elsympoly := proc(x,m) local p;

    convert( [seq( convert(p,`*`), p = combinat[choose](x,m) )], `+` )

end:

explist := proc(mon::monomial)
	if nops(indets(mon)) = 1
	then [degree(mon)];
	else map(degree, [op(select(has,mon,indets(mon)))])
	fi;
end:

symlist := proc(l) local n,l1,l2;
	n := nops(l);
	l1 := [op(l),0];
	l2 := [l1[i]$i=2..n+1];
	[l[i]-l2[i]$i=1..n];
end:

`type/symmetricpoly` := proc( poly::polynom ) local v,n,i,var,var1,newvar;
	v := indets(poly);
	n := nops(v);
	var := [op(v)];
	var1 := [op(v),op(1,v)];
	var1 := subs( { seq( op(i,var1)=op(i+1,var1),i=1..n) }, var1);
	newvar := [seq(var1[i], i=1..n)];
	if n > 1 then
	evalb( poly = subs( {seq(op(i,newvar)=op(i,var), i=1..n)}, poly)
		and poly = subs( {op(1,var)=op(2,var), op(2,var)=op(1,var)}, poly) );
	else true fi;
end:
	
symmetric := proc( poly::symmetricpoly, x ) local i,l,m,n,p,s,mon,symmon,sympoly;
	sympoly := 0;
	n := nops(x);
	s := array(1..n);
	p := sort(poly);
	while evalb( p<>0 ) do
		p := sort(p);
		if type( p, 'monomial' )
		then mon := p;
		else mon := op(1,p)
		fi;
		m := nops(indets(mon));
		l := symlist(explist(mon));
		symmon := convert( [s[i]^l[i]$i=1..m] ,`*` );	
		sympoly := sympoly + lcoeff(mon)*symmon;
		p := p - lcoeff(mon)*expand( subs( [seq(s[i]=elsympoly(x,i), i=1..m)], symmon) ) ;
	od;
	sympoly;
end: