DOCUMENTATION: Update math notations in corporation docs (#2452)

Author: catloversg

src/Documentation/doc/en/advanced/corporation/basic-gameplay-and-term.md

@@ -14,7 +14,9 @@ Each division can expand to 6 cities.
 
 Each industry has different input materials and output materials/products. For example: Agriculture needs Water and Chemicals to produce Plants and Food. The number next to each material is its "coefficient" (You can call it "weight" or "factor" if you want).
 
-$$0.5\ \textit{Water}+0.2\ \textit{Chemicals} \Rightarrow 1\ \textit{Plants}+1\ \textit{Food}$$
+$$
+0.5\ \textit{Water}+0.2\ \textit{Chemicals} \Rightarrow 1\ \textit{Plants}+1\ \textit{Food}
+$$
 
 There is no "offline progress" in corporation. When you go offline, the corporation accumulates bonus time.
 

src/Documentation/doc/en/advanced/corporation/boost-material.md

@@ -60,15 +60,21 @@ Let's define:
 
 Assuming the same warehouse setup in all cities, the division production multiplier is:
 
-$$F(x,y,z,w) = \sum_{i = 1}^{6}\left( (1 + 0.002\ast x)^{c_{1}}\ast(1 + 0.002\ast y)^{c_{2}}{\ast(1 + 0.002\ast z)}^{c_{3}}{\ast(1 + 0.002\ast w)}^{c_{4}} \right)^{0.73}$$
+$$
+F(x,y,z,w) = \sum_{i = 1}^{6}\left( (1 + 0.002\ast x)^{c_{1}}\ast(1 + 0.002\ast y)^{c_{2}}{\ast(1 + 0.002\ast z)}^{c_{3}}{\ast(1 + 0.002\ast w)}^{c_{4}} \right)^{0.73}
+$$
 
 In order to find the maximum of the function above, we can find the maximum of this function:
 
-$$F(x,y,z,w) = (1 + 0.002\ast x)^{c_{1}}\ast(1 + 0.002\ast y)^{c_{2}}{\ast(1 + 0.002\ast z)}^{c_{3}}{\ast(1 + 0.002\ast w)}^{c_{4}}$$
+$$
+F(x,y,z,w) = (1 + 0.002\ast x)^{c_{1}}\ast(1 + 0.002\ast y)^{c_{2}}{\ast(1 + 0.002\ast z)}^{c_{3}}{\ast(1 + 0.002\ast w)}^{c_{4}}
+$$
 
 Constraint function (S is storage space):
 
-$$G(x,y,z,w) = s_{1}\ast x + s_{2}\ast y + s_{3}\ast z + s_{4}\ast w = S$$
+$$
+G(x,y,z,w) = s_{1}\ast x + s_{2}\ast y + s_{3}\ast z + s_{4}\ast w = S
+$$
 
 Problem: Find the maximum of $F(x,y,z,w)$ with constraint $G(x,y,z,w)$.
 
@@ -80,88 +86,132 @@ Disclaimer: This is based on discussion between \@Jesus and \@yichizhng on Disco
 
 By using the [Lagrange multiplier](https://en.wikipedia.org/wiki/Lagrange_multiplier) method, we have this system:
 
-$$\begin{cases} \frac{\partial F}{\partial x} &= \lambda\frac{\partial G}{\partial x} \newline \frac{\partial F}{\partial y} &= \lambda\frac{\partial G}{\partial y} \newline \frac{\partial F}{\partial z} &= \lambda\frac{\partial G}{\partial z} \newline \frac{\partial F}{\partial w} &= \lambda\frac{\partial G}{\partial w} \newline G(x,y,z,w) &= S\end{cases}$$
+$$
+\begin{cases} \frac{\partial F}{\partial x} &= \lambda\frac{\partial G}{\partial x} \newline \frac{\partial F}{\partial y} &= \lambda\frac{\partial G}{\partial y} \newline \frac{\partial F}{\partial z} &= \lambda\frac{\partial G}{\partial z} \newline \frac{\partial F}{\partial w} &= \lambda\frac{\partial G}{\partial w} \newline G(x,y,z,w) &= S\end{cases}
+$$
 
 In order to solve this system, we have 2 choices:
 
 - Solve that system with [Ceres Solver](./miscellany.md).
 - Do the hard work with basic calculus and algebra. This is the optimal way in both accuracy and performance, so we'll focus on it. In the following sections, I'll show the proof for this solution.
 
