//----------------------------------------Calculating the Picard-Fuchs equation------------------------
//----------------------ring r------------------------

> pfe;
pfe[1,1]=-24/(625*z^4-625*z^3)
pfe[1,2]=(-24*z+5)/(5*z^4-5*z^3)
pfe[1,3]=(-72*z+35)/(5*z^3-5*z^2)
pfe[1,4]=(-8*z+6)/(z^2-z)
pfe[1,5]=-1


> print(gm);
0,      1,      0,      0,              
0,      0,      1,      0,              
0,      0,      0,      1,              
gm[4,1],gm[4,2],gm[4,3],(-8*z+6)/(z^2-z)
> gm;
gm[1,1]=0
gm[1,2]=1
gm[1,3]=0
gm[1,4]=0
gm[2,1]=0
gm[2,2]=0
gm[2,3]=1
gm[2,4]=0
gm[3,1]=0
gm[3,2]=0
gm[3,3]=0
gm[3,4]=1
gm[4,1]=-24/(625*z^4-625*z^3)
gm[4,2]=(-24*z+5)/(5*z^4-5*z^3)
gm[4,3]=(-72*z+35)/(5*z^3-5*z^2)
gm[4,4]=(-8*z+6)/(z^2-z)

//----------------------------------------Calculating the Gauss-Manin in t_0,t_4 parameter--------------
//-----------------------ring r1------------------------------------

print(gm);
-1/(5*t(4))*x(4),gm[1,2],         0,               0,      
0,               -2/(5*t(4))*x(4),gm[2,3],         0,      
0,               0,               -3/(5*t(4))*x(4),gm[3,4],
gm[4,1],         gm[4,2],         gm[4,3],         gm[4,4] 
> gm;
gm[1,1]=-1/(5*t(4))*x(4)
gm[1,2]=x(0)+(-t(0))/(5*t(4))*x(4)
gm[1,3]=0
gm[1,4]=0
gm[2,1]=0
gm[2,2]=-2/(5*t(4))*x(4)
gm[2,3]=x(0)+(-t(0))/(5*t(4))*x(4)
gm[2,4]=0
gm[3,1]=0
gm[3,2]=0
gm[3,3]=-3/(5*t(4))*x(4)
gm[3,4]=x(0)+(-t(0))/(5*t(4))*x(4)
gm[4,1]=(-t(0))/(t(0)^5-t(4))*x(0)+(t(0)^2)/(5*t(0)^5*t(4)-5*t(4)^2)*x(4)
gm[4,2]=(-15*t(0)^2)/(t(0)^5-t(4))*x(0)+(3*t(0)^3)/(t(0)^5*t(4)-t(4)^2)*x(4)
gm[4,3]=(-25*t(0)^3)/(t(0)^5-t(4))*x(0)+(5*t(0)^4)/(t(0)^5*t(4)-t(4)^2)*x(4)
gm[4,4]=(-10*t(0)^4)/(t(0)^5-t(4))*x(0)+(6*t(0)^5+4*t(4))/(5*t(0)^5*t(4)-5*t(4)^2)*x(4)






//------------------------------Calculating the intersection matrix in de Rham cohomology of the family W(t_0,t_4)------------
//-----------------ring r2---------------------------------------

> print(F);
0,     0,     0,     F[1,4],
0,     0,     F[2,3],F[2,4],
0,     F[3,2],0,     F[3,4],
F[4,1],F[4,2],F[4,3],0      
> F;
F[1,1]=0
F[1,2]=0
F[1,3]=0
F[1,4]=-1/(625*t(0)^5-625*t(4))
F[2,1]=0
F[2,2]=0
F[2,3]=1/(625*t(0)^5-625*t(4))
F[2,4]=(-t(0)^4)/(125*t(0)^10-250*t(0)^5*t(4)+125*t(4)^2)
F[3,1]=0
F[3,2]=-1/(625*t(0)^5-625*t(4))
F[3,3]=0
F[3,4]=(t(0)^3)/(125*t(0)^10-250*t(0)^5*t(4)+125*t(4)^2)
F[4,1]=1/(625*t(0)^5-625*t(4))
F[4,2]=(t(0)^4)/(125*t(0)^10-250*t(0)^5*t(4)+125*t(4)^2)
F[4,3]=(-t(0)^3)/(125*t(0)^10-250*t(0)^5*t(4)+125*t(4)^2)
F[4,4]=0
> 


//----------------------------Calculating the Gauss-Manin in t_0,t_1,t_2,t_3,t_4 paramers----------
//-------------ring r25----------------------------


> print(Sb);
1,      0,      0,      0,
Sb[2,1],Sb[2,2],0,      0,
Sb[3,1],Sb[3,2],Sb[3,3],0,
0,      0,      0,      1 
> Sb;
Sb[1,1]=1
Sb[1,2]=0
Sb[1,3]=0
Sb[1,4]=0
Sb[2,1]=(-t(0)^4-1/3125*t(3))
Sb[2,2]=(1/5*t(0)^5-1/5*t(4))
Sb[2,3]=0
Sb[2,4]=0
Sb[3,1]=(-14/5*t(0)^8+1/15625*t(0)^5*t(2)-1/625*t(0)^4*t(3)-1/5*t(0)^3*t(4)-1/15625*t(2)*t(4)-2/9765625*t(3)^2)
Sb[3,2]=(3/5*t(0)^9+2/15625*t(0)^5*t(3)-3/5*t(0)^4*t(4)-2/15625*t(3)*t(4))
Sb[3,3]=(1/25*t(0)^10-2/25*t(0)^5*t(4)+1/25*t(4)^2)
Sb[3,4]=0
Sb[4,1]=0
Sb[4,2]=0
Sb[4,3]=0
Sb[4,4]=1







> Ravec;
Ravec[1,1]=(6/5*t(0)^5+1/3125*t(0)*t(3)-1/5*t(4))
Ravec[1,2]=(-125*t(0)^6+t(0)^4*t(1)+125*t(0)*t(4)+1/3125*t(1)*t(3))
Ravec[1,3]=(-1875*t(0)^7-1/5*t(0)^5*t(1)+2*t(0)^4*t(2)+1875*t(0)^2*t(4)+1/5*t(1)*t(4)+2/3125*t(2)*t(3))
Ravec[1,4]=(-3125*t(0)^8-1/5*t(0)^5*t(2)+3*t(0)^4*t(3)+3125*t(0)^3*t(4)+1/5*t(2)*t(4)+3/3125*t(3)^2)
Ravec[1,5]=(5*t(0)^4*t(4)+1/625*t(3)*t(4))
> 



> print(gmRa);
0,1,        0,        0,        
0,0,        1,        0,        
0,gmRa[3,2],gmRa[3,3],gmRa[3,4],
0,0,        0,        0         
> gmRa;
gmRa[1,1]=0
gmRa[1,2]=1
gmRa[1,3]=0
gmRa[1,4]=0
gmRa[2,1]=0
gmRa[2,2]=0
gmRa[2,3]=1
gmRa[2,4]=0
gmRa[3,1]=0
gmRa[3,2]=(-72/5*t(0)^8-24/3125*t(0)^4*t(3)-3/5*t(0)^3*t(4)-2/1953125*t(3)^2)
gmRa[3,3]=(12*t(0)^4+2/625*t(3))
gmRa[3,4]=(-1/78125*t(0)^10+2/78125*t(0)^5*t(4)-1/78125*t(4)^2)
gmRa[4,1]=0
gmRa[4,2]=0
gmRa[4,3]=0
gmRa[4,4]=0




