would like to solve for x in terms of z from z in terms of x

however, x2 = RootOf(z2-z3-z1+_Z^3) , what is _Z ?

ex1 := {z1=x1, z2=x3-x2^3, z3=-x1+x3, z4=-x1+x4};
solve({z1=x1, z2=x3-x2^3, z3=-x1+x3, z4=-x1+x4},{x1,x2,x3,x4})

{x1 = z1, x2 = RootOf(z2-z3-z1+_Z^3), x3 = z3+z1, x4 = z4+z1}

old version define use
'homalg/default':=RPI;

in maple 15
libname := "D:/homoalg/10_homalg.lib",libname:
with(homalg):

> define(homalg, RPI, 'default');
Error, (in define) homalg is assigned
> hom2 := Hom(L, K, var);
Error, (in homalg/tablename) Since homalg/default is not defined, the last argument must be a table containing the (minimum) homalg conversions or an unassigned symbol pointing to such a table!
> define(homalg, 'RPI', 'default');

Calcution-A

with(VectorCalculus):
with(LinearAlgebra):
f := [x3*(1+x2),x1,x2*(1+x1)]:
g := [0,1+x2,-x3]:
fv := <x3*(1+x2),x1,x2*(1+x1)>:
gv := <0,1+x2,-x3>:
ad_f_g :=  MatrixAdd(MatrixVectorMultiply(Jacobian(g,[x1,x2,x3]),fv),-MatrixVectorMultiply(Jacobian(f,[x1,x2,x3]),gv)):
b := <Diff(w(x1,x2,x3),x1),Diff(w(x1,x2,x3),x2),Diff(w(x1,x2,x3),x3)>:
gv := <0,1+x2,-x3>:
c1 := DotProduct(b, gv):
c2 := DotProduct(b, ad_f_g):

http://aw.twi.tudelft.nl/~koekoek/askey/ch3/par28/par28.html

Which function represent phi in 3.28.1

with the information in the page

http://aw.twi.tudelft.nl/~koekoek/askey/ch3/par28/par28.html

what should do?

i guess to use Hn directly and use sum(Hn*z^m/m!)

is it possible in Maple?