Swap-less scheme: Divide based on ideal flush division

Even though the deposit is not made in the ideal deposit ratio, we can try to divide it according to the ideal flush division.

This has a nice property that the imbalance of tokens affects all Strategies in the same relative amount however, the flush division does not follow the vault its Strategy Allocation, which breaks the exposure promised to the user.

This scheme also has two alternative derivations, ending up with the same result.

Alternative: scale ideal

Here we first calculate the USD value of the deposit using the exchange rates. Now we can calculate the ideal number of tokens for each strategy following the procedure described in Dividing the Deposit Among the Strategies

Then we calculate the difference between the ideal amount of tokens and the actual amount of tokens. From this, we can find the scaling factor for each asset that would bring the ideal asset amount in line with the actual amount.

We then apply this factor back to the ideal flush division.

Alternative: idealize remainder

In this alternative, we also calculate the USD value of the deposit using the exchange rates, calculate the ideal number of tokens for each strategy following the procedure described in Dividing the Deposit Among the Strategies, and calculate the difference between the ideal and actual amount of tokens.

In contrast to the first alternative, we do not calculate the scaling factor, but divide the remainder by the ideal flush division, as we did with the whole deposit in the main scheme.

Then we add both to yield the final flush division.