-$$x\ast s_{1} = \frac{S - 500\ast\left( \frac{s_{1}}{c_{1}}\ast\left( c_{2} + c_{3} + c_{4} \right) - \left( s_{2} + s_{3} + s_{4} \right) \right)}{\frac{c_{1} + c_{2} + c_{3} + c_{4}}{c_{1}}}$$
+$$
+x\ast s_{1} = \frac{S - 500\ast\left( \frac{s_{1}}{c_{1}}\ast\left( c_{2} + c_{3} + c_{4} \right) - \left( s_{2} + s_{3} + s_{4} \right) \right)}{\frac{c_{1} + c_{2} + c_{3} + c_{4}}{c_{1}}}
+$$
 
-$$y\ast s_{2} = \frac{S - 500\ast\left( \frac{s_{2}}{c_{2}}\ast\left( c_{1} + c_{3} + c_{4} \right) - \left( s_{1} + s_{3} + s_{4} \right) \right)}{\frac{c_{1} + c_{2} + c_{3} + c_{4}}{c_{2}}}$$
+$$
+y\ast s_{2} = \frac{S - 500\ast\left( \frac{s_{2}}{c_{2}}\ast\left( c_{1} + c_{3} + c_{4} \right) - \left( s_{1} + s_{3} + s_{4} \right) \right)}{\frac{c_{1} + c_{2} + c_{3} + c_{4}}{c_{2}}}
+$$
 
-$$z\ast s_{3} = \frac{S - 500\ast\left( \frac{s_{3}}{c_{3}}\ast\left( c_{1} + c_{2} + c_{4} \right) - \left( s_{1} + s_{2} + s_{4} \right) \right)}{\frac{c_{1} + c_{2} + c_{3} + c_{4}}{c_{3}}}$$
+$$
+z\ast s_{3} = \frac{S - 500\ast\left( \frac{s_{3}}{c_{3}}\ast\left( c_{1} + c_{2} + c_{4} \right) - \left( s_{1} + s_{2} + s_{4} \right) \right)}{\frac{c_{1} + c_{2} + c_{3} + c_{4}}{c_{3}}}
+$$
 
-$$w\ast s_{4} = \frac{S - 500\ast\left( \frac{s_{4}}{c_{4}}\ast\left( c_{1} + c_{2} + c_{3} \right) - \left( s_{1} + s_{2} + s_{3} \right) \right)}{\frac{c_{1} + c_{2} + c_{3} + c_{4}}{c_{4}}}$$
+$$
+w\ast s_{4} = \frac{S - 500\ast\left( \frac{s_{4}}{c_{4}}\ast\left( c_{1} + c_{2} + c_{3} \right) - \left( s_{1} + s_{2} + s_{3} \right) \right)}{\frac{c_{1} + c_{2} + c_{3} + c_{4}}{c_{4}}}
+$$
 
 ## Proof
 
 Define: $k = 0.002$
 
-$$\begin{cases}\frac{\partial F}{\partial x} = \left( k\ast c_{1}\ast(1 + k\ast x)^{c_{1} - 1} \right)\ast(1 + k\ast y)^{c_{2}}\ast(1 + k\ast z)^{c_{3}}\ast(1 + k\ast w)^{c_{4}} = \lambda\ast s_{1} \newline \frac{\partial F}{\partial y} = (1 + k\ast x)^{c_{1}}\ast\left( k\ast c_{2}\ast(1 + k\ast y)^{c_{2} - 1} \right)\ast(1 + k\ast z)^{c_{3}}\ast(1 + k\ast w)^{c_{4}} = \lambda\ast s_{2} \end{cases}$$
+$$
+\begin{cases}\frac{\partial F}{\partial x} = \left( k\ast c_{1}\ast(1 + k\ast x)^{c_{1} - 1} \right)\ast(1 + k\ast y)^{c_{2}}\ast(1 + k\ast z)^{c_{3}}\ast(1 + k\ast w)^{c_{4}} = \lambda\ast s_{1} \newline \frac{\partial F}{\partial y} = (1 + k\ast x)^{c_{1}}\ast\left( k\ast c_{2}\ast(1 + k\ast y)^{c_{2} - 1} \right)\ast(1 + k\ast z)^{c_{3}}\ast(1 + k\ast w)^{c_{4}} = \lambda\ast s_{2} \end{cases}
+$$
 
