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

Synopsis

• 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

See also

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