SetDirectory["C:\\drorbn\\AcademicPensieve\\2011-08\\w-Computations"];
<< "Playground Program.m"

InfoPrint[s_String] := Print[s<>" is ", ToExpression[s]];

Vp[d=0]=0; eqns={};
While[d<7,
Print["At d=", ++d];
Vp[d]=PCollect[Vp[d-1]+ Sum[
c[d,2k]h^d*h[1]^k h[2]^(d-1-k)*ar[1,2]+ c[d,2k+1]h^d*h[1]^k h[2]^(d-1-k)*ar[2,1], {k,0,d-1}
]];
Print["Vp[d] is ", Vp[d]];
Print[eq1=PCollect[ToDegree[d+1,R4Eqn[Vp[d]]]]];
eqns = Union[Flatten[{eqns, 
CoefficientList[eq1/. {h[1]->x, h[2] -> y, h-> 1, ar[i_,j_] -> ar^(10i+j)}, {x,y, ar}]
}]];
eq2=PCollect[ToDegree[d,TwistEqn[Vp[d]]]];
InfoPrint["eq2"];
eqns = Union[Flatten[{eqns,
CoefficientList[eq2/. {h[1]->x, h[2] -> y, h-> 1, ar[i_,j_] -> ar^(10i+j)}, {x,y, ar}]
}]];
If[False, eqns=Union[eqns, {c[d,2d-2], c[d,1]}]];
vars=Flatten[Table[c[k,j], {k,d}, {j,0,2k-1}]];
InfoPrint["{eqns,vars}"];
sol = Solve[(#==0)& /@eqns, vars];
Print["sol is ",sol];
sol=First[sol];
Vp[d] = (Vp[d] /. sol);
Print["v is ", Vp[d]];
Print["{R4Eqn[d+1], TwistEqn[d]}=", {
ToDegree[d+1, R4Eqn[Vp[d]]],
ToDegree[d, TwistEqn[Vp[d]]]
}];
]

ToDegree[6, Vp[7]]

fb =-(1/4)+h ((x/32)+((5 y)/96))+(((h^3) (-57 (x^3)-169 (x^2) y-187 x (y^2)-99 (y^3)))/138240)+(1/69672960)(h^5) (555 (x^5)+2558 (x^4) y+5000 (x^3) (y^2)+5078 (x^2) (y^3)+2669 x (y^4)+780 (y^5))+(1/200658124800)(h^7) (-31989 (x^7)-205357 (x^6) y-592097 (x^5) (y^2)-964985 (x^4) (y^3)-949967 (x^3) (y^4)-565943 (x^2) (y^5)-186139 x (y^6)-34275 (y^7));
Vb=PCollect[
(fb /. {x->h[2], y->h[1]})h*ar[2,1] + (1/2 + fb /. {x->h[1], y->h[2]})h*ar[1,2]
+ 0 h (ar[1,1]+  ar[2,2])
+ 1/96 h^2 (h[1] ar[2,2]+h[2]ar[1,1])+0 h^2 (h[1]ar[1,1]+h[2]ar[2,2])
];
ToDegree[6, Vb] // PCollect

ToDegree[6, Vp[7]-Vb]