 ≡
 
-$$k\ast c_{1}\ast(1 + k\ast x)^{- 1}\ast s_{2} = k\ast c_{2}\ast(1 + k\ast y)^{- 1}\ast s_{1}$$
+$$
+k\ast c_{1}\ast(1 + k\ast x)^{- 1}\ast s_{2} = k\ast c_{2}\ast(1 + k\ast y)^{- 1}\ast s_{1}
+$$
 
 ≡
 
-$$c_{1}\ast s_{2}\ast(1 + k\ast y) = c_{2}\ast s_{1}\ast(1 + k\ast x)$$
+$$
+c_{1}\ast s_{2}\ast(1 + k\ast y) = c_{2}\ast s_{1}\ast(1 + k\ast x)
+$$
 
 ≡
 
-$$1 + k\ast y = \frac{c_{2}\ast s_{1}}{c_{1}\ast s_{2}}\ast(1 + k\ast x)$$
+$$
+1 + k\ast y = \frac{c_{2}\ast s_{1}}{c_{1}\ast s_{2}}\ast(1 + k\ast x)
+$$
 
 ≡
 
-$$y = \frac{c_{2}\ast s_{1} + k\ast x\ast c_{2}\ast s_{1} - c_{1}\ast s_{2}}{k\ast c_{1}\ast s_{2}}$$
+$$
+y = \frac{c_{2}\ast s_{1} + k\ast x\ast c_{2}\ast s_{1} - c_{1}\ast s_{2}}{k\ast c_{1}\ast s_{2}}
+$$
 
 ≡
 
-$$y\ast s_{2} = \frac{c_{2}\ast s_{1}\ast s_{2} + k\ast x\ast c_{2}\ast s_{1}\ast s_{2} - c_{1}\ast s_{2}\ast s_{2}}{k\ast c_{1}\ast s_{2}}$$
+$$
+y\ast s_{2} = \frac{c_{2}\ast s_{1}\ast s_{2} + k\ast x\ast c_{2}\ast s_{1}\ast s_{2} - c_{1}\ast s_{2}\ast s_{2}}{k\ast c_{1}\ast s_{2}}
+$$
 
 ≡
 
-$$y\ast s_{2} = \frac{c_{2}\ast s_{1}}{k\ast c_{1}} + \frac{x\ast c_{2}\ast s_{1}}{c_{1}} - \frac{s_{2}}{k}$$
+$$
+y\ast s_{2} = \frac{c_{2}\ast s_{1}}{k\ast c_{1}} + \frac{x\ast c_{2}\ast s_{1}}{c_{1}} - \frac{s_{2}}{k}
+$$
 
 ≡
 
-$$y\ast s_{2} = \frac{c_{2}}{c_{1}}\ast x\ast s_{1} + \frac{1}{k}\ast\frac{c_{2}\ast s_{1} - c_{1}\ast s_{2}}{c_{1}}$$
+$$
+y\ast s_{2} = \frac{c_{2}}{c_{1}}\ast x\ast s_{1} + \frac{1}{k}\ast\frac{c_{2}\ast s_{1} - c_{1}\ast s_{2}}{c_{1}}
+$$
 
 ≡
 
-$$y\ast s_{2} = \frac{c_{2}}{c_{1}}\ast x\ast s_{1} + 500\ast\frac{c_{2}\ast s_{1} - c_{1}\ast s_{2}}{c_{1}}$$
+$$
+y\ast s_{2} = \frac{c_{2}}{c_{1}}\ast x\ast s_{1} + 500\ast\frac{c_{2}\ast s_{1} - c_{1}\ast s_{2}}{c_{1}}
+$$
 
 Repeating the above steps, we have:
 
-$$z\ast s_{3} = \frac{c_{3}}{c_{1}}\ast x\ast s_{1} + 500\ast\frac{c_{3}\ast s_{1} - c_{1}\ast s_{3}}{c_{1}}$$
+$$
+z\ast s_{3} = \frac{c_{3}}{c_{1}}\ast x\ast s_{1} + 500\ast\frac{c_{3}\ast s_{1} - c_{1}\ast s_{3}}{c_{1}}
+$$
 
-$$w\ast s_{4} = \frac{c_{4}}{c_{1}}\ast x\ast s_{1} + 500\ast\frac{c_{4}\ast s_{1} - c_{1}\ast s_{4}}{c_{1}}$$
+$$
+w\ast s_{4} = \frac{c_{4}}{c_{1}}\ast x\ast s_{1} + 500\ast\frac{c_{4}\ast s_{1} - c_{1}\ast s_{4}}{c_{1}}
+$$
 
