verifyAllAssertionsOfThePaper -- Print the commands needed to verify all assertions

i1 : kk=ZZ/10007

o1 = kk

o1 : QuotientRing

i2 : verifyAllAssertionsOfThePaper kk

    ///
    x := symbol x
    -- kk = ZZ/10007
    S := kk[x_0..x_2] -- coordinate ring of P^2
    (I,Q,pencil) := randomCurveOfGenus9WithPencilOfDegree8 S;
    I
    (degree I, codim I) == (8,1)
    ordinaryDoublePoints I  
    (degree Q, codim Q) == (8,2)
    singI = saturate(ideal jacobian I + I)
    betti res singI
    betti res singI == betti res randomPlanePoints(12,S)
    (degree singI, codim singI) == (12,2)
    distinctPoints singI
    dim (singI+Q) == 0
    R := ideal pencil:intersect(singI,Q)
    (degree R, codim R) == (5,2)
    dim (I+R) == 0
    distinctPoints ideal pencil
    g := genus I - degree singI
    degrees pencil
    d = degree I * (degrees pencil)_1_0_0 - 2* degree singI - degree Q
    --Riemann-Hurwitz
    r := 2*g-2 +2*d
    r == 32
    (ans,b) := simpleRamification(I,pencil)
    ans and degree b == r
    cb = decompose b
    tally apply(cb,c->degree c)
    sum(cb,c->degree c) == 32
    ///