A direct sum decomposition is $S=\bigoplus_{a \ge 0} S_a$ (d is degree of forms homegeneous polynomial). I try to find and example of this definition, because I need to understand it. Can I take polynomial: $F_1=1+x_0^2+x_1+x_0x_3$, where $S=\mathbb{R[x_0,x_1,x_2]}$? $S_0= 1$, $S_1=x_1$, $S_2=x_0^2 +x_0x_3$. Is it correct or no? Is it wrong? When no could you explain why and give me better example?
2026-03-29 05:43:10.1774762990
Example to definition
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