How can I find an explicit algebra presentation of $\mathbb{P}(\mathcal{O}(a_1)\oplus \cdots \mathcal{O}(a_k))$ over the projective space $\mathbb{P}^n$? For example, how can I find the algebra for $\mathbb{P}(\mathcal{O}(2)\oplus\mathcal{O}(3))$ over $\mathbb{P}^2$?
How do I find the algebra representing the projective bundle of a direct sum of line bundles over a projective space?
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