MultiprojectiveVariety ** Ring -- change the coefficient ring of a multi-projective variety

Synopsis

• Operator: **

• Usage:

  X ** K

• Inputs:
  • X, a multi-projective variety, defined over a coefficient ring F
  • K, a ring, the new coefficient ring (which must be a field)
• Outputs:
  • a multi-projective variety, a multi-projective variety defined over K, obtained by coercing the coefficients of the multi-forms defining X into K

Description

It is necessary that all multi-forms in the old coefficient ring F can be automatically coerced into the new coefficient ring K.

i1 : use ring PP_QQ^{2,3};

i2 : X = projectiveVariety ideal(x1_2^2-x1_1*x1_3,x1_1*x1_2-x1_0*x1_3,x1_1^2-x1_0*x1_2,x0_1^2-x0_0*x0_2);

o2 : ProjectiveVariety, surface in PP^2 x PP^3

i3 : ideal X

              2                              2             2
o3 = ideal (x1  - x1 x1 , x1 x1  - x1 x1 , x1  - x1 x1 , x0  - x0 x0 )
              2     1  3    1  2     0  3    1     0  2    1     0  2

o3 : Ideal of QQ[x0 ..x0 , x1 ..x1 ]
                   0    2    0    3

i4 : K = ZZ/65521;

i5 : X' = X ** K;

o5 : ProjectiveVariety, surface in PP^2 x PP^3

i6 : ideal X'

              2                              2             2
o6 = ideal (x1  - x1 x1 , x1 x1  - x1 x1 , x1  - x1 x1 , x0  - x0 x0 )
              2     1  3    1  2     0  3    1     0  2    1     0  2

o6 : Ideal of K[x0 ..x0 , x1 ..x1 ]
                  0    2    0    3

See also

• coefficientRing(MultiprojectiveVariety) -- the coefficient ring of the variety
• MultirationalMap ** Ring -- change the coefficient ring of a multi-rational map