 Substituting into the constraint function:
 
-$$x\ast s_{1} + y\ast s_{2} + z\ast s_{3} + w\ast s_{4} = S$$
+$$
+x\ast s_{1} + y\ast s_{2} + z\ast s_{3} + w\ast s_{4} = S
+$$
 
 ≡
 
-$$x\ast s_{1} + \frac{c_{2}}{c_{1}}\ast x\ast s_{1} + 500\ast\frac{c_{2}\ast s_{1} - c_{1}\ast s_{2}}{c_{1}} + \frac{c_{3}}{c_{1}}\ast x\ast s_{1} + 500\ast\frac{c_{3}\ast s_{1} - c_{1}\ast s_{3}}{c_{1}} + \frac{c_{4}}{c_{1}}\ast x\ast s_{1} + 500\ast\frac{c_{4}\ast s_{1} - c_{1}\ast s_{4}}{c_{1}} = S$$
+$$
+x\ast s_{1} + \frac{c_{2}}{c_{1}}\ast x\ast s_{1} + 500\ast\frac{c_{2}\ast s_{1} - c_{1}\ast s_{2}}{c_{1}} + \frac{c_{3}}{c_{1}}\ast x\ast s_{1} + 500\ast\frac{c_{3}\ast s_{1} - c_{1}\ast s_{3}}{c_{1}} + \frac{c_{4}}{c_{1}}\ast x\ast s_{1} + 500\ast\frac{c_{4}\ast s_{1} - c_{1}\ast s_{4}}{c_{1}} = S
+$$
 
 ≡
 
-$$\frac{x\ast s_{1}\ast\left( c_{1} + c_{2} + c_{3} + c_{4} \right)}{c_{1}} + \frac{500}{c_{1}}\ast\left( c_{2}\ast s_{1} - c_{1}\ast s_{2} + c_{3}\ast s_{1} - c_{1}\ast s_{3} + c_{4}\ast s_{1} - c_{1}\ast s_{4} \right) = S$$
+$$
+\frac{x\ast s_{1}\ast\left( c_{1} + c_{2} + c_{3} + c_{4} \right)}{c_{1}} + \frac{500}{c_{1}}\ast\left( c_{2}\ast s_{1} - c_{1}\ast s_{2} + c_{3}\ast s_{1} - c_{1}\ast s_{3} + c_{4}\ast s_{1} - c_{1}\ast s_{4} \right) = S
+$$
 
 ≡
 
-$$\frac{x\ast s_{1}\ast\left( c_{1} + c_{2} + c_{3} + c_{4} \right)}{c_{1}} + \frac{500}{c_{1}}\ast\left( s_{1}\ast\left( c_{2} + c_{3} + c_{4}\  \right) - c_{1}\ast\left( s_{2} + s_{3} + s_{4} \right) \right) = S$$
+$$
+\frac{x\ast s_{1}\ast\left( c_{1} + c_{2} + c_{3} + c_{4} \right)}{c_{1}} + \frac{500}{c_{1}}\ast\left( s_{1}\ast\left( c_{2} + c_{3} + c_{4}\  \right) - c_{1}\ast\left( s_{2} + s_{3} + s_{4} \right) \right) = S
+$$
 
 ≡
 
-$$x\ast s_{1}\ast\frac{c_{1} + c_{2} + c_{3} + c_{4}}{c_{1}} + \frac{500}{c_{1}}\ast\left( s_{1}\ast\left( c_{2} + c_{3} + c_{4}\  \right) - c_{1}\ast\left( s_{2} + s_{3} + s_{4} \right) \right) = S$$
+$$
+x\ast s_{1}\ast\frac{c_{1} + c_{2} + c_{3} + c_{4}}{c_{1}} + \frac{500}{c_{1}}\ast\left( s_{1}\ast\left( c_{2} + c_{3} + c_{4}\  \right) - c_{1}\ast\left( s_{2} + s_{3} + s_{4} \right) \right) = S
+$$
 
 ≡
 
-$$x\ast s_{1} = \frac{S - 500\ast\left( \frac{s_{1}}{c_{1}}\ast\left( c_{2} + c_{3} + c_{4} \right) - \left( s_{2} + s_{3} + s_{4} \right) \right)}{\frac{c_{1} + c_{2} + c_{3} + c_{4}}{c_{1}}}$$
+$$
+x\ast s_{1} = \frac{S - 500\ast\left( \frac{s_{1}}{c_{1}}\ast\left( c_{2} + c_{3} + c_{4} \right) - \left( s_{2} + s_{3} + s_{4} \right) \right)}{\frac{c_{1} + c_{2} + c_{3} + c_{4}}{c_{1}}}
+$$
 
