# #MAPLE script designed to compute the number 67841053579508
# #of canonical curves in P^3 incident to 24 general lines
# #adapted by A. Meireles from a script by P. Meurer ,
# #The number of rational quartics on Calabi-Yau hypersurfaces in
# weighted
# #projective space $\ps{2,1^4}$} Math. Scandin, #78, 63-83 1996,
# #alg-geom/9409001

 n:=3;
 d1:= (n+2)*(n+1)/2 -1; d2:= (n+3)*(n+2)*(n+1)/6 -(n+1) -1; d:=d1+d2;
 xx:= seq(x.i, i=0..n);
 ww:= seq(w.i, i=0..n);
 sf:=proc(vars,d) local i;
 coeff(expand(series(product( (1/(1-t*vars[i])),i=1..nops(vars)
 ),t=0,d+1)),t^d)
 end:
 F:=sf([xx],1); S2F:=sf([xx],2): S3F:=sf([xx],3): S4F:=sf([xx],4):
 S5F:=sf([xx],5): S6F:=sf([xx],6):
 ######################################################################
 #############      some useful procedures        #############
 ######################################################################
# dual representation
 dualrep:= proc(C) local i;
   sort(expand(subs( seq(x.i=x.i^(-1), i=0..n), C)))
 end:
 # prodwts(H) product of all weights
 prodwts:= proc(H) local t, cof, mon, res, i;
   cof:= [coeffs(H, [seq(x.i, i=0..n)],'mon' )]:
   mon:= subs(seq(x.i=t^w.i, i=0..n),[mon]):
   res:=1:
   for i from 1 to nops(mon) do
     res:= res*subs(t=1,diff(mon[i],t))^cof[i]:
 od:end:
#  Tprodwts(H)product of all T-weights
 Tprodwts:= proc(H) local u, cof, mon, res, i; global t;
   cof:= [coeffs(H, [seq(x.i, i=0..n)],'mon' )]:
   mon:= subs(seq(x.i=u^w.i, i=0..n),[mon]):
   res:=1:
   for i from 1 to nops(mon) do
     res:= res*(t+subs(u=1,diff(mon[i],u)))^cof[i]:
   od:
 end:
 #  sumwts(H) sum of weights
 sumwts:= proc(H) local t, cof, mon, res, i;
   cof:= [coeffs(H, [seq(x.i, i=0..n)],'mon' )]:
   mon:= subs(seq(x.i=t^w.i, i=0..n), [mon]):
   res:=0:
   for i from 1 to nops(mon) do
     res:= res+subs(t=1,diff(mon[i],t))*cof[i]:
   od:
 end:
 #  Tsumwts(H) sum of T-weights
 Tsumwts:= proc(H) local u, cof, mon, res, i; global t;
   cof:= [coeffs(H, [seq(x.i, i=0..n)],'mon' )]:
   mon:= subs(seq(x.i=u^w.i, i=0..n), [mon]):
   res:=0:
   for i from 1 to nops(mon) do
     res:= res+(-t+subs(u=1,diff(mon[i],u)))*cof[i]:
od:end:
 # Blow_up(TB , TX ) tangent space and O_B(1)
 #blow up of X along B
 Blow_up:=proc(TB_,TX_) local Tang_, i_,ii_, N_, TL_, TPN_;
   N_:=expand(TX_-TB_):
   for i_ from 1 to nops(N_) do
