In "Calculating Liquidity", why pick the smaller L among the two calculated values?

[uniyj]

Would be useful to have a brief explanation of why the smaller L value is used. Thanks.

[0xtito]

Ya I am having troubling understanding why picking the smaller L would distribute the liquidity evenly along the curve while the bigger L wouldn't.

[uniyj]

This is now addressed in ed077b0
: )

[1NT18IS080]

What do we mean, when we say
Because the bigger one already includes the smaller one!
A bit more explanation will be very helpful

[uniyj]

If you follow the rest of the "Calculating Liquidity" chapter, you will see that you are calculating two Ls for the delta-x and delta-y that you are looking to add. Due to rounding errors, the two Ls will not be exactly equal. The liquidity you are adding (within the price range defined) is distributed evenly, and so the two Ls actually need to be equal. In the example given, with the intended delta-x and delta-y, the L calculated from delta-x is the bigger value. If you choose to use that bigger L, you will then need to add more delta-y than intended, to achieve that bigger L. But if you choose to use the smaller L (calculated from delta-y), then the actual delta-x needed is slightly less, and the leftover can just be unused. It's easier to have some leftover of delta-x by adding the smaller L, instead of having to calculate and add extra delta-y to achieve the bigger L.

Think of it like you have $10, and it's easier to buy something at $9.90 and get $0.10 change back, instead of trying to buy something at $10.10 and thus having to go add an extra $0.10 before you can do the purchase.