# unprojectionHomomorphism -- Compute the homomorphism associated to an unprojection pair

## Synopsis

• Usage:
unprojectionHomomorphism(I,J)
• Inputs:
• Outputs:
• f,

## Description

Compute the deformation associated to the unprojection of I in J (or equivalently of J ⊂R/I where R=ring(I)), i.e., a homomorphism phi:J →R/I such that the unprojected ideal is given by the ideal

(T*u-phi(u)| u ∈J )

of R[T].

The result is represented by a matrix f with source(f) = image generators I and target(f) = cokernel generators I.

 ```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 : unprojectionHomomorphism(I,J) o4 = | x_1x_3 x_1x_4 x_2x_3 x_2x_4 | o4 : Matrix```