 We can do the same steps for y,z,w.
 

src/Documentation/doc/en/advanced/corporation/demand-competition.md

@@ -40,7 +40,9 @@ During the START state, the game decreases `demand` and increases `competition`
 
 - Amount of change:
 
-$$AmountOfChange = Random(0,3)*0.0004$$
+$$
+AmountOfChange = Random(0,3)*0.0004
+$$
 
 - This amount is multiplied by 3 if the industry is Pharmaceutical, Software or Robotics.
 

src/Documentation/doc/en/advanced/corporation/financial-statement.md

@@ -33,7 +33,9 @@ Cycle's valuation:
 
 - AssetDelta:
 
-$$AssetDelta = \frac{TotalAssets - PreviousTotalAssets}{10}$$
+$$
+AssetDelta = \frac{TotalAssets - PreviousTotalAssets}{10}
+$$
 
 - Pre-IPO:
   - If `AssetDelta` is greater than 0, it's used for calculating valuation.
@@ -45,7 +47,9 @@ $$AssetDelta = \frac{TotalAssets - PreviousTotalAssets}{10}$$
     $$AssetDelta = AssetDelta\ast(1 - DividendRate)$$
   - Formula:
 
-$$Valuation = (Funds + AssetDelta\ast 85000)\ast\left(\sqrt[12]{1.1}\right)^{NumberOfOfficesAndWarehouses}$$
+$$
+Valuation = (Funds + AssetDelta\ast 85000)\ast\left(\sqrt[12]{1.1}\right)^{NumberOfOfficesAndWarehouses}
+$$
 
 - Minimum value of valuation is $10^{10}$.
 - Valuation is multiplied by `CorporationValuation`. Many BitNodes cripple Corporation via this multiplier.
@@ -65,7 +69,9 @@ Each round has its own `FundingRoundShares` and `FundingRoundMultiplier`.
 
 Formula:
 
-$$Offer = CorporationValuation\ast FundingRoundShares\ast FundingRoundMultiplier$$
+$$
+Offer = CorporationValuation\ast FundingRoundShares\ast FundingRoundMultiplier
+$$
 
 Analyses:
 
@@ -79,21 +85,29 @@ Analyses:
 
 Your dividend is negatively affected by a penalty modifier called `TributeModifier`. `TributeModifier` depends on `CorporationSoftcap`. In BN3, `CorporationSoftcap` is 1.
 
-$$TributeModifier = 1.15 - CorporationSoftcap$$
+$$
+TributeModifier = 1.15 - CorporationSoftcap
+$$
 
 `ShadyAccounting` reduces `TributeModifier` by 0.05.
 
 `GovernmentPartnership` reduces `TributeModifier` by 0.1.
 
 Formula:
 
-$$TotalDividends = DividendRate\ast(Revenue - Expenses)\ast 10$$
+$$
+TotalDividends = DividendRate\ast(Revenue - Expenses)\ast 10
+$$
 
-$$Dividend = \left(OwnedShares\ast\frac{TotalDividends}{TotalShares}\right)^{1 - TributeModifier}$$
+$$
+Dividend = \left(OwnedShares\ast\frac{TotalDividends}{TotalShares}\right)^{1 - TributeModifier}
+$$
 
 Retained earning:
 
-$$RetainedEarning = (1 - DividendRate)\ast(Revenue - Expenses)\ast 10$$
+$$
+RetainedEarning = (1 - DividendRate)\ast(Revenue - Expenses)\ast 10
+$$
 
 Dividend is added to player's money. Retained earning is added to corporation's funds. This means if we increase `DividendRate`, corporation's valuation is dwindled.
 
@@ -117,15 +131,21 @@ If your corporation is self-funded and you sell CEO position, you only need 50b
 
 `TargetSharePrice`:
 
-$$OwnershipPercentage = \frac{OwnedShares}{TotalShares}$$
+$$
+OwnershipPercentage = \frac{OwnedShares}{TotalShares}
+$$
 
-$$TargetSharePrice = \frac{CorporationValuation*\left(0.5+\sqrt{OwnershipPercentage}\right)}{TotalShares}$$
+$$
+TargetSharePrice = \frac{CorporationValuation*\left(0.5+\sqrt{OwnershipPercentage}\right)}{TotalShares}
+$$
 
 When corporation goes public, the initial share price is `TargetSharePrice`.
 
