# Stable Math

First introduced by Curve, the Stableswap is a hybrid algorithm, to bring solution to the problems of slippage and fixed liquidity. The Stableswap hybrid combines both **Constant Product** and **Constant Sum** models, and the following chart shows the Stableswap algorithm in relation to constant product and constant sum invariants.

The *amplification parameter*, $A$, defines the degree to which the Stable Math curve approximates the Constant Product curve (when $A=0$), or the Constant Sum curve (when $A\rightarrow \infty$).

**Constant Sum:**When the liquidity pool portfolio is balanced, the algorithm functions as a Constant Sum formula;**x + y = k**. You can observe the StableSwapstaying close to the Constant Sum**blue line**, and the price is stable.**red line****Constant Product:**As the liquidity pool portfolio becomes imbalanced, the StableSwap algorithm functions as a Constant Product formula;**x * y = k**. You can observe the StableSwapnow resembling the Constant Product**blue line**, and the price becoming expensive.**purple line**

### Invariant

Since the Stable Math equation is quite complex, determining the invariant, $D$, is typically done iteratively.

Where:

$n$ is the number of tokens

$x_i$ is is balance of token $i$

$A$ is the amplification parameter

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