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1440 J.M. Miret et al. / Journal of Symbolic Computation 44 (2009) 1425–1447

# PP is a projective bundle of planes over PU

# It has dimension 7 and its generating classes are b, m and p

# the later corresponds to the tautological

# "hyperplane" class of the bundle

PP=variety(7, {gcs=[b,m,p]});

# The table of monomial values of PP is computed as follows:

PP(monomial_values)=

{ m^i*b^j*p^(7-i-j) -> integral(m^i*b^j*segre(5-i-j,DP),PU)

with (i,j) in (0..3,0..min(3,5-i)) };

# Udp is the bundle Ud lifted to PP

Udp=sheaf(3,[m,m^2,m^3],PP);

# Qdp is the quotient of Udp by the line bundle of b on PP.

Qdp= Udp / o_(b,PP);

# Qqp is the quotient of Udp by Qdp

Qqp=Udp / Qdp;

# Enodp is Qqp twisted by 2m-p direct sum the third symmetric

# power of Qdp

Enodp=Qqp * o_(2*m-p,PP) + symm(3,Qdp);

# Dnodp is Enodp twisted by -3m

Dnodp= Enodp * o_(-3*m,PP);

# The table of monomial values of Knod, which is the table

# we were aiming at.

Knod(monomial_values)=

{ m^i*b^j*p^h*n^(11-i-j-h) ->

integral(m^i*b^j*p^h*segre(7-i-j-h,Dnodp),PP)

with (i,j,h) in (0..3,0..min(3,5-i),0..7-i-j) }

4.2. Intersection numbers on K z nod

# PP is a projective bundle of planes over PU

# It has dimension 7 and its generating classes are b, m and p

# Ud1 is the bundle Ud lifted to PP

Ud1=sheaf(3,[m,m^2,m^3],PP);

# Qd1 is the quotient of Ud1 by the line bundle of b on PP.

Qd1= Ud1 / o_(b,PP);

# Equot is the quotient of the third symmetric power of Qd1

# by Qd1 twisted by 2m-p

Equot = symm(3, Qd1) / (Qd1 * o_(2*m-p,PP));

# Dquot is Equot twisted by 2b-2p-m

Dquot= Equot * o_(2*b-2*p-m,PP);

# PZ is a projective bundle of planes over PP

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