Compute the deformation associated to the unprojection of $I \subset J$ (or equivalently of $J'\subset R/I$ where $R$ = ring $I$ and $J'=$substitute$(J,R/I)$), i.e., a homomorphism
$\phi : J' \to R/I$
such that the unprojected ideal $U\subset R[T]$ is the inverse image of
$U' = (T*u - \phi(u) | u \in J' ) \subset (R/I)[T]$
under the natural map $R[T]\to(R/I)[T]$.
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 |
The object unprojectionHomomorphism is a method function.