> gm;
gm[1,1]=(3125*t(0)^4+t(3))/(625*t(0)^5-625*t(4))*x(0)+(-3750*t(0)^5-t(0)*t(3)+625*t(4))/(3125*t(0)^5*t(4)-3125*t(4)^2)*x(4)
gm[1,2]=5/(t(0)^5-t(4))*x(0)+(-t(0))/(t(0)^5*t(4)-t(4)^2)*x(4)
gm[1,3]=0
gm[1,4]=0
gm[2,1]=(-9765625*t(0)^8-625*t(0)^5*t(2)-3125*t(0)^4*t(3)+9765625*t(0)^3*t(4)+625*t(2)*t(4)-t(3)^2)/(1953125*t(0)^5-1953125*t(4))*x(0)-1/3125*x(3)+(9765625*t(0)^9+625*t(0)^6*t(2)+5625*t(0)^5*t(3)-9765625*t(0)^4*t(4)-625*t(0)*t(2)*t(4)+t(0)*t(3)^2-2500*t(3)*t(4))/(9765625*t(0)^5*t(4)-9765625*t(4)^2)*x(4)
gm[2,2]=(-9375*t(0)^4-3*t(3))/(625*t(0)^5-625*t(4))*x(0)+(11250*t(0)^5+3*t(0)*t(3)-1875*t(4))/(3125*t(0)^5*t(4)-3125*t(4)^2)*x(4)
gm[2,3]=5/(t(0)^5-t(4))*x(0)+(-t(0))/(t(0)^5*t(4)-t(4)^2)*x(4)
gm[2,4]=0
gm[3,1]=(-87890625000*t(0)^12+390625*t(0)^10*t(1)-3906250*t(0)^9*t(2)-48828125*t(0)^8*t(3)+84228515625*t(0)^7*t(4)-781250*t(0)^5*t(1)*t(4)-625*t(0)^5*t(2)*t(3)+3906250*t(0)^4*t(2)*t(4)-15625*t(0)^4*t(3)^2+19531250*t(0)^3*t(3)*t(4)+3662109375*t(0)^2*t(4)^2+390625*t(1)*t(4)^2+625*t(2)*t(3)*t(4)-2*t(3)^3)/(6103515625*t(0)^5-6103515625*t(4))*x(0)+(1/15625*t(0)^5-1/15625*t(4))*x(2)+(-3/3125*t(0)^4-2/9765625*t(3))*x(3)+(87890625000*t(0)^13-390625*t(0)^11*t(1)+2734375*t(0)^10*t(2)+72265625*t(0)^9*t(3)-84228515625*t(0)^8*t(4)+781250*t(0)^6*t(1)*t(4)+625*t(0)^6*t(2)*t(3)-1562500*t(0)^5*t(2)*t(4)+20625*t(0)^5*t(3)^2-42968750*t(0)^4*t(3)*t(4)-3662109375*t(0)^3*t(4)^2-390625*t(0)*t(1)*t(4)^2-625*t(0)*t(2)*t(3)*t(4)+2*t(0)*t(3)^3-1171875*t(2)*t(4)^2-5000*t(3)^2*t(4))/(30517578125*t(0)^5*t(4)-30517578125*t(4)^2)*x(4)
gm[3,2]=(-121093750*t(0)^8+1250*t(0)^5*t(2)-68750*t(0)^4*t(3)-25390625*t(0)^3*t(4)-1250*t(2)*t(4)-8*t(3)^2)/(1953125*t(0)^5-1953125*t(4))*x(0)+2/3125*x(3)+(121093750*t(0)^9-1250*t(0)^6*t(2)+63750*t(0)^5*t(3)+25390625*t(0)^4*t(4)+1250*t(0)*t(2)*t(4)+8*t(0)*t(3)^2+5000*t(3)*t(4))/(9765625*t(0)^5*t(4)-9765625*t(4)^2)*x(4)
gm[3,3]=(15625*t(0)^4+3*t(3))/(625*t(0)^5-625*t(4))*x(0)+(-11250*t(0)^5-3*t(0)*t(3)-4375*t(4))/(3125*t(0)^5*t(4)-3125*t(4)^2)*x(4)
gm[3,4]=(-1/15625*t(0)^5+1/15625*t(4))*x(0)+(t(0)^6-t(0)*t(4))/(78125*t(4))*x(4)
gm[4,1]=(-19140625*t(0)^11+6250*t(0)^9*t(1)-3125*t(0)^8*t(2)-6250*t(0)^7*t(3)+18750000*t(0)^6*t(4)+2*t(0)^5*t(1)*t(3)-t(0)^5*t(2)^2-6250*t(0)^4*t(1)*t(4)+5*t(0)^4*t(2)*t(3)+18750*t(0)^3*t(2)*t(4)-5*t(0)^3*t(3)^2-9375*t(0)^2*t(3)*t(4)+390625*t(0)*t(4)^2-2*t(1)*t(3)*t(4)+t(2)^2*t(4))/(625*t(0)^10-1250*t(0)^5*t(4)+625*t(4)^2)*x(0)+x(1)+(3125*t(0)^4+t(3))/(625*t(0)^5-625*t(4))*x(2)+(-3125*t(0)^3-t(2))/(625*t(0)^5-625*t(4))*x(3)+(19140625*t(0)^12-7500*t(0)^10*t(1)-6250*t(0)^9*t(2)+18750*t(0)^8*t(3)-18750000*t(0)^7*t(4)-2*t(0)^6*t(1)*t(3)+t(0)^6*t(2)^2+8750*t(0)^5*t(1)*t(4)-4*t(0)^5*t(2)*t(3)-9375*t(0)^4*t(2)*t(4)+5*t(0)^4*t(3)^2-3125*t(0)^3*t(3)*t(4)-390625*t(0)^2*t(4)^2+2*t(0)*t(1)*t(3)*t(4)-t(0)*t(2)^2*t(4)-1250*t(1)*t(4)^2-t(2)*t(3)*t(4))/(3125*t(0)^10*t(4)-6250*t(0)^5*t(4)^2+3125*t(4)^3)*x(4)
gm[4,2]=(-87890625000*t(0)^12+390625*t(0)^10*t(1)-3906250*t(0)^9*t(2)-48828125*t(0)^8*t(3)+84228515625*t(0)^7*t(4)-781250*t(0)^5*t(1)*t(4)-625*t(0)^5*t(2)*t(3)+3906250*t(0)^4*t(2)*t(4)-15625*t(0)^4*t(3)^2+19531250*t(0)^3*t(3)*t(4)+3662109375*t(0)^2*t(4)^2+390625*t(1)*t(4)^2+625*t(2)*t(3)*t(4)-2*t(3)^3)/(78125*t(0)^15-234375*t(0)^10*t(4)+234375*t(0)^5*t(4)^2-78125*t(4)^3)*x(0)+5/(t(0)^5-t(4))*x(2)+(-9375*t(0)^4-2*t(3))/(125*t(0)^10-250*t(0)^5*t(4)+125*t(4)^2)*x(3)+(87890625000*t(0)^13-390625*t(0)^11*t(1)+2734375*t(0)^10*t(2)+72265625*t(0)^9*t(3)-84228515625*t(0)^8*t(4)+781250*t(0)^6*t(1)*t(4)+625*t(0)^6*t(2)*t(3)-1562500*t(0)^5*t(2)*t(4)+20625*t(0)^5*t(3)^2-42968750*t(0)^4*t(3)*t(4)-3662109375*t(0)^3*t(4)^2-390625*t(0)*t(1)*t(4)^2-625*t(0)*t(2)*t(3)*t(4)+2*t(0)*t(3)^3-1171875*t(2)*t(4)^2-5000*t(3)^2*t(4))/(390625*t(0)^15*t(4)-1171875*t(0)^10*t(4)^2+1171875*t(0)^5*t(4)^3-390625*t(4)^4)*x(4)
gm[4,3]=(9765625*t(0)^8+625*t(0)^5*t(2)+3125*t(0)^4*t(3)-9765625*t(0)^3*t(4)-625*t(2)*t(4)+t(3)^2)/(25*t(0)^15-75*t(0)^10*t(4)+75*t(0)^5*t(4)^2-25*t(4)^3)*x(0)+25/(t(0)^10-2*t(0)^5*t(4)+t(4)^2)*x(3)+(-9765625*t(0)^9-625*t(0)^6*t(2)-5625*t(0)^5*t(3)+9765625*t(0)^4*t(4)+625*t(0)*t(2)*t(4)-t(0)*t(3)^2+2500*t(3)*t(4))/(125*t(0)^15*t(4)-375*t(0)^10*t(4)^2+375*t(0)^5*t(4)^3-125*t(4)^4)*x(4)
gm[4,4]=(-3125*t(0)^4-t(3))/(625*t(0)^5-625*t(4))*x(0)+(3750*t(0)^5+t(0)*t(3)-625*t(4))/(3125*t(0)^5*t(4)-3125*t(4)^2)*x(4)






//---------------------------------------------Introducing the parameters t_5 and t_6--------------------
//---------------------------ring r3-------------------------------------

> Ravec*t(5);
_[1,1]=(6/5*t(0)^5+1/3125*t(0)*t(3)-1/5*t(4))
_[1,2]=(-125*t(0)^6+t(0)^4*t(1)+125*t(0)*t(4)+1/3125*t(1)*t(3))
_[1,3]=(-1875*t(0)^7-1/5*t(0)^5*t(1)+2*t(0)^4*t(2)+1875*t(0)^2*t(4)+1/5*t(1)*t(4)+2/3125*t(2)*t(3))
_[1,4]=(-3125*t(0)^8-1/5*t(0)^5*t(2)+3*t(0)^4*t(3)+3125*t(0)^3*t(4)+1/5*t(2)*t(4)+3/3125*t(3)^2)
_[1,5]=(5*t(0)^4*t(4)+1/625*t(3)*t(4))
_[1,6]=(t(6))
_[1,7]=(-72/5*t(0)^8*t(5)-24/3125*t(0)^4*t(3)*t(5)+12*t(0)^4*t(6)-3/5*t(0)^3*t(4)*t(5)-2/1953125*t(3)^2*t(5)+2/625*t(3)*t(6))


> print(gmRa);
0,1,0,                                            0, 
0,0,(t(0)^10-2*t(0)^5*t(4)+t(4)^2)/(78125*t(5)^3),0, 
0,0,0,                                            -1,
0,0,0,                                            0  





