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# eagonNorthcottType -- Computes the Eagon-Northcott type resolution

- Usage:
    `resX=resCurveOnScroll(Phi,b)`
- Inputs:
  - Phi, a matrix, the matrix whose maximal minors define the scroll
  - b, an integer, the twist
- Outputs:
  - ENresolution, a chain complex, the Eagon-Northcott type resolution

## Description

This function computes the Eagon-Northcott type resolution associated to the matrix Phi defining the scroll and an integer b defining the twist $O_{P(E)}(bR)$. The way the function works is similar to the way the "Eagon-Northcott" function by Greg Smith works.

    i1 : R = ZZ/12347[x_0..x_7]

    o1 = R

    o1 : PolynomialRing

    i2 : Phi = matrix{{x_0..x_3},{x_4..x_7}}

    o2 = | x_0 x_1 x_2 x_3 |
         | x_4 x_5 x_6 x_7 |

                 2      4
    o2 : Matrix R  <-- R

    i3 : betti(eagonNorthcottType(Phi,0))

                0 1 2 3
    o3 = total: 1 6 8 3
             0: 1 . . .
             1: . 6 8 3

    o3 : BettiTally

    i4 : betti(eagonNorthcottType(Phi,1))

                0 1 2 3
    o4 = total: 2 4 4 2
             0: 2 4 . .
             1: . . 4 2

    o4 : BettiTally

## See also

- liftMatrixToEN -- Lifts a matrix between bundles on the scroll to the associated Eagon-Northcott type complexes
- iteratedCone -- Computes a (possibly non-minimal) resolution of C in P^{g-1} starting from the relative canonical resolution of C in P(E)

## Ways to use eagonNorthcottType:

- `eagonNorthcottType(Matrix,ZZ)`

## For the programmer

The object eagonNorthcottType is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/RelativeCanonicalResolution.m2:662:0.