fmt

src/Advanced/Fast Inverse Root/parts/02 float.typ

@@ -31,7 +31,9 @@ Rewrite the following binary decimals in base 10: \
 #definition(label: "floatbits")
 Another way we can interpret a bit string is as a _signed floating-point decimal_, or a `float` for short. \
 Floats represent a subset of the real numbers, and are interpreted as follows: \
-#note([The following only applies to floats that consist of 32 bits. We won't encounter any others today.])
+#note(
+  [The following only applies to floats that consist of 32 bits. We won't encounter any others today.],
+)
 
 #align(center, box(inset: 2mm, cetz.canvas({
   import cetz.draw: *

src/Advanced/Fast Inverse Root/parts/03 approx.typ

@@ -131,9 +131,9 @@ $
   We then have:
   $
     log_2(x_f) & = log_2 ( 2^(E-127) times (1 + (F) / (2^23)) ) \
-               & = E - 127 + log_2(1 + F / (2^23))              \
-               & approx E-127 + F / (2^23) + epsilon            \
-               & = 1 / (2^23)(2^23 E + F) - 127 + epsilon       \
+               & = E - 127 + log_2(1 + F / (2^23)) \
+               & approx E-127 + F / (2^23) + epsilon \
+               & = 1 / (2^23)(2^23 E + F) - 127 + epsilon \
                & = 1 / (2^23)(x_i) - 127 + epsilon
   $
 ])

src/Advanced/Fast Inverse Root/parts/04 quake.typ

@@ -156,9 +156,9 @@ float Q_rsqrt( float number ) {
 Using a calculator and some basic algebra, we can find the $epsilon$ this code uses: \
 #note[Remember, #text[`0x5f3759df`] is $6240089$ in hexadecimal.]
 $
-  (3 times 2^22) (127 - epsilon) &= 6240089 \
-  (127 - epsilon) &= 126.955 \
-  epsilon &= 0.0450466
+  (3 times 2^22) (127 - epsilon) & = 6240089 \
+                 (127 - epsilon) & = 126.955 \
+                         epsilon & = 0.0450466
 $
 
 So, $0.045$ is the $epsilon$ used by Quake. \

src/Advanced/Tropical Polynomials/parts/00 arithmetic.typ

@@ -26,9 +26,9 @@ $
 
 #solution([
   - Is tropical addition commutative?\
-    Yes, $min(min(x,y),z) = min(x,y,z) = min(x,min(y,z))$
+    Yes, $min(min(x, y), z) = min(x, y, z) = min(x, min(y, z))$
   - Is tropical addition associative? \
-    Yes, $min(x,y) = min(y,x)$
+    Yes, $min(x, y) = min(y, x)$
   - Is there a tropical additive identity? \
     No. There is no $n$ where $x <= n$ for all real $x$
 ])
@@ -117,7 +117,7 @@ Do tropical multiplicative inverses always exist? \
 Is tropical multiplication distributive over addition? \
 #note([Does $x #tm (y #tp z) = x #tm y #tp x #tm z$?])
 
-#solution([Yes, $x + min(y,z) = min(x+y, x+z)$])
+#solution([Yes, $x + min(y, z) = min(x+y, x+z)$])
 
 #v(1fr)
 
@@ -134,14 +134,7 @@ Fill the following tropical addition and multiplication tables
     table(
       columns: (col, col, col, col, col, col),
       align: center,
-      table.header(
-        [$#tp$],
-        [$1$],
-        [$2$],
-        [$3$],
-        [$4$],
-        [$#sym.infinity$],
-      ),
+      table.header([$#tp$], [$1$], [$2$], [$3$], [$4$], [$#sym.infinity$]),
 
       box(inset: 3pt, $1$), [], [], [], [], [],
       box(inset: 3pt, $2$), [], [], [], [], [],
@@ -152,14 +145,7 @@ Fill the following tropical addition and multiplication tables
     table(
       columns: (col, col, col, col, col, col),
       align: center,
-      table.header(
-        [$#tm$],
-        [$0$],
-        [$1$],
-        [$2$],
-        [$3$],
-        [$4$],
-      ),
+      table.header([$#tm$], [$0$], [$1$], [$2$], [$3$], [$4$]),
 