     TL_:=op(i_,N_): TL_:=TL_/subs(seq(x.ii_=1,ii_=0..n),TL_):
     TPN_:=expand( (N_-TL_)/TL_ ):
     Tang_[1][i_]:= expand(TB_ + (TL_) + TPN_):
# Tang_[1] stores the total tangent  space
     Tang_[2][i_]:=op(i_,N_):# Tang_[2] stores  normal direction
   od:
   Tang_[3]:=nops(N_):
   Tang_[4]:=N_:
   Tang_
 end:
 ################ actual computation starts here
 fp:= 0: pf:=0:      ## fp counts the number of fixpts
             ## pf number of fixed P1's
 cont1:=0:cont2:=0:cont3:=0:cont4:=0:cont5:=0:cont6:=0:cont7:=0: cont8:=0:
 for j from 1 to nops(S2F) do
 quad:=op(j,S2F):
 S3Fq:= expand(S3F - quad*F):
 for k from 1 to nops(S3Fq) do
 cub:=op(k,S3Fq):
 # fixpts on X - Y ,  X = P(S3Fq) |P(S2F)
 # here  Y = P3* x P(B)
 chave:=false:
 for i from 0 to n do
   if ( member(quad/x.i,{op(F)}) and member(cub/x.i,{op(S2F)}) ) then
 chave:=true: H:=x.i: fi:
 od:
 if ( chave ) then
    cont1:=cont1+1:
    Aux1[cont1]:=[ H, quad , cub , (S2F-quad)/quad + (S3Fq -
 cub)/cub ]:
 else
    fp:=fp+1:
    A[fp]:=1/quad:
    B[fp]:=1/cub:
    idd[fp]:=[ quad , cub ]:
    T[fp]:=expand( (S2F-quad)/quad + (S3Fq - cub)/cub ):
    E1[fp]:=1:  E2[fp]:=1:
    E3[fp]:=1:  E4[fp]:=1:
    E5[fp]:=1:  #E6[fp]:=1: E7[fp]:=1:
    FF:={op(expand(idd[fp][1]*S5F)), op(expand(idd[fp][2]*S4F))}:
 fi:od:od:
# Now fixpts on Y = P3* x P(B) # At this point one has X^1 --> X, 1st blowup

 # Store fixpts of Y1
 for j from 1 to cont1 do
  H1:=Aux1[j][1]:
  H2:=Aux1[j][2]/H1:
  Q:=Aux1[j][3]/H1:
  l1:=op(1,Q):
  l2:=Q/l1:
  Tang:=Blow_up( (F-H1)/H1 + (F-H2)/H2 + (S2F -H2*F -Q)/Q ,
 Aux1[j][4] ):
  T1:=Tang[1]:
  T2:=Tang[2]:    # for tensor product  H1*H2*Q
  for i from 1 to Tang[3] do
    chave:=true:
    if ( member(T2[i]*H2*Q,{op(S3F)}) ) then # if the quartic factors H1
      if ( H1<>H2 ) then   # use cont2
        if ( member(Q/H1,{op(F)}) )  then
 # since H1<>H2 the intersect of H1 , H2 in H2 is H1 and l2=Q/H1
          chave:=false:
          cont2:=cont2+1:
          Aux2[cont2]:=[ H1, H2 , Q/H1 , T2[i]*H2*H1 , T1[i] ,
 T2[i] ]:
        fi:
      else # H1=H2   # use cont3
        if ( member(T2[i]*H2*l2,{op(S2F)}) ) then
          # if the quartic  factors H1 and l1
          chave:=false:
          cont3:=cont3+1:
          Aux3[cont3]:=[ H1,l1,l2,T2[i]*H2*l2,T1[i],T2[i] ]:
        elif ( member(T2[i]*H2*l1,{op(S2F)}) ) then
          # se a quartica fatora H1 e l2