> gm;
gm[1,1]=(3125*t(0)^4+t(3))/(625*t(0)^5-625*t(4))*x(0)+(-3750*t(0)^5-t(0)*t(3)+625*t(4))/(3125*t(0)^5*t(4)-3125*t(4)^2)*x(4)
gm[1,2]=(5*t(5))/(t(0)^5-t(4))*x(0)+(-t(0)*t(5))/(t(0)^5*t(4)-t(4)^2)*x(4)
gm[1,3]=0
gm[1,4]=0
gm[2,1]=(-9765625*t(0)^8-625*t(0)^5*t(2)-3125*t(0)^4*t(3)+9765625*t(0)^3*t(4)+625*t(2)*t(4)-t(3)^2)/(1953125*t(0)^5*t(5)-1953125*t(4)*t(5))*x(0)-1/(3125*t(5))*x(3)+(9765625*t(0)^9+625*t(0)^6*t(2)+5625*t(0)^5*t(3)-9765625*t(0)^4*t(4)-625*t(0)*t(2)*t(4)+t(0)*t(3)^2-2500*t(3)*t(4))/(9765625*t(0)^5*t(4)*t(5)-9765625*t(4)^2*t(5))*x(4)
gm[2,2]=(-9375*t(0)^4*t(5)-3*t(3)*t(5)+3125*t(6))/(625*t(0)^5*t(5)-625*t(4)*t(5))*x(0)+(11250*t(0)^5*t(5)+3*t(0)*t(3)*t(5)-3125*t(0)*t(6)-1875*t(4)*t(5))/(3125*t(0)^5*t(4)*t(5)-3125*t(4)^2*t(5))*x(4)-1/(t(5))*x(5)
gm[2,3]=(t(0)^5-t(4))/(15625*t(5)^2)*x(0)+(-t(0)^6+t(0)*t(4))/(78125*t(4)*t(5)^2)*x(4)
gm[2,4]=0
gm[3,1]=(-87890625000*t(0)^12*t(5)+390625*t(0)^10*t(1)*t(5)-3906250*t(0)^9*t(2)*t(5)-48828125*t(0)^8*t(3)*t(5)+30517578125*t(0)^8*t(6)+84228515625*t(0)^7*t(4)*t(5)-781250*t(0)^5*t(1)*t(4)*t(5)-625*t(0)^5*t(2)*t(3)*t(5)+1953125*t(0)^5*t(2)*t(6)+3906250*t(0)^4*t(2)*t(4)*t(5)-15625*t(0)^4*t(3)^2*t(5)+9765625*t(0)^4*t(3)*t(6)+19531250*t(0)^3*t(3)*t(4)*t(5)-30517578125*t(0)^3*t(4)*t(6)+3662109375*t(0)^2*t(4)^2*t(5)+390625*t(1)*t(4)^2*t(5)+625*t(2)*t(3)*t(4)*t(5)-1953125*t(2)*t(4)*t(6)-2*t(3)^3*t(5)+3125*t(3)^2*t(6))/(78125*t(0)^15-234375*t(0)^10*t(4)+234375*t(0)^5*t(4)^2-78125*t(4)^3)*x(0)+(5*t(5))/(t(0)^5-t(4))*x(2)+(-9375*t(0)^4*t(5)-2*t(3)*t(5)+3125*t(6))/(125*t(0)^10-250*t(0)^5*t(4)+125*t(4)^2)*x(3)+(87890625000*t(0)^13*t(5)-390625*t(0)^11*t(1)*t(5)+2734375*t(0)^10*t(2)*t(5)+72265625*t(0)^9*t(3)*t(5)-30517578125*t(0)^9*t(6)-84228515625*t(0)^8*t(4)*t(5)+781250*t(0)^6*t(1)*t(4)*t(5)+625*t(0)^6*t(2)*t(3)*t(5)-1953125*t(0)^6*t(2)*t(6)-1562500*t(0)^5*t(2)*t(4)*t(5)+20625*t(0)^5*t(3)^2*t(5)-17578125*t(0)^5*t(3)*t(6)-42968750*t(0)^4*t(3)*t(4)*t(5)+30517578125*t(0)^4*t(4)*t(6)-3662109375*t(0)^3*t(4)^2*t(5)-390625*t(0)*t(1)*t(4)^2*t(5)-625*t(0)*t(2)*t(3)*t(4)*t(5)+1953125*t(0)*t(2)*t(4)*t(6)+2*t(0)*t(3)^3*t(5)-3125*t(0)*t(3)^2*t(6)-1171875*t(2)*t(4)^2*t(5)-5000*t(3)^2*t(4)*t(5)+7812500*t(3)*t(4)*t(6))/(390625*t(0)^15*t(4)-1171875*t(0)^10*t(4)^2+1171875*t(0)^5*t(4)^3-390625*t(4)^4)*x(4)
gm[3,2]=(-121093750*t(0)^8*t(5)^2+1250*t(0)^5*t(2)*t(5)^2-68750*t(0)^4*t(3)*t(5)^2+78125000*t(0)^4*t(5)*t(6)-25390625*t(0)^3*t(4)*t(5)^2-1250*t(2)*t(4)*t(5)^2-8*t(3)^2*t(5)^2+18750*t(3)*t(5)*t(6)-9765625*t(6)^2)/(25*t(0)^15-75*t(0)^10*t(4)+75*t(0)^5*t(4)^2-25*t(4)^3)*x(0)+(50*t(5)^2)/(t(0)^10-2*t(0)^5*t(4)+t(4)^2)*x(3)+(121093750*t(0)^9*t(5)^2-1250*t(0)^6*t(2)*t(5)^2+63750*t(0)^5*t(3)*t(5)^2-70312500*t(0)^5*t(5)*t(6)+25390625*t(0)^4*t(4)*t(5)^2+1250*t(0)*t(2)*t(4)*t(5)^2+8*t(0)*t(3)^2*t(5)^2-18750*t(0)*t(3)*t(5)*t(6)+9765625*t(0)*t(6)^2+5000*t(3)*t(4)*t(5)^2-7812500*t(4)*t(5)*t(6))/(125*t(0)^15*t(4)-375*t(0)^10*t(4)^2+375*t(0)^5*t(4)^3-125*t(4)^4)*x(4)+(78125*t(6))/(t(0)^10-2*t(0)^5*t(4)+t(4)^2)*x(5)+(-78125*t(5))/(t(0)^10-2*t(0)^5*t(4)+t(4)^2)*x(6)
gm[3,3]=(9375*t(0)^4*t(5)+3*t(3)*t(5)-3125*t(6))/(625*t(0)^5*t(5)-625*t(4)*t(5))*x(0)+(-11250*t(0)^5*t(5)-3*t(0)*t(3)*t(5)+3125*t(0)*t(6)+1875*t(4)*t(5))/(3125*t(0)^5*t(4)*t(5)-3125*t(4)^2*t(5))*x(4)+1/(t(5))*x(5)
gm[3,4]=(-5*t(5))/(t(0)^5-t(4))*x(0)+(t(0)*t(5))/(t(0)^5*t(4)-t(4)^2)*x(4)
gm[4,1]=(-19140625*t(0)^11+6250*t(0)^9*t(1)-3125*t(0)^8*t(2)-6250*t(0)^7*t(3)+18750000*t(0)^6*t(4)+2*t(0)^5*t(1)*t(3)-t(0)^5*t(2)^2-6250*t(0)^4*t(1)*t(4)+5*t(0)^4*t(2)*t(3)+18750*t(0)^3*t(2)*t(4)-5*t(0)^3*t(3)^2-9375*t(0)^2*t(3)*t(4)+390625*t(0)*t(4)^2-2*t(1)*t(3)*t(4)+t(2)^2*t(4))/(625*t(0)^10-1250*t(0)^5*t(4)+625*t(4)^2)*x(0)+x(1)+(3125*t(0)^4+t(3))/(625*t(0)^5-625*t(4))*x(2)+(-3125*t(0)^3-t(2))/(625*t(0)^5-625*t(4))*x(3)+(19140625*t(0)^12-7500*t(0)^10*t(1)-6250*t(0)^9*t(2)+18750*t(0)^8*t(3)-18750000*t(0)^7*t(4)-2*t(0)^6*t(1)*t(3)+t(0)^6*t(2)^2+8750*t(0)^5*t(1)*t(4)-4*t(0)^5*t(2)*t(3)-9375*t(0)^4*t(2)*t(4)+5*t(0)^4*t(3)^2-3125*t(0)^3*t(3)*t(4)-390625*t(0)^2*t(4)^2+2*t(0)*t(1)*t(3)*t(4)-t(0)*t(2)^2*t(4)-1250*t(1)*t(4)^2-t(2)*t(3)*t(4))/(3125*t(0)^10*t(4)-6250*t(0)^5*t(4)^2+3125*t(4)^3)*x(4)
gm[4,2]=(-87890625000*t(0)^12*t(5)+390625*t(0)^10*t(1)*t(5)-3906250*t(0)^9*t(2)*t(5)-48828125*t(0)^8*t(3)*t(5)+30517578125*t(0)^8*t(6)+84228515625*t(0)^7*t(4)*t(5)-781250*t(0)^5*t(1)*t(4)*t(5)-625*t(0)^5*t(2)*t(3)*t(5)+1953125*t(0)^5*t(2)*t(6)+3906250*t(0)^4*t(2)*t(4)*t(5)-15625*t(0)^4*t(3)^2*t(5)+9765625*t(0)^4*t(3)*t(6)+19531250*t(0)^3*t(3)*t(4)*t(5)-30517578125*t(0)^3*t(4)*t(6)+3662109375*t(0)^2*t(4)^2*t(5)+390625*t(1)*t(4)^2*t(5)+625*t(2)*t(3)*t(4)*t(5)-1953125*t(2)*t(4)*t(6)-2*t(3)^3*t(5)+3125*t(3)^2*t(6))/(78125*t(0)^15-234375*t(0)^10*t(4)+234375*t(0)^5*t(4)^2-78125*t(4)^3)*x(0)+(5*t(5))/(t(0)^5-t(4))*x(2)+(-9375*t(0)^4*t(5)-2*t(3)*t(5)+3125*t(6))/(125*t(0)^10-250*t(0)^5*t(4)+125*t(4)^2)*x(3)+(87890625000*t(0)^13*t(5)-390625*t(0)^11*t(1)*t(5)+2734375*t(0)^10*t(2)*t(5)+72265625*t(0)^9*t(3)*t(5)-30517578125*t(0)^9*t(6)-84228515625*t(0)^8*t(4)*t(5)+781250*t(0)^6*t(1)*t(4)*t(5)+625*t(0)^6*t(2)*t(3)*t(5)-1953125*t(0)^6*t(2)*t(6)-1562500*t(0)^5*t(2)*t(4)*t(5)+20625*t(0)^5*t(3)^2*t(5)-17578125*t(0)^5*t(3)*t(6)-42968750*t(0)^4*t(3)*t(4)*t(5)+30517578125*t(0)^4*t(4)*t(6)-3662109375*t(0)^3*t(4)^2*t(5)-390625*t(0)*t(1)*t(4)^2*t(5)-625*t(0)*t(2)*t(3)*t(4)*t(5)+1953125*t(0)*t(2)*t(4)*t(6)+2*t(0)*t(3)^3*t(5)-3125*t(0)*t(3)^2*t(6)-1171875*t(2)*t(4)^2*t(5)-5000*t(3)^2*t(4)*t(5)+7812500*t(3)*t(4)*t(6))/(390625*t(0)^15*t(4)-1171875*t(0)^10*t(4)^2+1171875*t(0)^5*t(4)^3-390625*t(4)^4)*x(4)
gm[4,3]=(9765625*t(0)^8+625*t(0)^5*t(2)+3125*t(0)^4*t(3)-9765625*t(0)^3*t(4)-625*t(2)*t(4)+t(3)^2)/(1953125*t(0)^5*t(5)-1953125*t(4)*t(5))*x(0)+1/(3125*t(5))*x(3)+(-9765625*t(0)^9-625*t(0)^6*t(2)-5625*t(0)^5*t(3)+9765625*t(0)^4*t(4)+625*t(0)*t(2)*t(4)-t(0)*t(3)^2+2500*t(3)*t(4))/(9765625*t(0)^5*t(4)*t(5)-9765625*t(4)^2*t(5))*x(4)
gm[4,4]=(-3125*t(0)^4-t(3))/(625*t(0)^5-625*t(4))*x(0)+(3750*t(0)^5+t(0)*t(3)-625*t(4))/(3125*t(0)^5*t(4)-3125*t(4)^2)*x(4)