 Share price is updated in START state.
 
-$$SharePrice = \begin{cases} SharePrice\ast(1 + Math.random()\ast 0.01), & SharePrice \leq TargetSharePrice \newline SharePrice\ast(1 - Math.random()\ast 0.01), & SharePrice > TargetSharePrice\end{cases}$$
+$$
+SharePrice = \begin{cases} SharePrice\ast(1 + Math.random()\ast 0.01), & SharePrice \leq TargetSharePrice \newline SharePrice\ast(1 - Math.random()\ast 0.01), & SharePrice > TargetSharePrice\end{cases}
+$$
 
 Minimum share price is 0.01.
 
@@ -135,17 +155,28 @@ Issue new shares:
 - The number of new shares issued must be a multiple of 10 million.
 - New share price:
 
-$$NewOwnershipPercentage = \frac{OwnedShares}{TotalShares+NewShares}$$
+$$
+NewOwnershipPercentage = \frac{OwnedShares}{TotalShares+NewShares}
+$$
 
-$$NewSharePrice = \frac{CorporationValuation\ast\left(0.5+\sqrt{NewOwnershipPercentage}\right)}{TotalShares}$$
+$$
+NewSharePrice = \frac{CorporationValuation\ast\left(0.5+\sqrt{NewOwnershipPercentage}\right)}{TotalShares}
+$$
 
 - Profit:
 
-$$Profit = {NewShares\ast(SharePrice + NewSharePrice)}\ast{0.5}$$
+$$
+Profit = {NewShares\ast(SharePrice + NewSharePrice)}\ast{0.5}
+$$
 
 - Profit is added to corporation's funds.
 - `DefaultCooldown` is 4 hours.
-- Cooldown: $$Cooldown = DefaultCooldown\ast\frac{TotalShares}{10^{9}}$$
+- Cooldown:
+
+$$
+Cooldown = DefaultCooldown\ast\frac{TotalShares}{10^{9}}
+$$
+
 - Part of the new shares are added to `InvestorShares`. The remaining ones are added to `IssuedShares`.
   - `MaxPrivateShares`:
     $$MaxPrivateShares = {NewShares}\ast{0.5}\ast\frac{InvestorShares}{TotalShares}$$
@@ -174,8 +205,14 @@ Sold/bought back shares are processed in multiple "iterations".
 - Number of shares processed each iteration is shareSalesUntilPriceUpdate. Default value is $10^6$.
 - Share price is recalculated each iteration.
 
-$$OwnershipPercentage = \frac{OwnedShares - ProcessedShares}{TotalShares}$$
+$$
+OwnershipPercentage = \frac{OwnedShares - ProcessedShares}{TotalShares}
+$$
 
-$$TargetSharePrice = \frac{CorporationValuation\ast\left(0.5 + \sqrt{OwnershipPercentage}\right)}{TotalShares}$$
+$$
+TargetSharePrice = \frac{CorporationValuation\ast\left(0.5 + \sqrt{OwnershipPercentage}\right)}{TotalShares}
+$$
 
-$$SharePrice = \begin{cases} SharePrice\ast 1.005, SharePrice \leq TargetSharePrice \newline SharePrice\ast 0.995, SharePrice > TargetSharePrice\end{cases}$$
+$$
+SharePrice = \begin{cases} SharePrice\ast 1.005, SharePrice \leq TargetSharePrice \newline SharePrice\ast 0.995, SharePrice > TargetSharePrice\end{cases}
+$$

src/Documentation/doc/en/advanced/corporation/miscellany.md

@@ -48,7 +48,9 @@ The optimal export string is `(IPROD+IINV/10)*(-1)`. For example: export "Chemic
   - IINV = 700
 - "Export" is expressed by number of units per second, so we want to export:
 
-$$\left(100-\frac{700}{10}\right)=\left(-100+\frac{700}{10}\right)\ast(-1)=\left(IPROD+\frac{IINV}{10}\right)\ast(-1)$$
+$$
+\left(100-\frac{700}{10}\right)=\left(-100+\frac{700}{10}\right)\ast(-1)=\left(IPROD+\frac{IINV}{10}\right)\ast(-1)
+$$
 
 Export route is FIFO. You can remove an export route by using `cancelExportMaterial` NS API.