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0caedcc0df
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4c93277605
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@ -1,5 +0,0 @@
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To play around with IIPAU, run `julia --project=.` and start with:
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using Revise
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using Unitful
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using IIPAU
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@ -1,29 +0,0 @@
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# Useful information:
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#
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# https://en.wikipedia.org/wiki/List_of_physical_quantities
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# https://en.wikipedia.org/wiki/List_of_physical_constants
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module Constants
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import Unitful
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using Unitful: @unit
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export item
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function __init__()
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Unitful.register(Constants)
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end
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c = 1 * Unitful.c
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h = Unitful.h
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ħ = Unitful.ħ
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μ₀= Unitful.μ0
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Z₀= Unitful.Z0
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kₑ = 1 / (4 * π * Unitful.ϵ0) # Coulomb constant
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mₑ = Unitful.me
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mₚ = Unitful.mp
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mₙ = Unitful.mn
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kb = Unitful.k
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ϵ₀ = Unitful.ϵ0
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133
src/IIPAU.jl
133
src/IIPAU.jl
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@ -1,74 +1,105 @@
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# Useful information:
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# Useful information:
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#
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#
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# https://en.wikipedia.org/wiki/List_of_physical_quantities
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# https://en.wikipedia.org/wiki/List_of_physical_quantities
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# https://en.wikipedia.org/wiki/List_of_physical_constants
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# https://www.themeasureofthings.com/
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# https://www.themeasureofthings.com/
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# https://cs.uwaterloo.ca/~dtompkin/music/bpm/118.html
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# https://physics.stackexchange.com/questions/167720/what-is-the-correct-theoretical-formula-for-the-hyperfine-splitting-of-neutral-h
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#
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#
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# "free" Unitful units: f jno r v xzDEIOQUXZ |
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# "free" Unitful units: efijno r v xzDEIOQUXZ |
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# "used" Unitful units: e i p t w |
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# "used" Unitful units: e i p t w |
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module IIPAU
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module IIPAU
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include("Seximal.jl")
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include("Quantum.jl")
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include("Natural.jl")
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using .Seximal
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using .Quantum
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using .Natural
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import Unitful
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import Unitful
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using Unitful: @unit, @affineunit, @u_str
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using Unitful: @unit, @affineunit, @u_str
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export item
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export item
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export @b6_str
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export @b6_str
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export yocte, zepte, atte, femte, pice, nane, micre, mille, cente, dice
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export yocte, zepte, atte, femte, pice, nane, micre, mille, cente, dice
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export yotte, zette, exe, pete, tere, gige, mege, kile, hecte, dece
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export yotte, zette, exe, pete, tere, gige, mege, kile, hecte, dece
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export to₆
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export wave_number
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export pace, tick, egg, jolt, brr, °c
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export span, tick, egg, spark, lotta, alotta, brr
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export ball, touch, jolt
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function __init__()
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function __init__()
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Unitful.register(IIPAU)
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Unitful.register(IIPAU)
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end
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end
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#Unitful.register(IIPAU)
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# Additional Constants
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kₑ = 8987551792u"N*m^2/C^2"
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mₑ = 9.109e-31u"kg"
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mᵤ = 1.6605390666e-27u"kg"
