Stableswap.md

Stableswap

Notation

Variable	Description
$R_i$	Stableswap reserve of asset $i$
$S$	Shares in stableswap pool
$D$	Stableswap invariant

For a given state variable $X$, we will generally denote the value of $X$ after the operation by $X^+$.

Operation-specific

Swap

• After a swap, we should have

$$ D + 5000 \geq D^+ \geq D $$

Add Liquidity (arbitrary assets)

• After adding liquidity, we should have

$$ D^+ \geq D $$

$$ D^+ S \geq D S^+ \geq (D^+ - 1)S $$

Withdraw Liquidity (one asset)

• After removing liquidity, we should have

$$ D^+\leq D $$

$$ D(S^+ + 1) \geq D^+ S \geq D S^+ $$