fix readme

README.md

@@ -259,7 +259,7 @@ $L_c =$ current_liquidity\
 $\Delta{L} =$ liquidity_delta
 
 ##### Formula:
-const $a_{OneLP} = 2^{85-64} - $  scale of the LpToken based on $L_{max} $ for full range position ($<2^{85}$) and token precision ($2^{64} - 1 \approx 2^{64}$)
+const $a_{OneLP} = 2^{85-64}$ - scale of the LpToken based on $L_{max}$ for full range position ($<2^{85}$) and token precision ($2^{64} - 1 \approx 2^{64}$)
 
 $$ for \ L_c = 0, a_{LP} = \Delta{L}/a_{OneLP}$$
 $$ for \ L_c \ne 0, a_{LP} = \frac {\Delta{L}*a_T} {L_c}$$
@@ -319,12 +319,13 @@ $t_u =$ upper_tick\
 $\sqrt{p_c} =$ current_sqrt_price
 
 ##### Formula:
-$$ for \ \Delta{L_x} > \Delta{L_y} \land \Delta{y} \le y, (\Delta{L_{max}}, \Delta{x_{max}}, \Delta{y_{max}}) = (\Delta{L_x}, x, \Delta{y}) $$
+$$ for \ \Delta{L_x} > \Delta{L_y} \land \Delta{y} \le y, (\Delta{L_{max}}, \Delta{x_{max}}, \Delta{y_{max}}) = (\Delta{L_x}, x, \Delta{y})$$
+
+$$ for \ \Delta{L_x} > \Delta{L_y} \land \Delta{y} > y, (\Delta{L_{max}}, \Delta{x_{max}}, \Delta{y_{max}}) = (\Delta{L_y}, \Delta{x}, y)$$
 
-$$ for \ \Delta{L_x} > \Delta{L_y} \land \Delta{y} > y, (\Delta{L_{max}}, \Delta{x_{max}}, \Delta{y_{max}}) = (\Delta{L_y}, \Delta{x}, y) $$
+$$ for \ \Delta{L_y} > \Delta{L_x} \land \Delta{x} \le  x, (\Delta{L_{max}}, \Delta{x_{max}}, \Delta{y_{max}}) = (\Delta{L_y}, \Delta{x}, y)$$
 
-$$ for \ \Delta{L_y} > \Delta{L_x} \land \Delta{x} \le  x, (\Delta{L_{max}}, \Delta{x_{max}}, \Delta{y_{max}}) = (\Delta{L_y}, \Delta{x}, y) $$
-$$ for \ \Delta{L_y} > \Delta{L_x} \land \Delta{x}> x, (\Delta{L_{max}}, \Delta{x_{max}}, \Delta{y_{max}}) = (\Delta{L_x}, x, \Delta{y}) $$
+$$ for \ \Delta{L_y} > \Delta{L_x} \land \Delta{x}> x, (\Delta{L_{max}}, \Delta{x_{max}}, \Delta{y_{max}}) = (\Delta{L_x}, x, \Delta{y})$$
 
 #### Compute LpShare change
 Computation is performed as follows:
@@ -412,7 +413,7 @@ $x_{transfer} =$ amount of token x that will be transferred from the user to the
 $y_{transfer} =$ amount of token y that will be transferred from the user to the contract
 ##### Formula:
 $$ (x_{amount}, x_{fee}, x_{leftover}, y_{amount}, y_{fee}, y_{leftover}, a_T, L_c) $$
-$$ \downarrow $$
+$$  $$
 $$ Mint(\Delta{L}, x_{total},y_{total},t_c,\sqrt{p_c}, s(t), a_T) $$
 $$ \downarrow $$
 $$ (x_{amount}', x_{fee}', x_{leftover}', y_{amount}', y_{fee}', y_{leftover}', a_T', L_c') $$
@@ -438,18 +439,22 @@ $x_{leftover} =$  lp pool leftovers in token x\
 $y_{leftover} =$  lp pool leftovers in token y\
 $\Delta{a} =$ liquidity token amount that will be burned\
 $a_T=$ total liquidity token supply\
-$ x_{total} $ =$x_{amount}$ + $x_{fee}$ + $x_{leftover}$\
-$ y_{total} $ =$y_{amount}$ + $y_{fee}$ + $y_{leftover}$\
+$ x_{total}$ =$x_{amount}$ + $x_{fee}$ + $x_{leftover}$\
+$ y_{total}$ =$y_{amount}$ + $y_{fee}$ + $y_{leftover}$\
 $t_{min} = get\_min\_tick(s(t))$\
 $t_{max} = get\_max\_tick(s(t))$\
 $x_{transfer} =$ amount of token x that will be transferred from the contract to the user\
 $y_{transfer} =$ amount of token y that will be transferred from the contract to the user
 ##### Formula:
-$$ (x_{amount}, x_{fee}, x_{leftover}, y_{amount}, y_{fee}, y_{leftover}, a_T, L_c) $$
-$$ \downarrow $$
-$$ Burn(\Delta{L}, x_{total},y_{total},t_c,\sqrt{p_c}, s(t), a_T) $$
-$$ \downarrow $$
-$$ (x_{amount}', x_{fee}', x_{leftover}', y_{amount}', y_{fee}', y_{leftover}', a_T', L_c') $$
+$$(x_{amount}, x_{fee}, x_{leftover}, y_{amount}, y_{fee}, y_{leftover}, a_T, L_c)$$
+
+$$\downarrow$$
+
+$$Burn(\Delta{L}, x_{total},y_{total},t_c,\sqrt{p_c}, s(t), a_T)$$
+
+$$\downarrow$$
+
+$$ (x_{amount}', x_{fee}', x_{leftover}', y_{amount}', y_{fee}', y_{leftover}', a_T', L_c')$$
 \
 $ \Delta{LpShare} = compute\_lp\_share\_change(false, a_t, x_{total}, y_{total}, t_c, \sqrt{p_c}, s(t))$
 $ (position, (x_{transfer}, y_{transfer}), \Delta{a}, (x_{leftover}', y_{leftover}')) = \Delta{LpShare}$\