       box(inset: 3pt, $0$), [], [], [], [], [],
       box(inset: 3pt, $1$), [], [], [], [], [],
@@ -178,14 +164,7 @@ Fill the following tropical addition and multiplication tables
     table(
       columns: (col, col, col, col, col, col),
       align: center,
-      table.header(
-        [$#tp$],
-        [$1$],
-        [$2$],
-        [$3$],
-        [$4$],
-        [$#sym.infinity$],
-      ),
+      table.header([$#tp$], [$1$], [$2$], [$3$], [$4$], [$#sym.infinity$]),
 
       box(inset: 3pt, $1$),
       box(inset: 3pt, $1$),
@@ -225,14 +204,7 @@ Fill the following tropical addition and multiplication tables
     table(
       columns: (col, col, col, col, col, col),
       align: center,
-      table.header(
-        [$#tm$],
-        [$0$],
-        [$1$],
-        [$2$],
-        [$3$],
-        [$4$],
-      ),
+      table.header([$#tm$], [$0$], [$1$], [$2$], [$3$], [$4$]),
 
       box(inset: 3pt, $0$),
       box(inset: 3pt, $0$),
@@ -281,10 +253,9 @@ Adjacent parenthesis imply tropical multiplication
 
 #solution([
   $
-    (x #tp 2)(x #tp 3)
-    &= x^2 #tp 2x #tp 3x #tp (2 #tm 3) \
-    &= x^2 #tp (2 #tp 3)x #tp (2 #tm 3) \
-    &= x^2 #tp 2x #tp 5
+    (x #tp 2)(x #tp 3) & = x^2 #tp 2x #tp 3x #tp (2 #tm 3) \
+                       & = x^2 #tp (2 #tp 3)x #tp (2 #tm 3) \
+                       & = x^2 #tp 2x #tp 5
   $
 
   Also, $f(1) = 2$ and $f(4) = 5$.

src/Advanced/Tropical Polynomials/parts/02 cubic.typ

@@ -166,7 +166,7 @@ Find a formula for each $C_i$ in terms of $c_0, c_1, ..., c_n$.
 
 #solution([
   $
-    A_j & = min_(l<=j<k)( (a_l - a_k) / (k-l) (k-j) + a_k )       \
+    A_j & = min_(l<=j<k)( (a_l - a_k) / (k-l) (k-j) + a_k ) \
         & = min_(l<=j<k)( a_l (k-j) / (k-l) + a_k (j-l) / (k-l) )
   $
 

src/Advanced/Wallpaper/parts/00 intro.typ

@@ -12,7 +12,9 @@ There are four classes of Euclidean isometries:
 - reflections
 - rotations
 - glide reflections
-#note([We can prove there are no others, but this is beyond the scope of this handout.]) \
+#note(
+  [We can prove there are no others, but this is beyond the scope of this handout.],
+) \
 A simple example of each isometry is shown below:
 
 #let demo(c) = {

src/Warm-Ups/Adders/main.typ

@@ -46,10 +46,10 @@ Use two half adders to construct a full adder.
 
 #solution([
   $
-    s_1, c_1 &= "HA"(a, b) \
-    s_2, c_2 &= "HA"(s_1, c_"in") \
-    s_"out" &= s_2 \
-    c_"out" &= "OR"(c_1, c_2)
+    s_1, c_1 & = "HA"(a, b) \
+    s_2, c_2 & = "HA"(s_1, c_"in") \
+     s_"out" & = s_2 \
+     c_"out" & = "OR"(c_1, c_2)
   $
 
   #v(2mm)

src/Warm-Ups/Partition Products/main.typ

@@ -7,7 +7,7 @@
 
 #problem()
 Take any positive integer $n$. \
-Now, write it as sum of smaller positive integers: $n = a_1 + a_2 + ...  a_k$ \
+Now, write it as sum of smaller positive integers: $n = a_1 + a_2 + ... a_k$ \
 Maximize the product $a_1 #sym.times a_2 #sym.times ... #sym.times a_k$
 
 
@@ -17,7 +17,9 @@ Maximize the product $a_1 #sym.times a_2 #sym.times ... #sym.times a_k$
   Of course, all $a_i$ should be greater than $1$. \
   Also, all $a_i$ should be smaller than four, since $x <= x(x-2)$ if $x >= 4$. \
   Thus, we're left with sequences that only contain 2 and 3. \
-  #note([Note that two twos are the same as one four, but we exclude fours for simplicity.])
+  #note(
+    [Note that two twos are the same as one four, but we exclude fours for simplicity.],
+  )
 
   #v(2mm)