Good progress made

README.md

@@ -0,0 +1,5 @@
+To play around with IIPAU, run `julia --project=.` and start with:
+
+    using Revise
+    using Unitful
+    using IIPAU

src/IIPAU.jl

@@ -23,10 +23,12 @@ export item
 export @b6_str
 export yocte, zepte, atte, femte, pice, nane, micre, mille, cente, dice
 export yotte, zette, exe, pete, tere, gige, mege, kile, hecte, dece
+export to₆
 
 export wave_number
 
-export pace, tick, egg, jolt, brr, °c
+export span, tick, egg, spark, lotta, alotta, brr
+export ball, touch, jolt
 
 function __init__()
     Unitful.register(IIPAU)
@@ -36,29 +38,32 @@ end
 span = 1@unit ṡ "ṡ" Span (Unitful.c / Natural.HHz) false # ~21cm
 tick = 1@unit t "t" Tick (b6"2e15" / Natural.HHz) false # ~0.51s (1/tick is ~118 bpm)
 egg = 1@unit e "e" Egg (-b6"4e44" * Natural.ΔEₕ * tick^2 / span^2) false # ~136g
+spark = 1@unit ş "ş" Spark (b6"1e34" * Unitful.q) false # ~0.02C
 lotta = 1@unit ļ "ļ" Lotta (1u"mol" * egg / u"g") false # ~135mol
-alotta = (lotta |> item).val
-
-# Unit of charge at b6"1e34" * Unitful.q is about 0.02C
-# u"ṡ^2*e" / (b6"1e34" * Unitful.q) / u"t^2" is about 1.1V
-# (b6"1e34" * Unitful.q) / u"t" is about 0.04A
-#
-# A good target voltage is hydrogen fuel cell ideal voltage of 1.229V
-# A good target amperage could be near-life-threatening 0.8A
-#
-# Alternatively fix the coulomb constant?
-# That is below:
-touch = 1@unit ṫ "ṫ" Touch (egg * span / tick ^2) false # ~0.1N (10grams of weight)
-jolt = 1@unit j "j" Jolt (b6"1e10" * (span / tick) / sqrt(Natural.kₑ / touch)) false # ~0.067A
+alotta = (lotta |> item).val # ~81 septillion (81e24)
+brr = 1@unit bʳ "bʳ" Brr (Natural.ΔEₕ / Natural.hexit) false # ~0.04K
+@affineunit °c "°c" (Int(b6"-100000") * brr) # ~23°C -> 0°c, human's can't really survive past about -2000₆°c (too hot)
 
 # Derived Units
 ball = 1@unit ḃ "ḃ" Ball ((π/6)*span^3) false # ~5L (sphere of diameter 1ṡ)
+touch = 1@unit ṫ "ṫ" Touch (egg * span / tick ^2) false # ~0.1N (10grams of weight)
+jolt = 1@unit j "j" Jolt (spark / tick) false # ~0.04A
+cell = 1@unit ċ "ċ" Cell (span * touch / spark) false # ~1.1V (just shy of zinc/copper electrode)
+# TODO: resistance is at about 26.6Ω
 
+# Convenience Units
+instant = 1@unit i "i" Instant (b6"3e-2" * tick) false # ~5ms (300₆ instants to a tick)
+pause = 1@unit ṗ "ṗ" Pause (b6"300" * tick) false # ~55 seconds
+wait = 1@unit ẇ "ẇ" Wait (b6"300" * pause) false # ~100 minutes
+
+# Useful references
+resistance_of_wire(ρ, L, d) = ρ * L / (π * (d/2)^2)
+# Note: 1 kile span of 1 mille span diameter silver wire has a resistance of about 210Ω
 