//-------------------------------------------------Writing t_is in terms of periods-----------------------------
//----------------------------ring r4-----------------------------------------

> F-transpose(P)*Psi*P;  
_[1,1]=0
_[1,2]=25/6*x_(1)(2)*x_(2)(1)-25/6*x_(1)(1)*x_(2)(2)-5/2*x_(2)(2)*x_(3)(1)+5/2*x_(2)(1)*x_(3)(2)+5/6*x_(1)(2)*x_(4)(1)-5/6*x_(1)(1)*x_(4)(2)
_[1,3]=25/6*x_(1)(3)*x_(2)(1)-25/6*x_(1)(1)*x_(2)(3)-5/2*x_(2)(3)*x_(3)(1)+5/2*x_(2)(1)*x_(3)(3)+5/6*x_(1)(3)*x_(4)(1)-5/6*x_(1)(1)*x_(4)(3)
_[1,4]=25/6*x_(1)(4)*x_(2)(1)-25/6*x_(1)(1)*x_(2)(4)-5/2*x_(2)(4)*x_(3)(1)+5/2*x_(2)(1)*x_(3)(4)+5/6*x_(1)(4)*x_(4)(1)-5/6*x_(1)(1)*x_(4)(4)-1/(625*p^5-625)
_[2,1]=-25/6*x_(1)(2)*x_(2)(1)+25/6*x_(1)(1)*x_(2)(2)+5/2*x_(2)(2)*x_(3)(1)-5/2*x_(2)(1)*x_(3)(2)-5/6*x_(1)(2)*x_(4)(1)+5/6*x_(1)(1)*x_(4)(2)
_[2,2]=0
_[2,3]=25/6*x_(1)(3)*x_(2)(2)-25/6*x_(1)(2)*x_(2)(3)-5/2*x_(2)(3)*x_(3)(2)+5/2*x_(2)(2)*x_(3)(3)+5/6*x_(1)(3)*x_(4)(2)-5/6*x_(1)(2)*x_(4)(3)+1/(625*p^5-625)
_[2,4]=25/6*x_(1)(4)*x_(2)(2)-25/6*x_(1)(2)*x_(2)(4)-5/2*x_(2)(4)*x_(3)(2)+5/2*x_(2)(2)*x_(3)(4)+5/6*x_(1)(4)*x_(4)(2)-5/6*x_(1)(2)*x_(4)(4)+(-p^4)/(125*p^10-250*p^5+125)
_[3,1]=-25/6*x_(1)(3)*x_(2)(1)+25/6*x_(1)(1)*x_(2)(3)+5/2*x_(2)(3)*x_(3)(1)-5/2*x_(2)(1)*x_(3)(3)-5/6*x_(1)(3)*x_(4)(1)+5/6*x_(1)(1)*x_(4)(3)
_[3,2]=-25/6*x_(1)(3)*x_(2)(2)+25/6*x_(1)(2)*x_(2)(3)+5/2*x_(2)(3)*x_(3)(2)-5/2*x_(2)(2)*x_(3)(3)-5/6*x_(1)(3)*x_(4)(2)+5/6*x_(1)(2)*x_(4)(3)-1/(625*p^5-625)
_[3,3]=0
_[3,4]=25/6*x_(1)(4)*x_(2)(3)-25/6*x_(1)(3)*x_(2)(4)-5/2*x_(2)(4)*x_(3)(3)+5/2*x_(2)(3)*x_(3)(4)+5/6*x_(1)(4)*x_(4)(3)-5/6*x_(1)(3)*x_(4)(4)+(p^3)/(125*p^10-250*p^5+125)
_[4,1]=-25/6*x_(1)(4)*x_(2)(1)+25/6*x_(1)(1)*x_(2)(4)+5/2*x_(2)(4)*x_(3)(1)-5/2*x_(2)(1)*x_(3)(4)-5/6*x_(1)(4)*x_(4)(1)+5/6*x_(1)(1)*x_(4)(4)+1/(625*p^5-625)
_[4,2]=-25/6*x_(1)(4)*x_(2)(2)+25/6*x_(1)(2)*x_(2)(4)+5/2*x_(2)(4)*x_(3)(2)-5/2*x_(2)(2)*x_(3)(4)-5/6*x_(1)(4)*x_(4)(2)+5/6*x_(1)(2)*x_(4)(4)+(p^4)/(125*p^10-250*p^5+125)
_[4,3]=-25/6*x_(1)(4)*x_(2)(3)+25/6*x_(1)(3)*x_(2)(4)+5/2*x_(2)(4)*x_(3)(3)-5/2*x_(2)(3)*x_(3)(4)-5/6*x_(1)(4)*x_(4)(3)+5/6*x_(1)(3)*x_(4)(4)+(-p^3)/(125*p^10-250*p^5+125)
_[4,4]=0


detP;
12/(9765625*p^10-19531250*p^5+9765625)



> t_0;
(p)*x_(1)(1)
> t_1;
(3125*p^3)*x_(1)(1)*x_(1)(2)+(3125*p^4)*x_(1)(1)*x_(1)(3)+(625*p^5-625)*x_(1)(1)*x_(1)(4)
> t_2;
(-3125*p^3)*x_(1)(1)^3+(-625*p^5+625)*x_(1)(1)^2*x_(1)(3)
> t_3;
(-3125*p^4)*x_(1)(1)^4+(625*p^5-625)*x_(1)(1)^3*x_(1)(2)
> t_4;
x_(1)(1)^5
> t_5;
(-1/5*p^5+1/5)*x_(1)(1)^2*x_(1)(2)*x_(2)(1)+(1/5*p^5-1/5)*x_(1)(1)^3*x_(2)(2)
> t_6;
(-1/5*p^9+1/5*p^4)*x_(1)(1)^6*x_(1)(2)*x_(2)(1)+(-2/25*p^10+4/25*p^5-2/25)*x_(1)(1)^5*x_(1)(2)^2*x_(2)(1)+(-1/25*p^10+2/25*p^5-1/25)*x_(1)(1)^6*x_(1)(3)*x_(2)(1)+(1/5*p^9-1/5*p^4)*x_(1)(1)^7*x_(2)(2)+(2/25*p^10-4/25*p^5+2/25)*x_(1)(1)^6*x_(1)(2)*x_(2)(2)+(1/25*p^10-2/25*p^5+1/25)*x_(1)(1)^7*x_(2)(3)




> factorize(t_0);
[1]:
   _[1]=(p)
   _[2]=x_(1)(1)
[2]:
   1,1
> factorize(t_1);
[1]:
   _[1]=625
   _[2]=x_(1)(1)
   _[3]=(5*p^3)*x_(1)(2)+(5*p^4)*x_(1)(3)+(p^5-1)*x_(1)(4)
[2]:
   1,1,1
> factorize(t_2);
[1]:
   _[1]=-625
   _[2]=x_(1)(1)
   _[3]=(5*p^3)*x_(1)(1)+(p^5-1)*x_(1)(3)
[2]:
   1,2,1
> factorize(t_3);
[1]:
   _[1]=625
   _[2]=x_(1)(1)
   _[3]=(-5*p^4)*x_(1)(1)+(p^5-1)*x_(1)(2)
[2]:
   1,3,1
> factorize(t_4);
[1]:
   _[1]=1
   _[2]=x_(1)(1)
[2]:
   1,5
> factorize(t_5);
[1]:
   _[1]=(-1/5*p^5+1/5)
   _[2]=x_(1)(2)*x_(2)(1)-x_(1)(1)*x_(2)(2)
   _[3]=x_(1)(1)
[2]:
   1,1,2
> factorize(t_6);
[1]:
   _[1]=(1/25*p^5-1/25)
   _[2]=x_(1)(1)
   _[3]=(-5*p^4)*x_(1)(1)*x_(1)(2)*x_(2)(1)+(-2*p^5+2)*x_(1)(2)^2*x_(2)(1)+(-p^5+1)*x_(1)(1)*x_(1)(3)*x_(2)(1)+(5*p^4)*x_(1)(1)^2*x_(2)(2)+(2*p^5-2)*x_(1)(1)*x_(1)(2)*x_(2)(2)+(p^5-1)*x_(1)(1)^2*x_(2)(3)
[2]:
   1,5,1



