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

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

Ways to use this method:

The source of this document is in MultiprojectiveVarieties.m2:4051:0.