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forceImage -- declare which is the image of a rational map

Description

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

i1 : P6 = QQ[t_0..t_6]; X = minors(3,matrix{{t_0..t_4},{t_1..t_5},{t_2..t_6}});

o2 : Ideal of P6
 
i3 : Phi = rationalMap(X,Dominant=>2);

o3 : RationalMap (cubic rational map from PP^6 to 6-dimensional subvariety of PP^9)
 
i4 : time forceImage(Phi,ideal 0_(target Phi))
 -- used 0.00100049s (cpu); 0.000772239s (thread); 0s (gc)
 
i5 : Phi;

o5 : RationalMap (cubic 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 forceImage:

  • forceImage(RationalMap,Ideal)

For the programmer

The object forceImage is a method function.

The source of this document is in Cremona/documentation.m2:1012:0.