//---------------q expansion----------------------------------------

> coli1[1];
[1]:
   1/120
[2]:
   1
[3]:
   175
[4]:
   117625
[5]:
   111784375
[6]:
   126958105626
[7]:
   160715581780591
[8]:
   218874699262438350
[9]:
   314179164066791400375
[10]:
   469234842365062637809375
[11]:
   722875994952367766020759550
[12]:
   1141675905475884004867667570018
[13]:
   1840292432768195006213820794245975
[14]:
   3017411723059765906544794685667050875
[15]:
   5019474292099953072997017265599392306250
[16]:
   8454135395215640792118598334226588287586375
[17]:
   14393117470849214084329153580861023588917403831
[18]:
   24736319439029182902970332321048104309267605145900
[19]:
   42867801173749950224288846860983948227289576929739625
[20]:
   74841725615865562312312468224716465993767029001352137500
[21]:
   131533387101014239352654655996128490298528653430437570768750
[22]:
   232552602804067967131448392641705657004850136727220105475742434
[23]:
   413383803942320309501187085544610067977441784554521565840682212950
[24]:
   738448429782501257673418828362786421398551881599702173194613528972375
[25]:
   1325062428668557181750327725294460594501429985824890159210398165696684375
[26]:
   2387481249102873709396301851511994109103476698734650190971074350509956074376
[27]:
   4318057455991739433052929205132147861598767828269793750111083284848794501097909
[28]:
   7837100728598305607376973987407064317837038732862248780595769230100847305504951975
[29]:
   14270156140055539357713301433598776037072874758832553894647025971798965941197943404250
[30]:
   26062016294831381147181796820056664127574622104357099042008138409792960659701650558162500
[31]:
   47731308015232165604253573763779083829224048192367287069765783759552209875180332891388376841
[32]:
   87646324854904935060879838102913235349318893533184016092387532631445240571107567827475119951361
[33]:
   161334022995885194574052827331367177747693126010840453932893403285798161871052864240497445788680375
[34]:
   297655399720885626240655995812068575851317708590824410369496090821144986231809335419916352024831503625
[35]:
   550347250589751432978431859029198246505684951323936157442147577268635018482381476397456170502069989087500
[36]:
   1019624037886936157479939926749658652726698822254769475592403578692330064937082834572203543802506980132957100
[37]:
   1892662852090569303957952142709425325961876773183121023426463959675950979680603063134999818044377004938123570945
[38]:
   3519575310922382086564826065864756975174086065592386109352279899914420004219273630989648901674525314718645594404575
[39]:
   6556147182926300624155133845153436029193825297677919124044595312319482188813078558582293950756810198928792032272764500
[40]:
   12232339091921838969171822676974032497853105357816365171516287609322697730250639271909185897897993162017712967599798796875
[41]:
   22857917928928764782485597748222436738990908631149353287909802367492897701857332711900998437877620803864802916635403906384750
[42]:
   42775670203580533743278503757525127093835367247645300826657685865189131608693275402181482323728374777601407767065121137547144528
[43]:
   80160250440201269781842767425573135059970207773449598517135489689185508321918810038544892425273674953637624073521284762533194769550
[44]:
   150416228487190721097597049287860421252614362142227157826950210957533407950922246008972362516726607977677236847135849144650388936379375
[45]:
   282603157923094409633083671234151681409956403546611497536541670867320845703213115134892018840696751137333741364504744480135691620984143750
[46]:
   531595296456052914119126385218927835710290087519797786626917293670422920941260798372179832319016104864562439261652813163797024997901708121875
[47]:
   1001114675961747804698311425158123238530295258467241305864062335854346448730869908167074008827723929774524843109630433233765257660031179567490457
[48]:
   1887397584637268712308751271431654241435087849696563295843814271064549201837630721477133499277503145645807578265015136564083223892095667027045695575
[49]:
   3562045846648263459107110397826419531695426994464354632264210346346375461071768885940423896220011337645805497009551879072971693403293734236871345228375
[50]:
   6729349773419210938570918205303758530764380224735342625847648962753944554240241477343810789144789445369445962580433915198208851946921100188726152764934375
[51]:
   12725249259823686890076507014380354233349593140262602076315565578410007607926577629881774220263333623857996945588751888261126541534536152364099933229152790800
[52]:
   t(0)
> coli1[2];
[1]:
   1/30
[2]:
   3
[3]:
   930
[4]:
   566375
[5]:
   526770000
[6]:
   592132503858
[7]:
   745012928951258
[8]:
   1010500474677945510
[9]:
   1446287695614437271000
[10]:
   2155340222852696651995625
[11]:
   3314709711759484241245738380
[12]:
   5227889094376387636159454389314
[13]:
   8417409505759916157177888425688560
[14]:
   13788410980382173235507863529431349625
[15]:
   22918575609857989896613420832931782272500
[16]:
   38574205812410328214211297150177092404802125
[17]:
   65632680881329161229449598976351013035618245848
[18]:
   112737836815969584805068278669917251130955486079840
[19]:
   195281679152645688486494758108413835286513448492857750
[20]:
   340793876648058347631082212773836550424922150658035942500
[21]:
   598715219709624380064930967490121095512742674738685534520000
[22]:
   1058175424558765150851065230728361592973445263222688499678106462
[23]:
   1880423801467769362575238131519555078049948362529919740801119838620
[24]:
   3358149985055768677410189899813523311205754471467396381837370906741125
[25]:
   6024266856738999307740749174759251752729219837113142104528100439915455000
[26]:
   10851875942446171834252896039803140208063454963036611361903180368734174220508
[27]:
   19622676276166583134169891299809680619295269961985299916845519462583320309071702
[28]:
   35607157255338188053303623750429076609249381333904414176480903193402128709453497085
[29]:
   64822975181438463720297036477221486720666988882724848814690011920223183040174836768000
[30]:
   118367440145834844822361904957653674981984990346188930199066418798176697646532327323240000
[31]:
   216748780944866907058433247727098438279427405715427079532429976881529218666251208512008263038
[32]:
   397942845332800994734705934847684948505054864535091657537840230369619687012102830021632023348843
[33]:
   732404091968856281121717663778622632227079894818880340200796102293339761355233943477906894680384600
[34]:
   1351077111322080792825199686122338362614343398061616175002238286268836927938006193049513651039143224875
[35]:
   2497745439341192545860943735521958309212879825228980915776153553723029881703825953298324183860972277110000
[36]:
   4627000802347887896086612982078264782959764431222875990225372610262716223663296872084729734743041085561497660
[37]:
   8587836627846475699644244286784436974563702123004102609223684594181779566536248362281546842029068068742076468560
[38]:
   15968143303270315092810520686298132905282992907411738286616565841260536580267962265318987977213149012140730545195945
[39]:
   29741914730112382594426911499266235122060331114498424564363716367920163236315751494010711111929473965504170600309317000
[40]:
   55486592037697791557260232899535509557448765224974321130721089936856972342458859807241923279315316844368631275560496965625
[41]:
   103675369196728943476727363262519618806700148550518389285890590181239041601057338647841248278833592980541298807300460663822000
[42]:
   193998354071774730761188819648954967689688929104576548355278052999512606252844778004456883332731748289731396785374699604023962124
[43]:
   363516703029541902464171834573388774084857381758447528174241545675132709751010447645131578601292778709855965957540138119737036962580
[44]:
   682064962850361391333887678812519388306519811659421499692515697142816208683676618301400897247736323086610659764867245806719259850223125
[45]:
   1281372327263078358040423330568205013143934758683284700939008205684292116323319911604342079403925670141503297071754802128492089909478520000
[46]:
   2410172825086410584318155811388989318658041945457408189626668867593832931170813825233355415138636059894825608833062821121128677026239869870625
[47]:
   4538590049141866779202787545488555715475032621192617317579560152827813869391868251938330257432053655124677465715746851836226344858412422480440126
[48]:
   8556021309560213015811678421294139437553005188397517810218392294904038525314553099406701345310150940003504163643884181912319395963477254885127340445
[49]:
   16146577594964043303443747042202451387899030078719695900442374523339066325114863580455239567502870088703870679777997439745845306907993560832402713919000
[50]:
   30501957247085053807111011005256166469888634334345754374012469317302718185510790536480556142248979583232782932003270501628754355372852516859533774460095625
[51]:
   57676058525077055508469465200291509500002491130210346768401404231592670302280821655430764514308073279041193271412662294727146194568748057006255318316387471880
[52]:
   t(1)
> coli1[3];
[1]:
   7/10
[2]:
   107
[3]:
   50390
[4]:
   29007975
[5]:
   26014527500
[6]:
   28743493632402
[7]:
   35790559257796542
[8]:
   48205845153859479030
[9]:
   68647453506412345755300
[10]:
   101912303698877609329100625
[11]:
   156263153250677320910779548340
[12]:
   245861836198590385250547656583106
[13]:
   395077598235196324212047958360439980
[14]:
   646096440657879559086775953092890559825
[15]:
   1072403442164436800549815736692457434207500
[16]:
   1802770743296965594923915683039359386117805725
[17]:
   3064116498823459910651936631057146564863380819332
[18]:
   5258386232441765953442083563119313668787768890093920
[19]:
   9100982018347385959878664715523716000307406398101232450
[20]:
   15870888287721526032947526598017395686376023221361923922500
[21]:
   27864108883393912623637426510579197757443129366379289779275000
[22]:
   49218211039195057293849241660783586731971438057631062563295843918
[23]:
   87416044230059122274439032877318231097101298696501801435971003562660
[24]:
   156035531273453731011208033291575091439822590459119822697474898812159525
[25]:
   279790976457161161187353200358486464543349011472475128148672627384535622500
[26]:
   503797800199000207487252720619424330625185375256219534759942360595491014722252
[27]:
   910637670542685836174509081427678336432332368750510369105088838445954422251070738
[28]:
   1651859075700527060162361877944067919643221496362303461534965986855883320845773560205
[29]:
   3006242462678745250993570722258357273070484417301642195002193786144327845127567253431400
[30]:
   5487777864788534961215434666278455876901053109676209626024060633491062842708893017812580000
[31]:
   10046135180248369260272439647714914752289341942406999420049306055317734514023517550064559933562
[32]:
   18439499537996055684761315839366063281913606610080332586036114094935005455877109973725994064347307
[33]:
   33929111885603184017495746350936907906843543504249064672317271683871338595653857364070398177470599300
[34]:
   62575124894501402440997672835251289536359242104766009364611392521081965561998323644631760539609779472275
[35]:
   115657976871121710181753344458450598192801891580166307590271870228173541646662313368821962516478273517220000
[36]:
   214209273875620364261098483395649190013361435386638403443575088156703004864916917240940369264735566047976831180
[37]:
   397501465741157680064652366185447876126076445703290076528738203982645996127410331493678798013720974396695836501940
[38]:
   738975816769046637089226680393004703953190137997973049946874840381703487427999278097168956318988782796195677919617185
[39]:
   1376162707519106992641444390492844098456831513170716008936109477615564151836251701607497539438827697852404415619926764600
[40]:
   2566952610883845900048872132300420954477094156680648078069721667808901328295140380781971238491758770504598970619574931665625
[41]:
   4795544413549548913106762791194162647733996136393106972303346122852365625603598941570738422733432791999245181101418647445209800
[42]:
   8972143722353317595065473380394894194349386057333418804876402716958072235103808667410467061834314767434484048502946744540396428716
[43]:
   16809758692552512545734172371733259883460739895945355681410412833264061302753820788191908125054587235218801442015131890143296414084540
[44]:
   31535857566353810294895095682489202187816520343319895447845749829573823924397565600762316519805382006728113424446901694321570041508409125
[45]:
   59237771051068233804656534235767670284303179920556110154256258874878156774774097767534235491000449167523833058369449098235476700993525815000
[46]:
   111408545579074818944965935920097501127087185209775919832352281944226569739640841038819933301259500776676508063166009542162971124000417584115625
[47]:
   209768634068649274655761579911188862515579259849566859567659347206697847922407984780865013222110619514227092547109096303182877455754591230349713114
[48]:
   395405676104038923129743523344193122520295063015525440948066298364610776418119001076228423176263597578551207843203444301005851303000556247179124073885
[49]:
   746113693214518023227104741331629703347673934108210578812087859459385426204554220077792321693669763125265981701964867100210630722564862891269047878805700
[50]:
   1409313557979741474619870165028808629211578874386825688332968494200525140133086321808889575410285511784508362322490760346267247145795314410820641307495950625
[51]:
   2664604065918799298111739564984805532616760619498843987339578423461819722560400613756484357441008061172508705974520742298506123580045993768363025410271922256840
