polx0, pol0y: Files that contain the minpoly's (copied from Bostan/Kauers website)
polx0_comp: These steps are explained in the appendix. In this line:
P11 := factors(subs(v = 1/256*(3*s-1)*(s+1)^3/s^3, P10))[2]:
the subs command effectively makes a field extension from F(v) to F(s),
an extension of degree 4 with v = 1/256*(3*s-1)*(s+1)^3/s^3. Then
it factors P10 over the larger field F(s). The extension was found
by computing subfields; this subfields computation was not shown, it
was done interactively in Maple using subfields + reconstruction,
but the subfields computation was not saved in a file. Some of the
reconstruction computations have been stored, see for instance
the file pol0y_comp under the header "computing P7".
REWRITE_pol: Reverses the substitutions made in polx0_comp to compute a solution
of polx0, also makes some simplifications (file is messy).
pol0y_comp: Similar to polx0_comp, it read the file with the minpoly, and then
performs similar steps.
ANSWER: This puts everything together: G was computed from G(t;x,0) and G(t;0,y)
and then some further simplifications were made by putting well chosen
terms (not all terms) under common denominators.
If you put want_series:=true; then the series expansion of G(t;x,y)
is computed in this file; this is a good way to guard against errors.
Mark van Hoeij