(ns formulas.constants "Collection of physical constants and their formulas composed of physical quantities."
 (:require [clojure.math.numeric-tower :as math]))

(def pi
 {:value 3.14159265359
  :formulas
  {[:frequency :angular-frequency] (fn [& {:keys [frequency angular-frequency]}]
                                    (/ angular-frequency
                                       (* 2 frequency)))}})

(def planks-constant
 {:value 6.626070043e-34
  :formulas
  {[:frequency :energy] (fn [& {:keys [frequency energy]}]
                         (/ energy frequency))
   [:frequency :wavelength] (fn [& {:keys [frequency wavelength]}]
                             (* frequency wavelength))
   [:energy :wavelength] (fn [& {:keys [energy wavelength]}]
                          (/ (* wavelength energy)
                             (:value speed-of-light)))
   [:wavelength :momentum] (fn [& {:keys [wavelength momentum]}]
                            (* wavelength momentum))}})

(def reduced-planks-constant
 {:value (/ 6.626070043e-34 (* 2 (:value pi)))
  :formulas
  {[:angular-frequency :energy] (fn [& {:keys [frequency energy]}]
                                 (/ energy angular-frequency))
   [:wavenumber :momentum] (fn [& {:keys [wavelength momentum]}]
                            (/ momentum wavenumber))}})


(def speed-of-light
 {:value 299792458
  :formulas
  {[:energy :mass :momentum] (fn [& {:keys [energy mass momentum]}]
                              (math/sqrt (/ (+ (- (math/expt momentum 2))
                                               (math/sqrt (+ (math/expt momentum 4)
                                                             (* 4 (math/expt mass 2)
                                                                (math/expt energy 2)))))
                                            (* 2 (math/expt mass 2)))))
   [:frequency :wavelength] (fn [& {:keys [frequency wavelength]}]
                             (* frequency wavelength))
   [:energy :wavelength] (fn [& {:keys [energy wavelength]}]
                          (/ (* wavelength energy)
                             (:value planks-constant)))}})