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improve SILCM draft (#294)
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‎src/mentat_collective/emmy/emmy_interactive.clj‎

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^{:kindly/hide-code true
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:clay {:title "interactive"
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:quarto {:author :kloimhardt
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:type :draft
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:description "Demo of reagent and tex"
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:sidebar "emmy-fdg"
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:date "2026-01-11"
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:category :clay
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:tags [:browser :reagent]}}}
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(ns mentat-collective.emmy.emmy_interactive
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(:require [scicloj.kindly.v4.api :as kindly]
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[scicloj.kindly.v4.kind :as kind]
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[mentat-collective.emmy.scheme :refer [define-1 let-scheme lambda]]))
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^:kindly/hide-code
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(def render-mode {:browser true})
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^:kindly/hide-code
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(kind/hiccup
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[:div
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[:script {:src "https://cdn.jsdelivr.net/npm/scittle-kitchen@0.7.28-59/dist/scittle.js"}]
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[:script {:src "https://cdn.jsdelivr.net/npm/scittle-kitchen@0.7.28-59/dist/scittle.emmy.js"}]
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[:script {:src "https://cdn.jsdelivr.net/npm/scittle-kitchen@0.7.28-59/dist/scittle.cljs-ajax.js"}]
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[:script {:src "https://cdn.jsdelivr.net/npm/react@18/umd/react.production.min.js", :crossorigin ""}]
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[:script {:src "https://cdn.jsdelivr.net/npm/react-dom@18/umd/react-dom.production.min.js", :crossorigin ""}]
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[:script {:src "https://cdn.jsdelivr.net/npm/scittle-kitchen@0.7.28-59/dist/scittle.reagent.js"}]
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[:script {:type "application/x-scittle" :src "scheme.cljc"}]])
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^:kindly/hide-code
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(defmacro define [& b]
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(list 'do
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(cons 'mentat-collective.emmy.scheme/define b)
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(list 'kind/scittle (list 'quote (cons 'define b)))))
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(define simplify identity)
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(define ->infix identity)
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(define down vector)
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^:kindly/hide-code
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(kind/scittle
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'(defn show-expression [e]
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(simplify e)))
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^:kindly/hide-code
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(kind/scittle
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'(defn show-tex-expression [e]
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(->infix (simplify e))))
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^:kindly/hide-code
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(kind/scittle
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'(defn show-tex [e]
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(->infix e)))
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^:kindly/hide-code
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(define (eq-transformation f)
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(lambda (tuple)
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(apply down (map f tuple))))
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^:kindly/hide-code
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(kind/scittle
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'(defn show-eq [tuple]
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(->infix (simplify (down (first tuple) '= (second tuple))))))
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^:kindly/hide-code
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(def tex (comp kind/tex emmy.expression.render/->TeX))
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^:kindly/hide-code
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(def tex-simp (comp tex simplify))
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^:kindly/hide-code
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(defn fn-show-eq [tuple]
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(tex-simp (down (first tuple) '= (second tuple))))
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^:kindly/hide-code
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(define show-exp (comp str simplify))
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^:kindly/hide-code
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(defn reag-comp [b]
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(let [server-erg (show-exp (eval b))]
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(list 'kind/reagent
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[:div (list 'quote
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(list 'let ['a (list 'show-exp b)]
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[:div
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(when (:browser render-mode)
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[:div
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[:tt 'a]
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[:p (list 'str (list '= server-erg 'a))]])
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[:tt server-erg]]))])))
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^:kindly/hide-code
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(defmacro show-expression [e]
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(if (:browser render-mode)
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(reag-comp e)
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(list 'simplify e)
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))
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^:kindly/hide-code
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(defmacro show-tex-expression [e]
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(if (:browser render-mode)
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(reag-comp e)
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(list 'tex-simp e)))
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^:kindly/hide-code
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(defmacro show-tex [e]
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(if (:browser render-mode)
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(reag-comp e)
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(list 'tex e)))
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^:kindly/hide-code
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(defmacro show-eq [e]
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(if (:browser render-mode)
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(reag-comp e)
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(list 'fn-show-eq e)))
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(kind/tex "x^1")
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(kind/hiccup [:div
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[:div#kt2 "2"]
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[:div#kt3 "3"]
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[:div#kt4 "4"]
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[:script "katex.render(\"x^2\", document.getElementById(\"kt2\"))"]])
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(kind/scittle
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'(.render js/katex "x^3" (.getElementById js/document "kt3")))
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(kind/scittle
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'(def *click-count (reagent.core/atom 4)))
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(kind/scittle
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'(.render js/katex (str "x^" @*click-count) (.getElementById js/document "kt4")))
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(kind/reagent
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['(fn []
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[:div
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"The atom " [:code "*click-count"] " has value: "
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@*click-count ". "
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[:input {:type "button" :value "Click me!"
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:on-click #(swap! *click-count inc)}]])])
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(show-tex "x^2")