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mₙ = 1.674927498e-27u"kg"
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kb = 1.380649e-23u"J/K"
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ϵ₀ = 8.854e-12u"F/m"
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# Natural Units
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@unit lₛ "lₛ" StoneyLength (sqrt(Unitful.G * kₑ * Unitful.q^2 / Unitful.c^4) |> Unitful.upreferred) false
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@unit mₛ "mₛ" StoneyMass (sqrt(kₑ * Unitful.q^2 / Unitful.G) |> Unitful.upreferred) false
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@unit tₛ "tₛ" StoneyTime (sqrt(Unitful.G * kₑ * Unitful.q^2 / Unitful.c^6) |> Unitful.upreferred) false
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@unit lₚ "lₚ" PlanckLength sqrt(Unitful.ħ * Unitful.G / Unitful.c^3) false
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@unit mₚ "mₚ" PlanckMass sqrt(Unitful.ħ * Unitful.c / Unitful.G) false
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@unit tₚ "tₚ" PlanckTime sqrt(Unitful.ħ * Unitful.G / Unitful.c^5) false
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@unit Tₚ "Tₚ" PlanckTemperature sqrt(Unitful.ħ * Unitful.c ^ 5 / (Unitful.G * Unitful.k ^ 2)) false
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@unit qₚ "qₚ" Planckcharge sqrt(4π * Unitful.ϵ0 * Unitful.ħ * Unitful.c) false
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@unit Qₚ "Qₚ" PlanckCharge sqrt(Unitful.ϵ0 * Unitful.ħ * Unitful.c) false
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item = @unit count "count" Count (1 / Unitful.Na) false
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# Senary prefixes
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function base6(number::AbstractString)
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if occursin('e', number)
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(digits, exponent) = split(number, 'e')
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else
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(digits, exponent) = (number, "0")
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end
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if occursin('.', digits)
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value = parse(BigFloat, digits, base=6)
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else
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value = parse(BigInt, digits, base=6)
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end
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expval = parse(Int, exponent, base=6)
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if expval < 0
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return 1 // (value * BigInt(6) ^ (-expval))
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else
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return value * BigInt(6) ^ expval
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end
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end
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macro b6_str(digits)
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value = base6(digits)
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return :( $value )
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end
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yocte = b6"1e-52" # y |
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zepte = b6"1e-44" # z |
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atte = b6"1e-40" # a |
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femte = b6"1e-32" # f |
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pice = b6"1e-24" # p |
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nane = b6"1e-20" # n |
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micre = b6"1e-12" # μ |
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mille = b6"1e-4" # m |
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cente = b6"1e-2" # c |
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dice = b6"1e-1" # d |
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dece = b6"1e1" # de |
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hecte = b6"1e2" # h |
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kile = b6"1e4" # k |
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mege = b6"1e12" # M |
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gige = b6"1e20" # G |
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tere = b6"1e24" # T |
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pete = b6"1e32" # P |
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exe = b6"1e40" # E |
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zette = b6"1e44" # Z |
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yotte = b6"1e52" # Y |
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# Base Units
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# Base Units
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span = 1@unit ṡ "ṡ" Span (Unitful.c / Natural.HHz) false # ~21cm
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pace = 1@unit p "p" Pace (lₛ * b6"1e114") false # ~86cm
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tick = 1@unit t "t" Tick (b6"2e15" / Natural.HHz) false # ~0.51s (1/tick is ~118 bpm)
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tick = 1@unit t "t" Tick (tₛ * b6"3e132") false # ~0.52s = 300₆ instants (1/tick ~115bpm)
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egg = 1@unit e "e" Egg (-b6"4e44" * Natural.ΔEₕ * tick^2 / span^2) false # ~136g
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egg = 1@unit e "e" Egg (mₛ * b6"1e14") false # ~112g
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spark = 1@unit ş "ş" Spark (b6"1e34" * Unitful.q) false # ~0.02C
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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)
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lotta = 1@unit ļ "ļ" Lotta (1u"mol" * egg / u"g") false # ~135mol
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brr = 1@unit ḃ "ḃ" Brr (Tₚ * b6"1e-110") false # ~0.3K
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alotta = (lotta |> item).val # ~81 septillion (81e24)
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@affineunit °c "°c" (Int(b6"4400") * brr) # ~13°C -> 0°c
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brr = 1@unit bʳ "bʳ" Brr (Natural.ΔEₕ / Natural.hexit) false # ~0.04K
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@affineunit °c "°c" (Int(b6"-100000") * brr) # ~23°C -> 0°c, human's can't really survive past about -2000₆°c (too hot)
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# Derived Units