[52]:
   t(2)
> coli1[4];
[1]:
   6/5
[2]:
   71
[3]:
   188330
[4]:
   100324275
[5]:
   86097977000
[6]:
   93009679497426
[7]:
   114266677893238146
[8]:
   152527823430305901510
[9]:
   215812408812642816943200
[10]:
   318839967257572460805706125
[11]:
   487033977592346076373921829980
[12]:
   763967733846234737556371633129938
[13]:
   1224572111954870204216255256329810760
[14]:
   1998460225444046215735693942520196079925
[15]:
   3311234563797105542141334162599769833878500
[16]:
   5557942384802218734384032907390820991601440025
[17]:
   9434249505090813780150142801149462007234281102656
[18]:
   16171627952999596778384516221422703240906666850216440
[19]:
   27960630676200807516708351471522611140583448973348145550
[20]:
   48715373064765011413756209064330165309728882422122576240500
[21]:
   85458856103082629260403362860920383007541820555732610572062000
[22]:
   150841132394948130907244849138419243601396137948809016192257354774
[23]:
   267730055936637982105091000672590813613059443696763402942634310123820
[24]:
   477603414290211868881034446445091873029714160126178116673137275101604225
[25]:
   855929765057872601621124539016422375695050697290734170912608344670069228000
[26]:
   1540426447331322578895349982162258710348001820995478792191424001538657609081076
[27]:
   2783094795620205056331212563264491483912143592794826448266966583988874932372047214
[28]:
   5046246815281369636576511891840498528314978253197926096055264854911502083639057645385
[29]:
   9180077031670579318460648489860053624121461567214606837596204503406363503042292797467600
[30]:
   16751663092921561294798469869791596276846564421686707213901792163701873922191968654743549000
[31]:
   30655648677071219014575381994303252408673294281960912009860907681424515443494596326880265607126
[32]:
   56249752620697065635555826358609003717218457184220486050377935974826367255521152406013808205361791
[33]:
   103469637929259531890365968032395456311108855035699697068643972794873899971594731872943924648531153600
[34]:
   190774021721519324550625676917396014578415538469624258915419481614439576584392547471866125424763706016975
[35]:
   352514968453355698859617606607110830469118986044920362806987132590713478284525783643353594363966428184546000
[36]:
   652726797762134302895920343752882142601641348042306663320163980855166503114474282568834789957765771059584784060
[37]:
   1210958550617311510276463725074395368434950756702566585883769301429535516766435159406509199079019665727714333436920
[38]:
   2250732054670015531746607305800029186382407804191051205629130967715069839889486761479472791177166230407307442088592845
[39]:
   4190555355078103672330357308310173307736686478509569616967901238352874062894936931011024197417078567897126838740963223400
[40]:
   7815066325352920009231085348764292781532914144860970250506118046764852620797225512971338188233834209519310771816172272223125
[41]:
   14597220925586880054051407191682851938766369374013490327679190137148817802798629737350435196413438151002964222702554987609339200
[42]:
   27305493389468449846239478057207535574328498623953456798585761231654783834050052694550852223863281436295514404326215601561222984628
[43]:
   51149409845042392958187025288723526462597715834650422862819570527907316384800135002073450885915550824733521597951907014665717587015780
[44]:
   95942860833583168929577202519184048164023924540011815789566427623589968847594743085914864564915267445393209952140108276470956846877334625
[45]:
   180193401049970056196760065783774382710858939306740591845014369790717079272457172467950288714550514458158636023861428308293641930966201862000
[46]:
   338839392605169789537681107326709139746115248993556127070512072701809088710710967003450529490189366366196557721308029392209322638233136756396125
[47]:
   637902075669420056160211811203565735845531819548965826543883687850966720302918950673420439651437074057121007973796351744467837951657396588201602902
[48]:
   1202256442144062590450768500950105836437559316505574022474171060516362620987136581937667527407977951525985344578257038867948345559277626254648230235145
[49]:
   2268310359047311427706776274079758818921916559977661097370605025750429853368414550562030806090756424787779253066380733603814566250907033993662790994196800
[50]:
   4284012168754559024126822313887684527307083525391196546449946416599702470547118070424380174725752055670565685515405807745936437277980974835961890353688956125
[51]:
   8098853766284012937089853197307112828901208440547385755779846736272941993632257151008991818379484984364881643457656953885665067150446688576086985842178575569480
[52]:
   t(3)
> 
. ;
> coli1[5];
[1]:
   0
[2]:
   -1
[3]:
   170
[4]:
   41475
[5]:
   32183000
[6]:
   32678171250
[7]:
   38612049889554
[8]:
   50189141795178390
[9]:
   69660564113425804800
[10]:
   101431587084669781525125
[11]:
   153189681044166218779637500
[12]:
   238117137884014242081655168402
[13]:
   378843563125325644080443031890040
[14]:
   614425953661148814088877414205091325
[15]:
   1012694070952035493567234738799116966500
[16]:
   1692170635808901179410002578088581915765625
[17]:
   2861157324042688988975717979660678354661493504
[18]:
   4887715249050286161873337199575680029098776190360
[19]:
   8425444959655053294350196311379592903364866454059950
[20]:
   14640379037681972631771005449005991026126197944876804500
[21]:
   25621661757429623667755507813932247563253804314272161250000
[22]:
   45127254393241642809656225502207469277887765084541379148104486
[23]:
   79942019434732470881419568382298635793636325305843140335792282380
[24]:
   142358011685322783461637261745906168238057769798443431753684237599025
[25]:
   254716219964176818124003483272773706940089409026932519393042447045952000
[26]:
   457743745758422834006716691890895646238402361631433810906559281779501562500
[27]:
   825894002009372250644803632162940904032190616061280621254550203700951572846766
[28]:
   1495634640616474643232060368893916754155272099802640807717322332597005964066509865
[29]:
   2717720492070487205304581421885404201622468722397795705064260793913398523403796740400
[30]:
   4953978930798700246518106341270870824812259581526825081156432534547489703453581486021000
[31]:
   9056847035545054283522197624377789262319350994457136802124332762569457583601088714618283750
[32]:
   16603004649278517391356865237644762712398198540608036936416773660333164334418035305455440056559
[33]:
   30514407889941572542839006691070024871627561679692070267913398518769785048658427017508353366630400
[34]:
   56216149295796083882480427839643425918776483099767215901575045299658998089871724947891037187350120775
[35]:
   103798472618671735722092275245335233877506102728224211374903510926912985475642368961971158747581385954000
[36]:
   192059657490696265005155772544654620642592323315999715389179772803657821452088800957855815454766539965087500
[37]:
   356076525533716595686113880046852296868993915501867577668973073768611751740283997145324764600914009627750492680
[38]:
   661399329255099046238350620113519298978457474570774202099688200563256239854960448744401879564081875498837964970005
[39]:
   1230701125973440026786609050168550846526806167074358355436971331077844937940852295232939256358478147112720017727066600
[40]:
   2293869501742134982028477461365254125519819132686558326579139406749454245915249292167549854693802929834274727339111333125
[41]:
   4282270690753398514974431634735813742760101749363089648682359418339998934510045474753646804746892737260848061675108528000000
[42]:
   8006334954303797024277130147160944438064015400919784331989646662085588261980748121906304599689011330695652838296014442614569652
[43]:
   14990466882511082187213351622135754122660123551353791242868178503306453705468973112619419738852816886013738551375939306967669846820
[44]:
   28105299472325845891404665273072907627642550576128763965842565667834593717400621141440422660654127365157799111599934064074560836986625
[45]:
   52762449554974415399476515634021753556810256438832925189254113435821874823097153546303400305063558259020282129100718629781774484471018000
[46]:
   99174338775547921117240719115659400239381132816239698585647323575808728841053474236266580355075167568498569045153486379785502278651015703125
[47]:
   186632393298577003815946325223406872308211799876676867968782598118005082052082486343063234211976767461679556330917158685561383901303320016167878
[48]:
   351613392300394890086037846957940314701160115744015844790096210917444745563773693652133415910703117928717720143568376709475268730785656390228433305
[49]:
   663152258012995722017406035925016306104253293869113096585556350426185702495856169906479761409762618572579519213963099482901977638453782790620178579200
[50]:
   1252018347110434371076667977007203289310100849972605098270266453406907847724987185950070076461659238110482681617691192549575960811416643332669608485805125
[51]:
   2366132691632995512881218587436342407298607313693930201243578360597433055985037462219322112895351391386363325991256730537520695741795765935734147098015625000
[52]:
   t(4)
> coli1[6];
[1]:
   -1/125
[2]:
   15
[3]:
   938
[4]:
   587805
[5]:
   525369650
[6]:
   577718296190
[7]:
   716515428667010
[8]:
   962043316960737646
[9]:
   1366589803139580122090
[10]:
   2024744003173189934886225
[11]:
   3099476777084481347731347688
[12]:
   4870034033558566349001019848690
[13]:
   7816743648548988758641023335617706
[14]:
   12770767567983642899269923705231484185
[15]:
   21179360737708410511141102103685848159200
[16]:
   35577693608497947131754495232163187304174055
[17]:
   60431627386063337339079825297834877713365237050
[18]:
   103649128188765691494953391118447364279196869921604
[19]:
   179301020404731578305706216598284614259836333535942210
[20]:
   312536009213858802688130420502902651779987527231371644100
[21]:
   548488993440036915231168224695916585596529159251859997963400
[22]:
   968477119507129688761314639380250929816183280795141275393082430
[23]:
   1719531181244371250385970008160183535458152253546845192799666785632
[24]:
   3068389402744875574394876745842658649442126937904959836844443526437095
[25]:
   5500470786244669393416650655150565694060947845937541756930134412751880850
[26]:
   9901737520385668432576961439265351868194530868979178296554469367785194302440
[27]:
   17893628174018854677353089608503010614669059151368399037666866087194646328843590
[28]:
   32451229210183460848608180939591627358022202606262797977619198295251371963941959411
[29]:
   59046533521486028107544561338332998735728270203983264747338413299540222022717431320320
[30]:
   107766886854133567193573663818381925526631229809877846062599849548591232067190810722383300
[31]:
   197247629985944758823675386814228911038158520011129596314836483333494534200478064578613629810
[32]:
   361985253791387396013905835763520389667054182722768344470881000633907133931600547233501169392065
[33]:
   665959399545623159996574974207420194936894882719489365543083132310933775150487231376514154489901210
[34]:
   1228045962941928651415363548290265499308221450335827099800505016126404550737259061555624537838778335495
[35]:
   2269498397558337083617841211264895952852741461594317694918014270722304537503035581314196098433285545066700
[36]:
   4202787029605208897283812877986202145397188532524950362284382290896621114196007530770077491290716485789432396
[37]:
   7798046445863760612696149560860786033669328508666787322570928501843105555506605565631334330399726643929995678090
[38]:
   14495331929975333009718361256349040401764771879578257853671687510725896433636501683034456471004532787062840254907957
[39]:
   26991140445335965308288849113785928691496148106108758602348957680502323144794700557900130185736021364338415801050996280
[40]:
   50341396935679824180754588785471055132278243579877382317694125593305003400430837326311768297550822181960366090896084520875
[41]:
   94038036876535229612773890247124706636828425626605861975100412037256213288204236957608653087429026078882808830465343029430840
[42]:
   175922820736709647732051854226445267106244338262061666022959219856494599043423419673054183940957872337418154396369059560975687280
[43]:
   329571541205431705142049034633831406365875014023352570086842001711068691095295334627572173095133679811411777648462603325455879023348
[44]:
   618239774576299214770357507489952297242022040456704040104637593814445339473969942428959887127123014083941990983017416974284424948337675
[45]:
   1161226024673841555102399480358421126876539172311925940343804979838259891509153099651225620681553809708392993958609626247853884391760966400
[46]:
   2183754834131217613500470363720690893137095150343538988953368138632367393834608235847524006962571284551599660738763282590710552480859048386225
[47]:
   4111447157185115275675764248672641645602095803902773645253447754959621464636205276604035899278843852450526432876801131083478702793399178600345210
[48]:
   7749384671977763423291551994740837089876348392488687642193398101442414000340237986372428379571757638284358362615683337352887714081303420535588712727
[49]:
   14621797692892149521581516405136541937666424854958594223396825670303582270566804778701540686222241146010086578066240375254822864677493107407691043780610
[50]:
   27616970321556358212837887877090388450749869872564441452990461218243740809377267423518589728650901769346380539380751232480084145914678793131429854802085225
[51]:
   52212544948217661038620373233073901145742762593667750129906965170215137000755571523492524675726741340269191936537753879177649199999668908655210265966045785188
[52]:
   t(5)
> 


