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Use github math module for formulas #33

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Oct 9, 2023
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Use github math module for formulas #33

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19 changes: 18 additions & 1 deletion README.md
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Expand Up @@ -23,15 +23,32 @@

formulas without orderbook matching (Liquidity Pool Model only)

```math
Price = \frac{Target Coin Pool Amount \times (1 - Pool Fee)}{Source Coin Pool Amount + 2 \times Source Coin Amount}
```
<img src="https://latex.codecogs.com/png.image?\inline\dpi{150}\bg{white}Price&space;=&space;\frac{Target\&space;Coin\&space;Pool\&space;Amount\&space;*\&space;(1&space;-&space;Pool\&space;Fee)}{Source\&space;Coin\&space;Pool\&space;Amount\&space;&plus;\&space;2\&space;*\&space;Source\&space;Coin\&space;Amount}" />

```math
Target Coin Amount = \frac{Source Coin Amount \times Target Coin Pool Amount \times (1 - Pool Fee)}{Source Coin Pool Amount + 2 \times Source Coin Amount}
```

<img src="https://latex.codecogs.com/png.image?\inline\dpi{175}\bg{white}Target\&space;Coin\&space;Amount&space;=&space;\frac{Source\&space;Coin\&space;Amount\&space;*\&space;Target\&space;Coin\&space;Pool\&space;Amount\&space;*\&space;(1&space;-&space;Pool\&space;Fee)}{Source\&space;Coin\&space;Pool\&space;Amount\&space;&plus;\&space;2\&space;*\&space;Source\&space;Coin\&space;Amount}" />

where _Pool Fee = 0.003_ as most common value

#### Osmosis
[Module Gamm documentation](https://docs.osmosis.zone/osmosis-core/modules/gamm)

```math
Price = \frac{Target Coin Pool Amount \times (1 - Pool Fee)}{Source Coin Pool Amount + (1 - Pool Fee) \times Source Coin Amount} \times \frac{Source Coin Pool Weight}{Target Coin Pool Weight}
```

<img src="https://latex.codecogs.com/png.image?\inline\dpi{200}\bg{white}Price&space;=&space;\frac{Target\&space;Coin\&space;Pool\&space;Amount\&space;*\&space;(1&space;-&space;Pool\&space;Fee)}{Source\&space;Coin\&space;Pool\&space;Amount\&space;&plus;\&space;(1&space;-&space;Pool\&space;Fee)\&space;*\&space;Source\&space;Coin\&space;Amount}\&space;*\&space;\frac{Source\&space;Coin\&space;Pool\&space;Weight}{Target\&space;Coin\&space;Pool\&space;Weight}" />

```math
Target Coin Amount = \frac{Source Coin Amount \times Target Coin Pool Amount \times (1 - Pool Fee)}{Source Coin Pool Amount + (1 - Pool Fee) \times Source Coin Amount} \times \frac{Source Coin Pool Weight}{Target Coin Pool Weight}
```

<img src="https://latex.codecogs.com/png.image?\inline\dpi{175}\bg{white}Target\&space;Coin\&space;Amount&space;=&space;\frac{Source\&space;Coin\&space;Amount\&space;*\&space;Target\&space;Coin\&space;Pool\&space;Amount\&space;*\&space;(1&space;-&space;Pool\&space;Fee)}{Source\&space;Coin\&space;Pool\&space;Amount\&space;&plus;\&space;(1&space;-&space;Pool\&space;Fee)\&space;*\&space;Source\&space;Coin\&space;Amount}\&space;*\&space;\frac{Source\&space;Coin\&space;Pool\&space;Weight}{Target\&space;Coin\&space;Pool\&space;Weight}" />

### Analytics
Expand Down Expand Up @@ -84,4 +101,4 @@ pip install -r requirements.txt
run jupyter notebook
```bash
jupyter notebook
```
```