1
vote
1answer
270 views

Is it true that Sym[P]!=0 and Sym[Q]!=0 implies Sym[PQ]!=0 ?

Let $P,Q$ be homogenous polynomials in variables $x=x_1,\dots,x_n$ resp. $y=y_1,\dots,y_m.$ We know that $Sym_x[P]$ and $Sym_y[Q]$ are not identically zero. Does it follow that $Sym_{x \cup y}[PQ]$ ...