hydradx/spec/OmnipoolSpec.ipynb

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   "source": [
    "# Omnipool Specification"
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   "source": [
    "## State Variables"
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    "| Symbol | Description | Domain |\n",
    "| -------- | ------- | ----- |\n",
    "| $R_i$ | Quantity of asset $i$ in Omnipool | $\\mathbb{R}_{++}$ |\n",
    "| $Q_i$ | Quantity of LRNA matching asset $i$ | $\\mathbb{R}_{++}$ |\n",
    "| $A_i$ | Quantity of asset $i$ in protocol treasury | $\\mathbb{R}_{+}$ |\n",
    "| $D$ | Quantity of LRNA in protocol treasury | $\\mathbb{R}_{+}$ |\n",
    "| $S_i$ | Quantity of LP shares for pool $i$ | $\\mathbb{R}_{++}$ |\n",
    "| $B_i$ | Quantity of LP shares for pool $i$ owned by protocol | $\\mathbb{R}_{+}$ |\n",
    "| $H$ | Current LRNA global supply | $\\mathbb{R}_{++}$ |\n",
    "| $f_P$ | Protocol fee | $[0,1)$\n",
    "| $f_A$ | Asset fee | $[0,1)$\n",
    "| $L$ | LRNA imbalance | $\\mathbb{R}$ |\n",
    "| $\\omega_i$ | Soft caps on asset $i$ weight in Omnipool | $[0,1]$ |"
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    "| Symbol | Description | Equation                         |\n",
    "| -------- | ------- |----------------------------------|\n",
    "| $n$ | Number of Risk Assets  | $\\vert \\vec{R}\\vert$             |\n",
    "| $Q$ | Total LRNA in Omnipool  | $\\sum_i Q_i$                     |\n",
    "| $p_i^Q$ | Price of asset $i$ in LRNA | $\\frac{Q_i}{R_i}$                |\n",
    "| $p_i^j$ | Price of asset $i$ denominated in $j$ | $\\frac{Q_i}{Q_j}\\frac{R_j}{R_i}$ |\n",
    "| $W_i$ | Weight of asset $i$ in pool | $\\frac{Q_i}{Q}$                  |\n",
    "| $Y_i$ | Swap invariant of asset $i$ in pool | $Q_i R_i$                        |"
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   "source": [
    "## LP Variables"
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    "| Symbol | Description | Domain  |\n",
    "| -------- | ------- | ----------------- |\n",
    "| $i_\\alpha$ | LP $\\alpha$ is providing asset $i_\\alpha$  | $\\{1,\\ldots, n\\}$ |\n",
    "| $r_\\alpha$ | Quantity of asset $i_\\alpha$ that LP $\\alpha$ has outside of pool | $\\mathbb{R}_{+}$ |\n",
    "| $q_\\alpha$ | Quantity of LRNA that LP $\\alpha$ has outside of pool | $\\mathbb{R}_{+}$ |\n",
    "| $s_\\alpha$ | Quantity of LP shares for pool $i_\\alpha$ in position $\\alpha$  | $\\mathbb{R}_{++}$ |\n",
    "| $p_\\alpha$ | Price at which position $\\alpha$ was created | $\\mathbb{R}_{++}$ |"
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   "source": [
    "## Identities"
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   "source": [
    "$$\n",
    "S_i = B_i + \\sum_\\alpha s_i^\\alpha\\\\\n",
    "$$"
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   "source": [
    "## Notation"
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    "For a variable $A$, we will use the notation $A^+ = A + \\Delta A$ for the variable in a state change. The sign of $\\Delta A$ for a pool variable $A$ will always reflect the change from the perspective of the pool. If $A$ is an agent variable, the sign of $\\Delta A$ will reflect the change fromt he perspective of the agent."
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   "source": [
    "## Operations\n",
    "- Add new token : AddToken.ipynb\n",
    "- Add Asset Liquidity : AddLiquidity.ipynb\n",
    "- Withdraw Asset Liquidity : WithdrawLiquidity.ipynb\n",
    "- Swap $i$ with LRNA : SwapLRNA.ipynb\n",
    "- Swap between two risk assets: Swap.ipynb"
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