canonical curves

# #MAPLE script 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
(versão .txt)
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):
######################################################################
############# Alguns setups e rotinas utilizadas
######################################################################
# dualrep(C) retorna a representação de C * ( = espaço vetorial #dual a C )
dualrep:= proc(C) local i;
sort(expand(subs( seq(x.i=x.i^(-1), i=0..n), C)))
end:
# prodwts(H) calcula o produto de todos os pesos da representação H
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) calcula o produto de todos os T-pesos da representação H
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) calcula a soma de todos os pesos da representação H
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) calcula a soma de todos os T-pesos da representação H
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 ) clacula o espaco tangente ( e o fibrado O(B') )
#blow up de X ao longo de 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] guarda o espaco tangente total
Tang_[2][i_]:=op(i_,N_):# Tang_[2] guarda a direcao normal
od:
Tang_[3]:=nops(N_):
Tang_[4]:=N_:
Tang_
end:
################ Aqui começa o cálculo efetivo
fp:= 0: pf:=0: ## fp contará o número de pontos fixos
## pf contará o número de P1's fixos
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):
# Primeiro calculamos para pontos fixos em X - Y , X = P(S3Fq) |P(S2F)
# onde Y = P3* x P(B) contido em X
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:
# Agora, calculamos para pontos fixos Y = P3* x P(B) contido em X
# Nesta etapa, explodimos X ao longo de Y e obtemos X1 ( E1 sera' o
# div. exc. )
# Guadamos os pontos pertecentes a Y1 contido em X1.
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]: # fator de tensorizacao H1*H2*Q
for i from 1 to Tang[3] do
chave:=true:
if ( member(T2[i]*H2*Q,{op(S3F)}) ) then # se a quartica fatora H1
if ( H1<>H2 ) then # usamos cont2
if ( member(Q/H1,{op(F)}) ) then
# como H1<>H2 a equacao da inter. de H1 e H2 em H2 eh H1 e 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 # usamos cont3
if ( member(T2[i]*H2*l2,{op(S2F)}) ) then
# se a quartica fatora H1 e 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:
# Agora, calculamos para pontos fixos 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)vira 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