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ball = 1@unit ḃ "ḃ" Ball ((π/6)*span^3) false # ~5L (sphere of diameter 1ṡ)
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touch = 1@unit ṫ "ṫ" Touch (egg * span / tick ^2) false # ~0.1N (10grams of weight)
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jolt = 1@unit j "j" Jolt (spark / tick) false # ~0.04A
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cell = 1@unit ċ "ċ" Cell (span * touch / spark) false # ~1.1V (just shy of zinc/copper electrode)
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# TODO: resistance is at about 26.6Ω
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# Convenience Units
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instant = 1@unit i "i" Instant (b6"3e-2" * tick) false # ~5ms (300₆ instants to a tick)
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pause = 1@unit ṗ "ṗ" Pause (b6"300" * tick) false # ~55 seconds
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wait = 1@unit ẇ "ẇ" Wait (b6"300" * pause) false # ~100 minutes
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# Useful references
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resistance_of_wire(ρ, L, d) = ρ * L / (π * (d/2)^2)
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# Note: 1 kile span of 1 mille span diameter silver wire has a resistance of about 210Ω
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#egg = 1@unit e "e" Egg (b6"1e53" * (Unitful.mp + Unitful.me)) false # ~80g
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#=
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# pace = 1@unit p "p" Pace (lₛ * b6"1e114") false # ~86cm
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# tick = 1@unit t "t" Tick (tₛ * b6"3e132") false # ~0.52s = 300₆ instants (1/tick ~115bpm)
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# egg = 1@unit e "e" Egg (mₛ * b6"1e14") false # ~112g
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# 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)
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# brr = 1@unit ḃ "ḃ" Brr (Tₚ * b6"1e-110") false # ~0.3K
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# @affineunit °c "°c" (Int(b6"4400") * brr) # ~13°C -> 0°c
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# Convenience Units
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# Convenience Units
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instant = 1@unit i "i" Instant (tₛ * b6"1e130") false # ~5ms (1000₆ instants is about a second)
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instant = 1@unit i "i" Instant (tₛ * b6"1e130") false # ~5ms (1000₆ instants is about a second)
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@ -78,7 +109,7 @@ wait = 1@unit ẇ "ẇ" Wait (pause * b6"100") false # ~34 minutes
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# Derived Units
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# Derived Units
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walk = 1@unit w "w" Walk (1 * pace / tick) false # ~6km/h (pretty quick walk)
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walk = 1@unit w "w" Walk (1 * pace / tick) false # ~6km/h (pretty quick walk)
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# touch = 1@unit ṫ "ṫ" Touch (1 * egg * pace / tick ^ 2) false # ~0.36N (half what it takes to press a key on a keyboard)
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touch = 1@unit ṫ "ṫ" Touch (1 * egg * pace / tick ^ 2) false # ~0.36N (half what it takes to press a key on a keyboard)
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nosh = 1@unit n "n" Nosh (b6"1e11" * pace * touch) false # ~20.5 kcal
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nosh = 1@unit n "n" Nosh (b6"1e11" * pace * touch) false # ~20.5 kcal
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#= Useful Constants ============================================================
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#= Useful Constants ============================================================
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@ -86,8 +117,6 @@ nosh = 1@unit n "n" Nosh (b6"1e11" * pace * touch) false # ~20.5 kcal
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Speed of light: c ≡ 3e14₆p/t
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Speed of light: c ≡ 3e14₆p/t
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===============================================================================#
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===============================================================================#
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=#
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#=
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#=
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export stride, skip, bed, gulp
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export stride, skip, bed, gulp
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export moment, instant, wait
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export moment, instant, wait
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@ -1,35 +0,0 @@
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module Natural
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|
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import Unitful
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|
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using Unitful:@unit
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||||||
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|
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export lₛ, mₛ, tₛ
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export lₚ, mₚ, tₚ, Tₚ, qₚ, Qₚ, item
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# Additional constants (not in Unitful)
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kₑ = 1 / (4 * π * Unitful.ϵ0) # Coulomb constant
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gₑ = − 2.00231930436256 # Electron g-factor
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gₚ = 5.5856946893 # Proton g-factor
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α = Unitful.q^2 / (4 * π * Unitful.ϵ0 * Unitful.ħ * Unitful.c) # fine structure constant
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a₀= Unitful.ħ / (Unitful.me * Unitful.c * α) # bohr radius
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ΔEₕ = 2 * gₑ * α^4 * gₚ * Unitful.me^2 * Unitful.c^2 / (3 * Unitful.mp) # hydrogen hyperfine transition energy
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HHz = -ΔEₕ / Unitful.h # Hydrogen hyperfine transition frequency
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bit = Unitful.k * log(2)