//Yukawa coupling q-expansion
> jf;
jf[1,1]=5
jf[1,2]=2875
jf[1,3]=4876875
jf[1,4]=8564575000
jf[1,5]=15517926796875
jf[1,6]=28663236110956000
jf[1,7]=53621944306062201000
jf[1,8]=101216230345800061125625
jf[1,9]=192323666400003538944396875
jf[1,10]=367299732093982242625847031250
jf[1,11]=704288164978454714776724365580000
jf[1,12]=1354842473951260627644461070753075500
jf[1,13]=2613295702542192770504516764304958585000
jf[1,14]=5051976384195377826370376750184667397150000
jf[1,15]=9784992122065556293839548184561593434114765625
jf[1,16]=18983216783256131050355758292004110332155634496875
jf[1,17]=36880398908911843175757970052077286676680907186572875
jf[1,18]=71739993072775923425756947313710004388338109828244718125
jf[1,19]=139702324572802672116486725324237666156179096139345867681250
jf[1,20]=272313733853214419087881850261769922004501925400113727301718750
jf[1,21]=531268826499235771139178144834727844957387657693379506761647500000
jf[1,22]=1037289278470514923963804027990086045322927638356202870346111556068375
jf[1,23]=2026718782119899203055096833146387701702166133913697744360195741751307500
jf[1,24]=3962477866285127276849207199163283567073477542806145226422135415424327753125
jf[1,25]=7751671052387017667704546265579390655291817901717789487883605657643514005625000
jf[1,26]=15172508464248403775808524087852296102148852200164615668664257115489030148661737250
jf[1,27]=29712146684679793082608370585286281102398137030203631681771823698875610947300125604000
jf[1,28]=58211456912102114576073795249782983915325805479753656718257727679349791603970280960213125
jf[1,29]=114094780815226988137684405525841058542798682490951797476339306987262265811824896479359565625
jf[1,30]=223713728155276341673221527582384824014518762633064814122475032120104110952503157103749887187500
jf[1,31]=438810588514451090792854649487758206537115971495424322689157796940723913901465484048678881021122875
jf[1,32]=861010456921190414771209087071578168966940976641592090592658920885614256433992398528500556218188664750
jf[1,33]=1689961926053043998345098582574915985500341556125285655786658102575245429917877640454320848136035328396875
jf[1,34]=3317980269054667921844703450655982968783715670568220741669395941490045582924686302924748782545178677788518750
jf[1,35]=6516150162957696664519458965101765881914802792699788759337596020564579153145227117438616353078567534052122578125
jf[1,36]=12800340020354018830223869186355032004248032897271533799620072663241522351658751768932978214040538515005945851281875
jf[1,37]=25151183478569638669397943705648486663957254188588531189324771618264924149519971499681798546270870886629122275434401250
jf[1,38]=49430586142003486548103692607793118046572302624566458148439117406774139327974302681590476331159050512204255600194637916875
jf[1,39]=97169043453608553483650392788901340573002646444197268124506921580679844396501023218667853700188786742480699543854237115918750
jf[1,40]=191051208590129413809558540082037000619796566340604226908603187899272886116834132693167997231615400734467086321744179130641015625
jf[1,41]=375713333870535251379161321529307720500662806439238436410726833215720778330315318307854732368380200795611632518699111420257865100000
jf[1,42]=738999264259417388699401933651310805322613159979616383398105430917801769803898676137100764279787192892294845840863082489298434948825500
jf[1,43]=1453810928809578017321313898159128395566287077332136991505971843319887370573427984347919714563547087035256418507287882448638930008252664375
jf[1,44]=2860517559129775707547452063821380613777444038778667327507994431584793993668567938819490299199060573952272801302614608566478628215536890359375
jf[1,45]=5629250540917569726814909330486726613617348961072914526312913600716528140384412462589675193814255205288291564223335039526057696028333174402187500
jf[1,46]=11079561122649959088741031460481964982716129415517643412347669843599414463601641904267082802503909006266595081785742277410044105068029716321286484375
jf[1,47]=21810093344730718860685223601333761686951857086859423077830985839113991817737559120417379906959636992902327613072980926374699742463132769220339612035125
jf[1,48]=42939071263631788680375846170607350753728347207631624952403852020733515502209744570071471844074788408736996749341403006406688810188660778685962152527585625
jf[1,49]=84548377426634153890974208017344931939466971162443059564733310304470497136694353506996713412840430443710949420168022584496891459186548589801913050223356025000
jf[1,50]=166499501241946310532395154311470012120699677640350081386134631549334383010738631213566818430628971666375584452279601006105166586343057014112827102450730888437500
jf[1,51]=327924073429426827767007204246936685266656320311075195889622314074742049365081208467909867257642513193110793057363848560264527857918633173624174171082419179853861250



