Single Sided Deposits

How does a single sided deposit work?

The pool tokens issued to a depositor of a single asset can be determined by utilizing the change in the value function (invariant) of the pool. As seen in the whitepaper the ratio of the change in the value function will yield the number of tokens issued. This information will become even more important when discussing multi-asset deposits:

This can be simplified for our purpose of a single sided deposit where all other tokens in a pool maintain constant balances. The token which we are investing into a pool will be denoted with the letter “t”. Amount in (At), Balance-In (Bt), Weight-In (Wt) and the pool token supply will be the variables in concern. When simplified the equation is as follows:

$$P_{issued}=P_{supply} * \Bigg(\bigg(1+ {\frac {A_{t}}{B_{t}}} \bigg)^{W_{t}}-1 \Bigg)$$