homomorphism0 -- compute the homomorphism corresponding to an element in Hom0

i1 : kk=ZZ/10007;R=kk[y_0..y_2];

i3 : m=transpose random(R^{1,2},R^2);E=annihilator  coker m;

             2       2
o3 : Matrix R  <--- R

o4 : Ideal of R

i5 : (degree E, genus E) ==(3,1)

o5 = true

i6 : RE=R/E; M= coker m**RE; N=coker transpose m**RE;

i9 : betti(phi'= Hom0(M,N))

            0 1
o9 = total: 4 5
        -2: 2 .
        -1: 2 5

o9 : BettiTally

i10 : phi=homomorphism0(M,N,phi'_{1})

o10 = {-1} | -642y_0-2535y_1-2040y_2    1302y_1+4870y_2       |
      {-2} | y_1^2+4616y_1y_2+1975y_2^2 -4464y_1y_2+1432y_2^2 |

o10 : Matrix

i11 : degree coker phi

o11 = 5

i12 : betti M, betti N, betti Hom(M,N)

              0 1         0 1         0 1
o12 = (total: 2 2, total: 2 2, total: 2 2)
           0: 2 1     -2: 1 .     -1: 2 1
           1: . 1     -1: 1 2      0: . 1

o12 : Sequence

i13 : apply(4,i->hilbertFunction(i-2,Hom(M,N)))

o13 = {0, 2, 5, 8}

o13 : List