Compute the deformation associated to the unprojection of I ⊂J (or equivalently of J’⊂R/I where R = ring I and J’=substitute(J,R/I)), i.e., a homomorphism
φ: J’ →R/I
such that the unprojected ideal U⊂R[T] is the inverse image of
U’ = (T*u - φ(u) | u ∈J’ ) ⊂(R/I)[T]
under the natural map R[T]→(R/I)[T].
The result is represented by a matrix f with source f = J’ and target f = (R/I)1.
i1 : R = QQ[x_1..x_4,z_1..z_4, T] o1 = R o1 : PolynomialRing |
i2 : I = ideal(z_2*z_3-z_1*z_4,x_4*z_3-x_3*z_4,x_2*z_2-x_1*z_4,x_4*z_1-x_3*z_2,x_2*z_1-x_1*z_3)
o2 = ideal (z z - z z , x z - x z , x z - x z , x z - x z , x z - x z )
2 3 1 4 4 3 3 4 2 2 1 4 4 1 3 2 2 1 1 3
o2 : Ideal of R
|
i3 : J = ideal (z_1..z_4)
o3 = ideal (z , z , z , z )
1 2 3 4
o3 : Ideal of R
|
i4 : phi = unprojectionHomomorphism(I,J) o4 = | x_2x_4 x_2x_3 x_1x_4 x_1x_3 | o4 : Matrix |
i5 : S = ring target phi; |
i6 : I == ideal S o6 = true |
i7 : source phi
o7 = image | z_4 z_3 z_2 z_1 |
1
o7 : S-module, submodule of S
|
i8 : target phi
1
o8 = S
o8 : S-module, free
|