Help:=proc():print(`IsPos(f,x,K),Sam(f,x,w,K)`):end:

#IsPos(f,x,K): inputs a function of the
#list of variables x, and a pos. integer K
#outputs true iff all the Taylor coeff. up
#to K are non-negative
IsPos:=proc(f,x,K) local g,i,S:
g:=mtaylor(f,x,K):
S:={}:

for i from 1 to nops(g) do
 S:=S union {subs({seq(x[i]=1,i=1..nops(x))},
op(i,g))}:
od:
evalb(min(op(S)) >=0):
end:

#Sam(f,x,w,K): inputs a function of the
#of list of variables z, and w and a pos. integer K
#outputs true iff all the Taylor coeff. up
#to K are non-negative
#Here f is a f.p.s in z with coeff. that
#are Laurent polynomials in w
Sam:=proc(f,x,w,K) local g,i,S,S1,T,j,i1,t:
g:=mtaylor(f,x,K):
S:={}:

for i from 1 to nops(g) do
 S:=S union {subs({seq(x[i1]=1,i1=1..nops(x))},
op(i,g))}:
od:



S:=expand(S):

{seq(coeffs(S[i],w),i=1..nops(S))}:
end: