next | previous | forward | backward | up | top | index | toc | Macaulay2 web site

MatFac15 :: constructEx4

constructEx4 -- randomly choose a module N with Betti table as indicated in o4 below

Synopsis

Usage:
constructEx4(S)
Inputs:
- S, a polynomial ring, coordinate ring of P⁴
Outputs:
- a module, an S-module with desired betti numbers

Description

We follow the random construction of an element of the family from Thm 4.6 as explained in Matrix factorizations and families of curves of genus 15

i1 : kk=ZZ/10007;S=kk[x_0..x_4]

o2 = S

o2 : PolynomialRing

i3 : N=constructEx4(S);

i4 : betti res N

            0 1  2 3 4
o4 = total: 3 9 14 9 1
         0: 2 .  . . .
         1: 1 9  . . .
         2: . . 14 9 1

o4 : BettiTally

i5 : (M0,M1)=matrixFactorizationFromModule(N);

i6 : tangentKernelDimension(N,M0)==0

o6 = true

Ways to use `constructEx4` :

constructEx4(PolynomialRing)