 #egg = 1@unit e "e" Egg (b6"1e53" * (Unitful.mp + Unitful.me)) false # ~80g
 
-
-pace = 1@unit p "p" Pace (lₛ * b6"1e114") false              # ~86cm
+#=
+# pace = 1@unit p "p" Pace (lₛ * b6"1e114") false              # ~86cm
 # tick = 1@unit t "t" Tick (tₛ * b6"3e132") false              # ~0.52s = 300₆ instants (1/tick ~115bpm)
 # egg = 1@unit e "e" Egg (mₛ * b6"1e14") false                 # ~112g
 # jolt = 1@unit j "j" Jolt (b6"1e34" * Unitful.q / tick) false # ~40mA painful jolt (https://electronics.stackexchange.com/questions/19103/how-much-voltage-current-is-dangerous)
@@ -81,6 +86,8 @@ nosh = 1@unit n "n" Nosh (b6"1e11" * pace * touch) false # ~20.5 kcal
  Speed of light: c ≡ 3e14₆p/t
 ===============================================================================#
 
+=#
+
 #=
 export stride, skip, bed, gulp
 export moment, instant, wait

src/Natural.jl

@@ -16,6 +16,8 @@ a₀= Unitful.ħ / (Unitful.me * Unitful.c * α) # bohr radius
 ΔEₕ = 2 * gₑ * α^4 * gₚ * Unitful.me^2 * Unitful.c^2 / (3 * Unitful.mp) # hydrogen hyperfine transition energy
 HHz = -ΔEₕ / Unitful.h # Hydrogen hyperfine transition frequency
 bit = Unitful.k * log(2)
+hexit = Unitful.k * log(6)
+natit = Unitful.k * log(1/α)
 
 # Natural Units
 @unit lₛ "lₛ" StoneyLength (sqrt(Unitful.G * kₑ * Unitful.q^2 / Unitful.c^4) |> Unitful.upreferred) false

src/Seximal.jl

@@ -54,4 +54,68 @@ exe = b6"1e40" # E    |
 zette = b6"1e44" # Z  |
 yotte = b6"1e52" # Y  |
 
+#=
+def longdiv(numerator,denominator):
+    digits = []
+    remainders = [0]
+    n = numerator
+    while n not in remainders:              #   until repeated remainder or no remainder
+        remainders.append(n)                #   add remainder to collection
+        digits.append(n//denominator)       #   add integer division to result
+        n = n%denominator * 10              #   remainder*10 for next iteration
+
+    #   Result
+    result = list(map(str,digits))          #   convert digits to strings
+    result = ''.join(result)                #   combine list to string
+
+    if not n:
+        result = result[:1]+'.'+result[1:]  #   Insert . into string
+    else:
+        recurring = remainders.index(n)-1   #   first recurring digit
+        #   Insert '.' and then surround recurring part in brackets:
+        result = result[:1]+'.'+result[1:recurring]+'['+result[recurring:]+']'
+
+    return result;
+
+print(longdiv(31,8))    #   3.875
+print(longdiv(2,13))    #   0.[153846]
+print(longdiv(13,14))   #   0.9[285714]
+
+=#
+
+"Converts x to an exact seximal number. Repeated digits are shown in brackets."
+function to₆(x :: Rational{BigInt})
+    if x < 0
+        return "-" * to₆(-x)
+    end
+
+    if x > 1
+        intpart = floor(x)
+        return string(intpart.num, base=6) * to₆(x - intpart)
+    end
+
+    digits = []
+    remainders = [BigInt(0)]
+    remset = Set{BigInt}()
+    n = x.num
+    d = x.den
+    while !(n in remset)
+        append!(remainders, n)
+        push!(remset, n)
+        append!(digits, floor(n // d).num)
+        n = (n % d) * 6
+    end
+
+    if n == 0
+        return "." * prod(map(string, digits[2:end]))
+    end
+
+    recur = findfirst(==(n), remainders) - 1
+    return "." * prod(map(string, digits[2:recur - 1])) * "(" * prod(map(string, digits[recur:end])) * ")"
+end
+
+to₆(x) = to₆(Rational{BigInt}(x))
+
+# TODO: custom base6 version of @prefixed_unit_symbol
+
 end # module Seximal