Help:=proc(): print(` GenPol(varL, degL,a) `) :end:


#GenPol(varL,degL,a): inputs a list of variables
#a list of non-negative integers, and a symbol a
#outputs a polynomial (of degrees given by degL)
#whose coefficients are a[s0],a[s0+1], ...
#and the set of coefficients 
GenPol:=proc(varL,degL,a,s0) local P,var,x,n,d,i,varL1,P1,aek,c,degL1:

if nops(degL)<>nops(varL) then
  ERROR(`Bad input`):
fi:

n:=nops(varL):

x:=varL[n]:

d:=degL[n]:

if n=1 then

 RETURN(add(a[i+s0]*x^i,i=0..d), {seq(a[i],i=s0..s0+d)}):
fi:

varL1:=[op(1..n-1,varL)]:degL1:=[op(1..n-1,degL)]:



P:=0:

c:=s0:
var:={}:

for i from 0 to d do
 aek:=GenPol(varL1,degL1,a,c):
 P1:=aek[1]: 
 var:=var union aek[2]: c:=c+nops(aek[2]):
 P:=expand(P+P1*x^i):

od:

P,var:

end: