From b70ba3406d00075dc6234d2249b238e6eb2d405d Mon Sep 17 00:00:00 2001
From: Daira Hopwood <daira@jacaranda.org>
Date: Tue, 17 Mar 2020 18:40:57 +0000
Subject: [PATCH] ZIP 207: use math markup.

Signed-off-by: Daira Hopwood <daira@jacaranda.org>
---
 zip-0207.rst | 48 +++++++++++++++++++++++++++---------------------
 1 file changed, 27 insertions(+), 21 deletions(-)

diff --git a/zip-0207.rst b/zip-0207.rst
index 18b44d5b..985ff0d8 100644
--- a/zip-0207.rst
+++ b/zip-0207.rst
@@ -83,16 +83,16 @@ Definitions
 We use the following constants and functions defined in [#protocol-constants]_,
 [#protocol-subsidies]_, and [#protocol-foundersreward]_:
 
-- ``BlossomActivationHeight``
-- ``PostBlossomHalvingInterval``
-- ``Halving(height)``
-- ``BlockSubsidy(height)``
-- ``RedeemScriptHash(height)``.
+- :math:`\mathsf{BlossomActivationHeight}`
+- :math:`\mathsf{PostBlossomHalvingInterval}`
+- :math:`\mathsf{Halving}(\mathsf{height})`
+- :math:`\mathsf{BlockSubsidy}(\mathsf{height})`
+- :math:`\mathsf{RedeemScriptHash}(\mathsf{height})`.
 
 We also define the following function:
 
-- ``HeightForHalving(halving)``: Smallest ``height`` such that
-  ``Halving(height) = halving``
+- :math:`\mathsf{HeightForHalving}(\mathsf{halving})`: Smallest :math:`\mathsf{height}` such that
+  :math:`\mathsf{Halving}(\mathsf{height}) = \mathsf{halving}`
 
 
 Funding streams
@@ -107,12 +107,14 @@ than absolute zatoshis, this ZIP dovetails with any changes to both block
 target spacing and issuance-per-block rates. Such a change occurred at the
 Blossom network upgrade, for example. [#zip-0208]_
 
-The value of a funding stream at a given block height is defined as::
+The value of a funding stream at a given block height is defined as:
 
-    FundingStream[FUND].Value(height) =
-        floor((
-            BlockSubsidy(height) * FundingStream[FUND].ValueNumerator
-        ) / FundingStream[FUND].ValueDenominator)
+.. math::
+
+    \mathsf{FundingStream[FUND].Value}(\mathsf{height}) =
+        \mathsf{floor}\left(
+            \frac{\mathsf{BlockSubsidy}(\mathsf{height}) \,\cdot\, \mathsf{FundingStream[FUND].ValueNumerator}}{\mathsf{FundingStream[FUND].ValueDenominator}}
+        \right)
 
 An active funding stream at a given block height is defined as a funding
 stream for which the block height is less than its end height, but not less
@@ -123,16 +125,20 @@ each of which MUST be either a transparent P2SH address or a Sapling address.
 
 Each address is used for at most 1/48th of a halving interval, creating a
 roughly-monthly sequence of funding periods. The address to be used for a
-given block height is defined as follows::
+given block height is defined as follows:
 
-    AddressChangeInterval = PostBlossomHalvingInterval / 48
-    AddressPeriod(height) =
-        floor((
-            height + PostBlossomHalvingInterval - HeightForHalving(1)
-        ) / AddressChangeInterval)
-    FundingStream[FUND].AddressIndex(height) =
-        AddressPeriod(height) - AddressPeriod(FundingStream[FUND].StartHeight)
-    Address(height) = FundingStream[FUND].Addresses[FundingStream[FUND].AddressIndex(height)]
+.. math::
+
+    \begin{eqnarray*}
+        \mathsf{AddressChangeInterval} &=& \mathsf{PostBlossomHalvingInterval} / 48 \\
+        \mathsf{AddressPeriod}(\mathsf{height}) &=&
+            \mathsf{floor}\left(
+                {\small\frac{\mathsf{height} + \mathsf{PostBlossomHalvingInterval} - \mathsf{HeightForHalving}(1)}{\mathsf{AddressChangeInterval}}}
+            \right) \\
+        \mathsf{FundingStream[FUND].AddressIndex}(\mathsf{height}) &=&
+            \mathsf{AddressPeriod}(\mathsf{height}) - \\&&\hspace{2em} \mathsf{AddressPeriod}(\mathsf{FundingStream[FUND].StartHeight}) \\
+        \mathsf{Address}(\mathsf{height}) &=& \mathsf{FundingStream[FUND].Addresses[} \\&&\hspace{2em} \mathsf{FundingStream[FUND].AddressIndex}(\mathsf{height})\mathsf{]}
+    \end{eqnarray*}
 
 This has the property that all active funding streams change the address they
 are using on the same block height schedule, aligned to the height of the