//Yukawa coupling in Lambert series form: First eleven instanton numbers
> jf2[1,1..11];
5 2875 609250 317206375 242467530000 229305888887625 248249742118022000 295091050570845659250 375632160937476603550000 503840510416985243645106250 704288164978454686113488249750
> 








//The j function
 jfun;
jfun[1,1]=1
jfun[1,2]=770
jfun[1,3]=421375
jfun[1,4]=274007500
jfun[1,5]=236982309375
jfun[1,6]=251719793608904
jfun[1,7]=304471121626588125
jfun[1,8]=401431674714748714500
jfun[1,9]=562487442070502650877500
jfun[1,10]=824572505123979141773850000
jfun[1,11]=1251589997037399017354527578093
jfun[1,12]=1952974988198071415457170414000000
jfun[1,13]=3116643666832537130225160043324497875
jfun[1,14]=5067136850744905843795122675191963715000
jfun[1,15]=8368480844949494796987740413574991486368750
jfun[1,16]=14006903442500342554415693057136099104655559184
jfun[1,17]=23716780589669257042355190554935858464116276718750
jfun[1,18]=40564465634823478801356291170183734314800923219252000
jfun[1,19]=69998052093156682753775630306152988098907912255275950625
jfun[1,20]=121741712782839757076614897643246070629409553672802141587500
jfun[1,21]=213225639119840966243040068402125726815007680297390441482079799
jfun[1,22]=375816002150479164061706161153257079687994197879508886731487500000
jfun[1,23]=666164267575454488895430928943732604438740327555216276318862037039875
jfun[1,24]=1186940158032495812929179271951857979419391517493372123955230784367230000
jfun[1,25]=2124805850737136173414469656968214503157200278656156826912625745386146112500
jfun[1,26]=3820140445776977285832487548512656931983805584507278797274608559734124569859696
jfun[1,27]=6895358721636225526789047742351877802460707781144165422734870317693385446018737500
jfun[1,28]=12491583225945821048364480171006722148875334575740663752299245897971648251590768370500
jfun[1,29]=22706069537603178706909809865000097806150908655341254348706019391960053892537915436211875
jfun[1,30]=41402257315820723128651938758065536102674170460523320977538964019317080756138350637849800000
jfun[1,31]=75712663015942075658972603058832835172880344790051024136433502553499354155317150315670220302589
jfun[1,32]=138832126025946456099955345334855141633654509682333119634614706232198691668391087262154513645022500
jfun[1,33]=255217979216892336874216397260197698983790566827081699608182492076678008196442385867841598019939626375
jfun[1,34]=470286600859030376242599597635067825165551548882696485980347549462514644470496712303869186036651767400000
jfun[1,35]=868521606552765464163324715146098501763639086785236823524662777051368344772098484020024205014200525660550000
jfun[1,36]=1607339528187294949777462136499762904267778152579079691437719521780608536474788334289032062869391146672967380472
jfun[1,37]=2980512173759731987952324257969903590249643981444641421162425123556786089166488226901841653580275759601031477843750
jfun[1,38]=5537097823890751481715830552379180381292226564924289523040572588680595800292533074896431411112406386932459082253865000
jfun[1,39]=10304744236630322809688428424275942147434708975257948419782640273361837703555325485815738182339144150911344520596617745625
jfun[1,40]=19209462072181188395226539541917956042505730313306260887680874332193298854877163796936891542371527020998713464769615197950000
jfun[1,41]=35865638530276812174706870748174759344490351399763462178690880459696521821422437880875373249120000225165635871407789337525937417
jfun[1,42]=67064481516171575343612809470093833088838676623672660596929801693746791395520001222085291395639115512222683736733666639326195000000
jfun[1,43]=125581321494907164303462469475203698690290118327509895674525087366369111945145964347871369100299994277074544267956606768564894267360375
jfun[1,44]=235475731859502777364499028410601093930634439147790117654195441791102725359195171660532384775781188094939091224374415840396209775584595000
jfun[1,45]=442107773799535983585051536463771858110781113523912923599538905221542600857840283642792558058077261555279139876008416170914504459724959421875
jfun[1,46]=831084550331292344100330577234068637838523095755919128296998833076244130855119881490274045842783722771056408170687540168130041878866676148911040
jfun[1,47]=1564131420051763869633321360956039512773808604379189885894113806204772593388291830529735854952232508775486597463894274352633950351020651480028125000
jfun[1,48]=2947065202225909795267849514302993243701697875832679006131213772569701694741719028721347211939135382111688222730177057737252866177080728678375438576500
jfun[1,49]=5558705585961062984469497178918307716041955780718619050819004456961318938081588402171463419166935134003000987908747483359747412460096083890525608064264375
jfun[1,50]=10495552458401777407585089765575765018056726992341414567968900579478298828530482079794172581032599976604339525573197741394351018523245405284051689155437900000
jfun[1,51]=15360643773526377518668633811190238108194176535943216360810584277323022265374173906300029868178746330288210185300960811513198937137984861492535139596431429875056
> 






//----------------------Basis of the homology group----------------------------
> print(Psi);
0,    25/6,0, 5,
-25/6,0,   -5,0,
0,    5,   0, 0,
-5,   0,   0, 0 
> print(T);
1,1,1/2,1/6,
0,1,1,  1/2,
0,0,1,  1,  
0,0,0,  1   
> print(S);
1,    0,0,0,
-25/6,1,0,0,
0,    0,1,0,
-5,   0,0,1 
> 

//The basis in my article
> print(Psi2);
0,  0,   0,  -6/5,
0,  0,   2/5,0,   
0,  -2/5,0,  2,   
6/5,0,   -2, 0    
> print(T2);
1,0,0,0,
1,1,0,0,
1,2,1,0,
1,3,3,1 
> print(S2);
1,-25/6,0,-5/6,
0,1,    0,0,   
0,0,    1,0,   
0,0,    0,1   

//Symplectic basis

> print(Psisym)
0, 0, 1,0,
0, 0, 0,1,
-1,0, 0,0,
0, -1,0,0 
. ;
> print(Tsym);
1,1, 0, 0,
0,1, 0, 0,
5,5, 1, 0,
0,-5,-1,1 
> print(Ssym);
1,0,0,0,
0,1,0,1,
0,0,1,0,
0,0,0,1 

//The base change from the basis in my article to the symplectic basis

> print(C);
0, -1,  0,   0, 
-1,0,   0,   0, 
0, -5/2,-5/2,0, 
0, 25/6,0,   5/6


//We restrict the period map 


> print(P);
1,       0,       0,       0,  
x_(2)(1),1,       0,       0,  
x_(3)(1),x_(3)(2),x_(3)(3),0,  
x_(4)(1),x_(4)(2),x_(4)(3),-6/5


//modulo the ideal of polynomial relations between xij s this is reduced to

> print(P);
1,           0,       0,       0,  
5/6*x_(4)(3),1,       0,       0,  
x_(3)(1),    x_(3)(2),2/5,     0,  
x_(4)(1),    x_(4)(2),x_(4)(3),-6/5


//its determinant is

> detP;
-12/25


//We want the variable x21 back to P

> print(P);
1,       0,       0,           0,  
x_(2)(1),1,       0,           0,  
x_(3)(1),x_(3)(2),2/5,         0,  
x_(4)(1),x_(4)(2),6/5*x_(2)(1),-6/5



//The final form
> P[4,2]=3*x_(2)(1)*x_(3)(2)-3*x_(3)(1)-5;
> print(F0-transpose(P)*transpose(inverse(Psi))*P);
0,0,0,0,
0,0,0,0,
0,0,0,0,
0,0,0,0 

> print(P);
1,       0,                               0,           0,  
x_(2)(1),1,                               0,           0,  
x_(3)(1),x_(3)(2),                        2/5,         0,  
x_(4)(1),3*x_(2)(1)*x_(3)(2)-3*x_(3)(1)-5,6/5*x_(2)(1),-6/5
> 


//The differential of the period matrix
> print(dP);
0,       0,       0,  0,
1,       0,       0,  0,
y_(3)(1),y_(3)(2),0,  0,
y_(4)(1),y_(4)(2),6/5,0 

//Without reducing modulo Griffiths transversality, the Gauss-Manin connection is

>print(gm);
0,1,gm[1,3],     gm[1,4],
0,0,5/2*y_(3)(2),gm[2,4],
0,0,0,           -1,     
0,0,0,           0    

> gm[1,3]*2/5;
-x_(3)(2)+y_(3)(1)
> gm[1,4]*2/5;
x_(2)(1)*y_(3)(1)-x_(3)(1)-1/3*y_(4)(1)-5/3
> gm[2,4]*2/5;
x_(2)(1)*y_(3)(2)-1/3*y_(4)(2)


//The connection matrix
> print(gm);
0,1,0,           0, 
0,0,5/2*y_(3)(2),0, 
0,0,0,           -1,
0,0,0,           0  


//In the symplectic basis
> matrix Psym=C*P;
> print(Psym);
-x_(2)(1),                 -1,                                0,       0,
-1,                        0,                                 0,       0,
-5/2*x_(2)(1)-5/2*x_(3)(1),-5/2*x_(3)(2)-5/2,                 -1,      0,
25/6*x_(2)(1)+5/6*x_(4)(1),5/2*x_(2)(1)*x_(3)(2)-5/2*x_(3)(1),x_(2)(1),-1