          chave:=false:
          cont3:=cont3+1:
          Aux3[cont3]:=[ H1,l2,l1,T2[i]*H2*l1,T1[i],T2[i] ]:
      fi:fi:
      if (chave and (H1=H2) ) then
        chave:=false:
        cont5:=cont5+1:
        C:=T2[i]*H2*Q:
        Aux5[cont5]:=[ H1 ,l1,l2 ,C ,0, 0,0,
        expand( (F-H1)/H1+(S2F-H1*F-Q)/Q
                +( (S3F-H1*S2F)-Q*(F-H1)-C)/C ),
                T1[i], T2[i] ,1,1 ,1]:
        Ideal5[cont5]:=[H1*H2, H1*l1*l2, H1*C, 0, 0]:
      fi:fi:
    if (chave) then
      fp:=fp+1:
      A[fp]:=1/(H1*H2):
      B[fp]:=1/(H1*Q):
      idd[fp]:=[ H1*H2,H1*Q,T2[i]*H1*H2*Q ]:
      T[fp]:=T1[i]:
      E1[fp]:=T2[i]:
      E2[fp]:=1:  E3[fp]:=1:
      E4[fp]:=1:  E5[fp]:=1:
      #E6[fp]:=1:  E7[fp]:=1:
      FF:={op(expand(idd[fp][1]*S5F)),
 op(expand(idd[fp][2]*S4F)), op(expand(idd[fp][3]*S3F))}:
fi:od:od:
 # time now for fixpts Y1
 for j from 1 to cont2 do
  H1:=Aux2[j][1]:
  H2:=Aux2[j][2]:
  K:=Aux2[j][3]:
  Q:=Aux2[j][4]:
  Tang:=Blow_up( (F-H2)/H2 + (F-H2-K)/K + (F-H2-H1)/H1 +
     (S2F+H1*H2-H1*F-H2*F-Q)/Q +H2/H1,Aux2[j][5] ):
  T1:=Tang[1]:
  T2:=Tang[2]:
  for i from 1 to Tang[3] do
    chave:=true:
    if ( member(T2[i]*Q*H2*K,{op(S4F)}) and (H1=K) and (
 T2[i]=Q/(H2*K) ) )then
      chave:=false:
      cont6:=cont6+1:
      TY2_8:= (F-H2-H1)*dualrep(H1+H2) + H1/H2 +H2/H1 +
 (S2F-H1*F-H2*F+H1*H2-Q)/Q :
      Aux6[cont6]:=[ H1, H2, K, Q, T2[i]*Q*H2*K, 0, TY2_8, T1[i],
 Aux2[j][6], T2[i], 1,1]:
    fi:
    if chave then
      fp:=fp+1:
      A[fp]:=1/(H1*H2):
      B[fp]:=1/(H1*H1*K):
      idd[fp]:=[ H1*H2,H1*H1*K,H1*K*Q, T2[i]*H1*H2*K*Q ]:
      T[fp]:=T1[i]:
      E1[fp]:=Aux2[j][6]:
      E2[fp]:=T2[i]:
      E3[fp]:=1:  E4[fp]:=1:
      E5[fp]:=1:  #E6[fp]:=1: E7[fp]:=1:
      FF:={op(expand(idd[fp][1]*S5F)),
 op(expand(idd[fp][2]*S4F)),
          op(expand(idd[fp][3]*S3F)),
 op(expand(idd[fp][4]*S2F))}:
fi od od:
 for j from 1 to cont3 do
  H:=Aux3[j][1]:
  l:=Aux3[j][2]: m:=Aux3[j][3]:
  Q:=Aux3[j][4]: p:=op(1,Q): q:=Q/p:
  Tang:=Blow_up( (F-H)/H + (F-H-l)/l + (F-H-m)/m + (S2F+m*H-m*F -
 H*F-Q)/Q + m/H,Aux3[j][5] ):
  T1:=Tang[1]:
  T2:=Tang[2]:
  for i from 1 to Tang[3] do
    chave:=true:
    if ( member(T2[i]*l*m*p*q,{op(S4F)}) ) then
      if ( l=m ) then
        if ( member(T2[i]*m*p,{op(S2F)})  ) then
          chave:=false:
          cont4:=cont4+1:
          Aux4[cont4]:=[H,l,m,p,q,T2[i]*m*p,T1[i],Aux3[j][6],T2[i]]:
        elif ( (p<>q) and member(T2[i]*m*q,{op(S2F)})  ) then
          chave:=false:
          cont4:=cont4+1:
          Aux4[cont4]:=[H,l,m,q,p,T2[i]*m*q,T1[i],Aux3[j][6],T2[i]]:
        fi:
      else # l<>m
        if ( (p=l) and member(T2[i]*m*p,{op(S2F)}) ) then
          chave:=false:
          cont4:=cont4+1:
          Aux4[cont4]:=[H,l,m,p,q,T2[i]*m*p,T1[i],Aux3[j][6],T2[i]]:
        elif ( (q=l) and (q<>p) and member(T2[i]*m*q,{op(S2F)})) then
          chave:=false:
          cont4:=cont4+1:
          Aux4[cont4]:=[H,l,m,q,p,T2[i]*m*q,T1[i],Aux3[j][6],T2[i]]:
      fi:fi:
      if chave then
        chave:=false:
        Tb:= (F-H)/H+(F-H-m)/m+(F-H-l)/l+(S2F-H*F-m*F+H*m-Q)/Q:
        TY1_14:=(F-H)/H+(S2F-H*F-l*m)/(l*m)+
         ((S3F-H*S2F)-l*m*(F-H)-l*Q)/(l*Q):
        N_T:= TY1_14-Tb:
        TP_N:=expand((N_T-T2[i])/T2[i]):
        TY2_14:= T2[i]+Tb+TP_N:
        cont5:=cont5+1:
Aux5[cont5]:=[H,l,m,p,q,T2[i]*l*m*p*q,0,TY2_14,T1[i],Aux3[j][6],T2[i],1,1]:
        Ideal5[cont5]:=[H^2,H*l*m,H*l*p*q, H*T2[i]*l*m*p*q, 0]:
    fi:fi:
    if (chave) then
      fp:=fp+1:
      A[fp]:=1/(H*H):
      B[fp]:=1/(H*l*m):
      idd[fp]:=[ H^2,H*l*m,H*l*Q, T2[i]*H*l*m*p*q ]:
      T[fp]:=T1[i]:
      E1[fp]:=Aux3[j][6]:
      E2[fp]:=T2[i]:
      E3[fp]:=1:  E4[fp]:=1:
      E5[fp]:=1:  #E6[fp]:=1: E7[fp]:=1:

      FF:={op(expand(idd[fp][1]*S5F)),
 op(expand(idd[fp][2]*S4F)),op(expand(idd[fp][3]*S3F)),
 op(expand(idd[fp][4]*S2F))}:
fi:od:od:
 for j from 1 to cont4 do
 H:=Aux4[j][1]:
 l:=Aux4[j][2]: m:=Aux4[j][3]:
 p:=Aux4[j][4]: q:=Aux4[j][5]: Q:=Aux4[j][6]:
 Tang:=Blow_up( expand( (F-H)/H + (F-H-m)/m + (F-H-m-p)/p +(m+p-l)/l +
 (F-H-m-q)/q ),Aux4[j][7] ):
 T1:=Tang[1]:
 T2:=Tang[2]:
 for i from 1 to Tang[3] do
 chave:=true:
 if ( member(T2[i]*m*p*q*Q,{op(S5F)}) ) then
    cont5:=cont5+1:
    chave:=false:
Tb:=expand((F-H)/H+(F-H-m)/m+(F-H-l)/l+(S2F-H*F-m*F+H*m-p*q)/(p*q)):
     TY1_14:=expand( (F-H)/H +(S2F-H*F-l*m)/(l*m)
     +((S3F-H*S2F)-l*m*(F-H)-l*p*q)/(l*p*q) ):
     N_T:=expand(TY1_14-Tb):
     TP_N:=expand(N_T-Aux4[j][9])/Aux4[j][9]:
     TY2_14:=expand(Aux4[j][9]+Tb+TP_N):
     Tb:=expand((F-H)/H+(F-H-m)/m+(F-H-m-p)/p+(m+p-l)/l+(F-H-m-q)/q):
     N_T:=expand(TY2_14-Tb):
     TP_N:=expand(N_T-T2[i])/T2[i]:
     TY3_14:=expand(T2[i]+Tb+TP_N):
