6 to 6-dimensional subvariety of PP^9)

## Caveat

If the declaration is false, nonsensical answers may result.

## See also

- image(MultirationalMap) -- image of a multi-rational map
- forceImage(RationalMap,Ideal) -- declare which is the image of a rational map

## Ways to use this method:

- forceImage(MultirationalMap,MultiprojectiveVariety) -- declare which is the image of a multi-rational map
- `forceImage(MultirationalMap,ZZ)`

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/MultiprojectiveVarieties.m2:4051:0.