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hexit = Unitful.k * log(6)
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|
||||||
natit = Unitful.k * log(1/α)
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|
||||||
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||||||
# Natural Units
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|
||||||
@unit lₛ "lₛ" StoneyLength (sqrt(Unitful.G * kₑ * Unitful.q^2 / Unitful.c^4) |> Unitful.upreferred) false
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|
||||||
@unit mₛ "mₛ" StoneyMass (sqrt(kₑ * Unitful.q^2 / Unitful.G) |> Unitful.upreferred) false
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|
||||||
@unit tₛ "tₛ" StoneyTime (sqrt(Unitful.G * kₑ * Unitful.q^2 / Unitful.c^6) |> Unitful.upreferred) false
|
|
||||||
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|
||||||
@unit lₚ "lₚ" PlanckLength sqrt(Unitful.ħ * Unitful.G / Unitful.c^3) false
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|
||||||
@unit mₚ "mₚ" PlanckMass sqrt(Unitful.ħ * Unitful.c / Unitful.G) false
|
|
||||||
@unit tₚ "tₚ" PlanckTime sqrt(Unitful.ħ * Unitful.G / Unitful.c^5) false
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|
||||||
@unit Tₚ "Tₚ" PlanckTemperature sqrt(Unitful.ħ * Unitful.c ^ 5 / (Unitful.G * Unitful.k ^ 2)) false
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|
||||||
@unit qₚ "qₚ" Planckcharge sqrt(4π * Unitful.ϵ0 * Unitful.ħ * Unitful.c) false
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|
||||||
@unit Qₚ "Qₚ" PlanckCharge sqrt(Unitful.ϵ0 * Unitful.ħ * Unitful.c) false
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|
||||||
item = @unit ç "ç" Count (1 / Unitful.Na) false
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|
||||||
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|
||||||
end # module Natural
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|
||||||
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@ -1,14 +0,0 @@
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||||||
module Quantum
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|
||||||
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|
||||||
import Unitful
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|
||||||
|
|
||||||
export wave_number
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|
||||||
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|
||||||
RH = Unitful.R∞ * Unitful.mp / (Unitful.mp + Unitful.me)
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|
||||||
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|
||||||
Rₙ(z::Integer) = (Unitful.R∞ * Unitful.mp * z) / (Unitful.mp * z + Unitful.me)
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|
||||||
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|
||||||
# Inverse wavelength
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|
||||||
wave_number(z::Integer, n1::Integer, n2::Integer) = Rₙ(z) * z^2 * ((1 / n1^2) - (1 / n2^2))
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|
||||||
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|
||||||
end # module Quantum
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|
||||||
125
src/Seximal.jl
125
src/Seximal.jl
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|
@ -1,125 +0,0 @@
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||||||
module Seximal
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|
||||||
|
|
||||||
export @b6_str
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|
||||||
export yocte, zepte, atte, femte, pice, nane, micre, mille, cente, dice
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|
||||||
export yotte, zette, exe, pete, tere, gige, mege, kile, hecte, dece
|
|
||||||
|
|
||||||
# Senary prefixes
|
|
||||||
function base6(number::AbstractString)
|
|
||||||
if occursin('e', number)
|
|
||||||
(digits, exponent) = split(number, 'e')
|
|
||||||
else
|
|
||||||
(digits, exponent) = (number, "0")
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|
||||||
end
|
|
||||||
|
|
||||||
if occursin('.', digits)
|
|
||||||
value = parse(BigFloat, digits, base=6)
|
|
||||||
else
|
|
||||||
value = parse(BigInt, digits, base=6)
|
|
||||||
end
|
|
||||||
|
|
||||||
expval = parse(Int, exponent, base=6)
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|
||||||
|
|
||||||
if expval < 0
|
|
||||||
return 1 // (value * BigInt(6) ^ (-expval))
|
|
||||||
else
|
|
||||||
return value * BigInt(6) ^ expval
|
|
||||||
end
|
|
||||||
end
|
|
||||||
|
|
||||||
macro b6_str(digits)
|
|
||||||
value = base6(digits)
|
|
||||||
|
|
||||||
return :( $value )
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|
||||||
end
|
|
||||||
|
|
||||||
quecte = b6"1e-64" # q |
|
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ronte = b6"1e-60" # r |
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yocte = b6"1e-52" # y |
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zepte = b6"1e-44" # z |
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atte = b6"1e-40" # a |
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femte = b6"1e-32" # f |
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pice = b6"1e-24" # p |
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nane = b6"1e-20" # n |
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micre = b6"1e-12" # μ |
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mille = b6"1e-4" # m |
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cente = b6"1e-2" # c |
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dice = b6"1e-1" # d |
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dece = b6"1e1" # de |
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hecte = b6"1e2" # h |
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kile = b6"1e4" # k |
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mege = b6"1e12" # M |
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gige = b6"1e20" # G |
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tere = b6"1e24" # T |
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pete = b6"1e32" # P |
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exe = b6"1e40" # E |
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zette = b6"1e44" # Z |
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yotte = b6"1e52" # Y |
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ronne = b6"1e60" # R |
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quette = b6"1e64" # Q |
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#=
|
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def longdiv(numerator,denominator):
|
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digits = []
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|
||||||
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
|
|
||||||
Loading…
Reference in a new issue