     Aux5[cont5]:=[H,l,m,p,q,Q*l*p,T2[i]*m*p*q*Q,TY3_14,
      T1[i],Aux4[j][8],Aux4[j][9],T2[i],1]:
     Ideal5[cont5]:=[H^2,H*l*m,H*l*p*q,H*l*q*Q,H*T2[i]*m*p*q*Q,0]:
 fi:
 if (chave) then
 fp:=fp+1:
 A[fp]:=1/(H*H):
 B[fp]:=1/(H*l*m):
 idd[fp]:=[ H^2,H*l*m,H*l*p*q, H*p*q*Q, T2[i]*H*m*q*p*Q ]:
 T[fp]:=T1[i]:
 E1[fp]:=Aux4[j][8]:
 E2[fp]:=Aux4[j][9]:
 E3[fp]:=T2[i]:
 E4[fp]:=1:  E5[fp]:=1:
 #E6[fp]:=1:  E7[fp]:=1:
 FF:={op(expand(idd[fp][1]*S5F)), op(expand(idd[fp][2]*S4F)),
 op(expand(idd[fp][3]*S3F)),
 op(expand(idd[fp][4]*S2F)),op(expand(idd[fp][5]*F))}:
 fi:od:od:
 print('fp'=fp, 'cont5'=cont5);
 for j from 1 to cont5 do
 H:=Aux5[j][1]:
 l:=Aux5[j][2]: m:=Aux5[j][3]:
 p:=Aux5[j][4]: q:=Aux5[j][5]: Q:=Aux5[j][6]:
 Tang:=Blow_up( Aux5[j][8], Aux5[j][9] ):
 T1:=Tang[1]:
 T2:=Tang[2]:
 for i from 1 to Tang[3] do
 T3:=subs(seq(x.ii=1,ii=0..n),T2[i]):
 if T3=1 then chave:=false else chave:=true fi:
 if (chave) then
        cont6:=cont6+1:
        TY4_8:=(F-H-l)*dualrep(l+H)+2*l/H+(S2F-l*F-H*F+l*H-p*q)/(p*q):
        Aux6[cont6]:=[H,H,l,p*q,(p*q)^2,0,TY4_8,
         T1[i],Aux5[j][10],Aux5[j][11],Aux5[j][12],T2[i]/T3,1, 1]:
 pf:=pf+1:
 AA[pf]:=1/(H*H):
 BB[pf]:=1/(H*l*m):
 idd1[pf]:=[ 1/A[pf],1/B[pf],H*l*Q, T2[i]*H*m*q*p*Q ]:
 TInt:=expand( (F-H-l)*dualrep(l+H) + l/H + (S2F-l*F-H*F+l*H-p*q)/(p*q)
 ): # Y4_8 inter Y4_14
 NInt:=expand(Aux5[j][8]-TInt):
 TB[pf]:=TInt:
 TL[pf]:=T2[i]/T3:
 TN1[pf]:=NInt:
 TN2[pf]:=expand(T1[i]+1-T3-TB[pf]-TL[pf]-NInt):
 EE1[pf]:=Aux5[j][10]:
 EE2[pf]:=Aux5[j][11]:
 EE3[pf]:=Aux5[j][12]:
 EE4[pf]:=T2[i]/T3:  EE5[pf]:=1:
 #EE6[pf]:=1:  EE7[pf]:=1:
 else
 if l=m then
 g2:=Ideal5[j][3]/(l*H): h3:=Ideal5[j][4]/(l*H):
 q4:=Ideal5[j][2]*Ideal5[j][3]/H*Aux5[j][11]*Aux5[j][12]*T2[i]/l^2:
 R10:={op(expand(l^2*(S2F-H*F))),op(expand(l*g2*(F-H) )), l*h3,g2^2}:
 if (member(q4,R10) and member(g2,{op(expand(S2F-H*F-l*F+l*H))}) and
 member(h3,{op(S3F)}) and (member(Ideal5[j][5]/(H*l),{op(S4F)}) or
 Ideal5[j][5]=0) ) then
 chave:=true:
 R10:=convert(convert(R10,list),`+`):
 cont7:=cont7+1:
 TY17_5:=expand( (F-H)/H + (F-H-l)/l + (S2F-l*F-H*F+H*l-g2)/g2 + (
 sf([op(expand(F-H-l))],3)-g2*(F-H-l)-h3)/h3 + (R10-q4)/q4) :
 Aux7[cont7]:=[ H, l, g2, h3, q4, TY17_5, T1[i], Aux5[j][10],
 Aux5[j][11], Aux5[j][12], T2[i], 1]:
 Ideal7[cont7]:=op(Ideal5[j]) :
 fi:
 else # l<>m
 q4:=Ideal5[j][2]*Ideal5[j][3]/H*Aux5[j][11]*Aux5[j][12]*T2[i]/l^2:
