Notes for AKT-090924-2/0:36:01

Exercise. If [math]\displaystyle{ f \in {\mathcal V}_n }[/math] and [math]\displaystyle{ g \in {\mathcal V}_m }[/math] then [math]\displaystyle{ f \cdot g \in {\mathcal V}_{n+m} }[/math] (as what one would expect by looking at degrees of polynomials) and [math]\displaystyle{ W_{f \cdot g} = m_\mathbb{Q} \circ (W_f \otimes W_g) \circ \Delta }[/math] where [math]\displaystyle{ (W_f \otimes W_g) \circ \Delta: {\mathcal A} \rightarrow \mathbb{Q} \otimes \mathbb{Q} }[/math] and [math]\displaystyle{ m_\mathbb{Q} }[/math] is the multiplication of rationals.