Apply suggestions from code review

Co-authored-by: David Peter <sharkdp@users.noreply.github.com>

numbat/modules/core/strings.nbt

@@ -7,7 +7,7 @@ use core::error
 fn str_length(s: String) -> Scalar
 
 @description("Subslice of a string")
-@example("str_slice(\"Numbat\", 0, 2)")
+@example("str_slice(\"Numbat\", 3, 6)")
 fn str_slice(s: String, start: Scalar, end: Scalar) -> String
 
 @description("Get a single-character string from a Unicode code point.")

numbat/modules/math/geometry.nbt

@@ -2,11 +2,11 @@ use core::functions
 use math::constants
 
 @description("The length of the hypotenuse of a right-angled triangle $\\sqrt\{x^2+y^2\}$.")
-@example("hypot2(3, 4)")
+@example("hypot2(3 m, 4 m)")
 fn hypot2<T: Dim>(x: T, y: T) -> T = sqrt(x^2 + y^2)
 
 @description("The Euclidean norm of a 3D vector $\\sqrt\{x^2+y^2+z^2\}$.")
-@example("hypot3(4, 1, 4)")
+@example("hypot3(8, 9, 12)")
 fn hypot3<T: Dim>(x: T, y: T, z: T) -> T = sqrt(x^2 + y^2 + z^2)
 
 # The following functions use a generic dimension instead of

numbat/modules/math/number_theory.nbt

@@ -4,7 +4,7 @@ use core::functions
 @name("Greatest common divisor")
 @description("The largest positive integer that divides each of the integers $a$ and $b$.")
 @url("https://en.wikipedia.org/wiki/Greatest_common_divisor")
-@example("gcd(60,42)")
+@example("gcd(60, 42)")
 fn gcd(a: Scalar, b: Scalar) -> Scalar =
   if b == 0
     then abs(a)

numbat/modules/numerics/diff.nbt

@@ -3,7 +3,8 @@ use core::quantities
 @name("Numerical differentiation")
 @url("https://en.wikipedia.org/wiki/Numerical_differentiation")
 @description("Compute the numerical derivative of the function $f$ at point $x$ using the central difference method.")
-@example("fn polynomial(x) = x² -x -1\ndiff(polynomial, 1)", "Compute the drivative of $f(x) = x² -x -1$ at $x=1$.")
+@example("fn polynomial(x) = x² - x - 1\ndiff(polynomial, 1)", "Compute the derivative of $f(x) = x² -x -1$ at $x=1$.")
+@example("fn distance(t) = 0.5 g0 t²\nfn velocity(t) = diff(distance, t)\nvelocity(2 s)", "Compute the free fall velocity after $t=2 s$.")
 fn diff<X: Dim, Y: Dim>(f: Fn[(X) -> Y], x: X) -> Y / X =
   (f(x + Δx) - f(x - Δx)) / 2 Δx
   where

numbat/modules/physics/temperature_conversion.nbt

@@ -5,24 +5,24 @@ use units::si
 let _offset_celsius = 273.15
 
 @description("Converts from degree Celsius (°C) to Kelvin.")
-@example("from_celsius(300)", "$300 °C$ in Kelvin.")
+@example("from_celsius(300)", "300 °C in Kelvin.")
 @url("https://en.wikipedia.org/wiki/Conversion_of_scales_of_temperature")
 fn from_celsius(t_celsius: Scalar) -> Temperature = (t_celsius + _offset_celsius) kelvin
 
 @description("Converts from Kelvin to degree Celcius (°C). This can be used on the right hand side of a conversion operator: `200 K -> celsius`.")
-@example("300K -> celsius", "$300K$ in degree Celsius.")
+@example("300K -> celsius", "300 K in degree Celsius.")
 @url("https://en.wikipedia.org/wiki/Conversion_of_scales_of_temperature")
 fn celsius(t_kelvin: Temperature) -> Scalar = t_kelvin / kelvin - _offset_celsius
 
 let _offset_fahrenheit = 459.67
 let _scale_fahrenheit = 5 / 9
 
 @description("Converts from degree Fahrenheit (°F) to Kelvin.")
-@example("from_fahrenheit(300)", "$300 °F$ in Kelvin.")
+@example("from_fahrenheit(300)", "300 °F in Kelvin.")
 @url("https://en.wikipedia.org/wiki/Conversion_of_scales_of_temperature")
 fn from_fahrenheit(t_fahrenheit: Scalar) -> Temperature = ((t_fahrenheit + _offset_fahrenheit) × _scale_fahrenheit) kelvin
 
 @description("Converts from Kelvin to degree Fahrenheit (°F). This can be used on the right hand side of a conversion operator: `200 K -> fahrenheit`.")
-@example("300K -> fahrenheit", "$300K$ in degree Fahrenheit.")
+@example("300K -> fahrenheit", "300 K in degree Fahrenheit.")
 @url("https://en.wikipedia.org/wiki/Conversion_of_scales_of_temperature")
 fn fahrenheit(t_kelvin: Temperature) -> Scalar = (t_kelvin / kelvin) / _scale_fahrenheit - _offset_fahrenheit

numbat/modules/units/mixed.nbt

@@ -5,27 +5,27 @@ use units::imperial
 @name("Degrees, minutes, seconds")
 @description("Convert an angle to a mixed degrees, (arc)minutes, and (arc)seconds representation. Also called sexagesimal degree notation.")
 @url("https://en.wikipedia.org/wiki/Sexagesimal_degree")
-@example("DMS(46.5858°)")
+@example("46.5858° -> DMS")
 fn DMS(alpha: Angle) -> String =
   _mixed_units(alpha, [deg, arcmin, arcsec], ["° ", "′ ", "″"], true)
 
 @name("Degrees, decimal minutes")
 @description("Convert an angle to a mixed degrees and decimal minutes representation.")
-@example("DM(46.5858°)")
+@example("46.5858° -> DM")
 @url("https://en.wikipedia.org/wiki/Decimal_degrees")
 fn DM(alpha: Angle) -> String =
   _mixed_units(alpha, [deg, arcmin], ["° ", "′"], false)
 
 @name("Feet and inches")
 @description("Convert a length to a mixed feet and inches representation.")
 @url("https://en.wikipedia.org/wiki/Foot_(unit)")
-@example("feet_and_inches(180cm)")
+@example("180 cm -> feet_and_inches")
 fn feet_and_inches(length: Length) -> String =
   _mixed_units(length, [foot, inch], [" ft ", " in"], false)
 
 @name("Pounds and ounces")
 @description("Convert a mass to a mixed pounds and ounces representation.")
 @url("https://en.wikipedia.org/wiki/Pound_(mass)")
-@example("pounds_and_ounces(1kg)")
+@example("1 kg -> pounds_and_ounces")
 fn pounds_and_ounces(mass: Mass) -> String =
   _mixed_units(mass, [pound, ounce], [" lb ", " oz"], false)