 V10:={op(expand(m*l*(S2F-H*F))),op(expand(m^2*(S2F-H*F) )), l^4}:
 if ( member(q4,V10) and Ideal5[j][3]=H*l^3 and
 member(Ideal5[j][4]/(H*l^2),{op(S2F)}) and (
 member(Ideal5[j][5]/(H*l),{op(S4F)}) ) ) then
 chave:=true:
 V10:=convert(convert(V10,list),`+`):
 cont8:=cont8+1:
 TY16_5:=expand( (F-H)/H + (F-H-l)/l + (F-H-m)/m + (V10-q4)/q4) :
 Aux8[cont8]:=[ H,l,m, l, q4, TY16_5, T1[i], Aux5[j][10],
 Aux5[j][11], Aux5[j][12], T2[i], 1,1]:
 Ideal8[cont8]:=[op(1..5,Ideal5[j]), q4*l^2 ] :
 fi:fi:fi:
 if not(chave) then
 fp:=fp+1:
 A[fp]:=1/(H*H):
 B[fp]:=1/(H*l*m):
 idd[fp]:=[ 1/A[fp],1/B[fp],H*l*Q, T2[i]*H*m*q*p*Q ]:
 T[fp]:=T1[i]:
 E1[fp]:=Aux5[j][10]:
 E2[fp]:=Aux5[j][11]:
 E3[fp]:=Aux5[j][12]:
 E4[fp]:=T2[i]:  E5[fp]:=1:
 #E6[fp]:=1:  E7[fp]:=1:
 fi:od:od:
 for j from 1 to cont6 do
 H1:=Aux6[j][1]:
 H2:=Aux6[j][2]: K:=Aux6[j][3]:
 Q:=Aux6[j][4]:
 Tang:=Blow_up( Aux6[j][7], Aux6[j][8] ):
 T1:=Tang[1]:
 T2:=Tang[2]:
 for i from 1 to Tang[3] do
 chave:=true:
 if T2[i]=1 then chave:=false: fi:
 if (chave) then
 fp:=fp+1:
 A[fp]:=1/(H1*H2):
 B[fp]:=1/(H1*K^2):
 idd[fp]:=[ 1/A[fp],1/B[fp],H1*K*Q, T2[i]*H1*H2*Q^2 ]:
 T[fp]:=T1[i]:
 E1[fp]:=Aux6[j][9]:
 E2[fp]:=Aux6[j][10]:
 E3[fp]:=Aux6[j][11]:
 E4[fp]:=Aux6[j][12]:
 E5[fp]:=T2[i]:
 #E6[fp]:=1:  E7[fp]:=1:
 fi:od:od:
 print('fp'=fp);
 cont7;
 for j from 1 to cont7 do
 H:=Aux7[j][1]:
 l:=Aux7[j][2]: g2:=Aux7[j][3]:
 h3:=Aux7[j][4]: q4:=Aux7[j][5]:
 Tang:=Blow_up( Aux7[j][6], Aux7[j][7] ):
 T1:=Tang[1]:
 T2:=Tang[2]:
 for i from 1 to Tang[3] do
 T3:=subs(seq(x.ii=1,ii=0..n),T2[i]):
 if T3=1 then chave:=false else chave:=true fi:
 if (chave) then
        cont8:=cont8+1: lp:=op(1,g2):
        TY6_16:= Aux7[j][6] - (S2F-l*F-H*F+H*l-g2)/g2 +lp/l :
        Aux8[cont8]:=[H,l,l,lp, q4, TY6_16,
 T1[i],Aux7[j][8],Aux7[j][9],Aux7[j][10],Aux7[j][11],Aux7[j][12],
 T2[i]/T3]:
 pf:=pf+1:
 AA[pf]:=1/(H*H):
 BB[pf]:=1/(H*l^2):
 NInt:=expand( (S2F-l*F-H*F+H*l-g2)/g2 ):
 TInt:=expand( Aux7[j][6] - NInt ): # Y5_16 inter Y5_17
 TB[pf]:=TInt:
 TL[pf]:=T2[i]/T3:
 TN1[pf]:=NInt:
 TN2[pf]:=expand(T1[i]+1-T3-TB[pf]-TL[pf]-NInt):
 EE1[pf]:=Aux7[j][8]:
 EE2[pf]:=Aux7[j][9]:
 EE3[pf]:=Aux7[j][10]:
 EE4[pf]:=Aux7[j][11]:  EE5[pf]:=Aux7[j][12]:
 #EE6[pf]:=T2[i]/T3:  EE7[pf]:=1:
 else
 fp:=fp+1:
 A[fp]:=1/(H*H):
 B[fp]:=1/(H*l^2):
 idd[fp]:=[ 1/A[fp],1/B[fp],H*l*Q, T2[i]*H*m*q*p*Q ]:
 T[fp]:=T1[i]:
 E1[fp]:=Aux7[j][8]:
 E2[fp]:=Aux7[j][9]:
 E3[fp]:=Aux7[j][10]:
 E4[fp]:=Aux7[j][11]:
 E5[fp]:=Aux7[j][12]:
 #E6[fp]:=T2[i]:  E7[fp]:=1:
 fi:od:od:
 for j from 1 to cont8 do
 H:=Aux8[j][1]:
 l:=Aux8[j][2]: m:=Aux8[j][3]:
 lp:=Aux8[j][4]: q4:=Aux8[j][5]:
 Tang:=Blow_up( Aux8[j][6], Aux8[j][7] ):
 T1:=Tang[1]:
 T2:=Tang[2]:
 for i from 1 to Tang[3] do
 chave:=true:
 if T2[i]=1 then chave:=false: fi:
 if (chave) then
 fp:=fp+1:
 A[fp]:=1/(H^2):
 B[fp]:=1/(H*l*m):
# idd[fp]:=[ 1/A[fp],1/B[fp],H1*K*Q, T2[i]*H1*H2*Q^2 ]:
 T[fp]:=T1[i]:
 E1[fp]:=Aux8[j][8]:
 E2[fp]:=Aux8[j][9]:
 E3[fp]:=Aux8[j][10]:
 E4[fp]:=Aux8[j][11]:
 E5[fp]:=Aux8[j][12]:
 #E6[fp]:=Aux8[j][13]: E7[fp]:=T2[i]:
 fi:od:od:
 print('fp'=fp,'pf'=pf);
# save fp,pf, #
AA,BB,EE1,EE2,EE3,EE4,EE5,E1,E2,E3,E4,E5,TN1,TL,TB,TN2,T,A,B,`dados.m`;
#read(`\\andre\\can\\dados.m`);
 wg := [w0 = -2, w1 = 3, w2 = 41, w3 = 119];
 for i from 1 to pf do
den[i]:=subs(wg,subs(t=-t,Tprodwts(TN1[i]+TL[i]))*prodwts(TB[i]+TN2[i])):
 f1[i]:=subs(wg,sumwts(AA[i])):
 f2[i]:=subs(wg,sumwts(BB[i])):
 e1[i]:=subs(wg,sumwts(EE1[i])):
 e2[i]:=subs(wg,sumwts(EE2[i])):
 e3[i]:=subs(wg,sumwts(EE3[i])):
 e4[i]:=subs(wg,Tsumwts(EE4[i])):
 e5[i]:=subs(wg,subs(t=-t,Tsumwts(EE5[i]))):#O(-1) becomes O(1)em P1~
 #e6[i]:=subs(wg,sumwts(EE6[i])):
 #e7[i]:=subs(wg,sumwts(EE7[i])):
 od:
 for i from 1 to fp do if i mod 1000=1 then print(i)fi :
 den[i+pf]:=subs(wg,prodwts(T[i])): f1[i+pf]:=subs(wg,sumwts(A[i])
 ):
 f2[i+pf]:=subs(wg,sumwts(B[i])):
 e1[i+pf]:=subs(wg,sumwts(E1[i])):
 e2[i+pf]:=subs(wg,sumwts(E2[i])):
 e3[i+pf]:=subs(wg,sumwts(E3[i])):
 e4[i+pf]:=subs(wg,sumwts(E4[i])):
 e5[i+pf]:=subs(wg,sumwts(E5[i])):
 # e6[i+pf]:=subs(wg,sumwts(E6[i])):
 # e7[i+pf]:=subs(wg,sumwts(E7[i])):
 od:
# save n,d,d1,d2,fp,pf,den,f1,f2,e1,e2,e3,e4,e5,`dados1.m`: # save
n,d,d1,d2,fp,pf,den,f1,f2,e1,e2,e3,e4,e5,`dados1.txt`:
 f:=0:
 for j from 1 to fp do if j mod 1000=1 then print(fp-j)fi:
 h:= 3*f1[j+pf]+2*f2[j+pf] -e1[j+pf] -e2[j+pf] -e3[j+pf] -e4[j+pf]
     -e5[j+pf]: # -e6[j+pf] -e7[j+pf]:
 f:=f+((h)^d)/den[j+pf]:
 od:
 #print(f);
 g:=f:
 for j from 1 to pf do if j mod 50=1 then print(pf-j)fi:
 h:=3*f1[j]+2*f2[j]-e1[j]-e2[j]-e3[j]-e4[j]-e5[j]:
 g:=g+coeff(series(((h)^d)/den[j],t=0,2),t):
 od:
 print(g);
#> ifactor(67841053579508); #> kernelopts(cputime);#pentium300mhz #1132.114