‎src/mentat_collective/emmy/silcm_ch01.clj‎

Lines changed: 141 additions & 33 deletions
Original file line numberDiff line numberDiff line change
@@ -16,6 +16,8 @@
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[mentat-collective.emmy.scheme :refer [define-1 let-scheme lambda]]
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[civitas.repl :as repl]))
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;; TODO: Make a button for @path-dimension to make dimensions switchable from 4 -> 2
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;; I investigate a Lorentz covariant Lagrangian that is not widely known. It is discussed in the textbooks of Greiner, "Systems of Particles and Hamiltonian Mechanics" (chapter 21), and also [on-line in: Cline, "Variational Principles in Classical Mechanics"](https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Variational_Principles_in_Classical_Mechanics_(Cline)/17%3A_Relativistic_Mechanics/17.06%3A_Lorentz-Invariant_Formulation_of_Lagrangian_Mechanics).
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;; Then I derive, along deBroglie's argument, the momentum-wavelength relation of a free particle.
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'(defn show-tex [e]
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(->infix e)))
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^:kindly/hide-code
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(define (eq-transformation f)
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(lambda (tuple)
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(apply down (map f tuple))))
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^:kindly/hide-code
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(kind/scittle
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'(defn show-eq [tuple]
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(->infix (simplify (down (first tuple) '= (second tuple))))))
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^:kindly/hide-code
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(def tex (comp kind/tex emmy.expression.render/->TeX))
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^:kindly/hide-code
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(def tex-simp (comp tex simplify))
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^:kindly/hide-code
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(defn fn-show-eq [tuple]
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(tex-simp (down (first tuple) '= (second tuple))))
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^:kindly/hide-code
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(define show-exp (comp str simplify))
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(list 'tex e)
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(reag-comp e)))
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^:kindly/hide-code
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(defmacro show-eq [e]
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(if prod
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(list 'fn-show-eq e)
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(reag-comp e)))
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^:kindly/hide-code
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(define velocities velocity)
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@@ -157,9 +178,7 @@
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(let ((v (velocity local)))
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(* 1/2 mass (square c)
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(- (* (/ 1 (square c))
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(+ (square (ref v 1))
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(square (ref v 2))
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(square (ref v 3))))
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(square (apply up (rest v))))
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(square (ref v 0))
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1))))
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(show-tex-expression
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((Gamma Lc-test-path) 's))
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^:kindly/hide-code
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(define path-dimension (atom true)) #_"true = 4D , false = 2D"
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(define three-path (up (literal-function 'x)
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(literal-function 'y)
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(literal-function 'z)))
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^:kindly/hide-code
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(define three-path
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(if @path-dimension
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(up (literal-function 'x)
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(literal-function 'y)
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(literal-function 'z))
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(up (literal-function 'x))))
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(show-tex-expression
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((Gamma three-path) 't))
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(show-tex-expression
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((compose (L-free-particle 'm) (Gamma three-path)) 't))
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(define four-path (up identity
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(literal-function 'x)
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(literal-function 'y)
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(literal-function 'z)))
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^:kindly/hide-code
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(define four-path
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(if @path-dimension
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(up identity
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(literal-function 'x)
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(literal-function 'y)
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(literal-function 'z))
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(up identity
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(literal-function 'x))))
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(show-tex-expression
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((Gamma four-path) 's))
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;; The first $0$ is because we set $t=s$ for the path. This reduces the extended Lagrangian to the "conventional" case. Reassuring. Now we can allow arbitrary functions $t(s)$, making the path truely 4-dimensional.
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(define Lc-path (up (literal-function 't)
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(literal-function 'x)
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(literal-function 'y)
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(literal-function 'z)))
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^:kindly/hide-code
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(define Lc-path
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(if @path-dimension
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(up (literal-function 't)
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(literal-function 'x)
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(literal-function 'y)
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(literal-function 'z))
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(up (literal-function 't)
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(literal-function 'x))))
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#_(define Lc-path (up (literal-function 't)
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(literal-function 'x)))
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;; It is very interesting that a constant term can lead to a new formalism. Cline: "It provides a plausible manifestly-covariant Lagrangian for the one-body system, but serious problems exist extending this to the N-body system when N>1".
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;; Nobody possesses a Lorentz covariant N-body mechanics. Goldstein "Classical Mechanics", chapter 7,9: "Hitherto, there does not exist a satisfying description of the relativistic many body system."
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;; Nobody possesses a Lorentz covariant N-body mechanics. Goldstein "Classical Mechanics", chapter 7.9: "Hitherto, there does not exist a satisfying description of the relativistic many body system."
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;; This non-homogeneous business requires an implicit $L - pv = 0$ constraint (Cline Eq. 17.6.12, Struckmeier Eq. 21.9)
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;; ### The Constraint on the four dimensional path
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(define (Lc1-Lagrange-constraint Lagrangian)
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;; The Lagranian above looks very nice because it is symmtreic in t, x, y, z. But there is a caveat which ultimately brings it in line with the orthodox formulation.
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;; Non-homogeneous but symmetric Lagrangians of this type require a general implicit constraint: $L - pv = 0$ (Cline Eq. 17.6.12, Struckmeier Eq. 21.9)
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(define (Lc-Lagrange-constraint Lagrangian)
253292
(- Lagrangian (* ((partial 2) Lagrangian) velocity)))
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255-
;; By multiplication this with a constant factor, this leads to Struckmeier Eq. 21.12:
294+
;; Applied to the free particle (and multiplication with a constant factor), leads to (Struckmeier Eq. 21.12):
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257-
(define Lc1-constr (compose (* (/ 2 (square 'c) 'm_0)
258-
(Lc1-Lagrange-constraint (Lc-free-particle 'm_0 'c))) (Gamma Lc-path)))
296+
(define Lc-constraint-s
297+
(down (constantly 0) (compose (* (/ 2 (square 'c) 'm_0)
298+
(Lc-Lagrange-constraint (Lc-free-particle 'm_0 'c)))
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(Gamma Lc-path))))
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260-
(show-tex-expression
261-
(Lc1-constr 's))
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^:kindly/hide-code
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(show-eq
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(Lc-constraint-s 's))
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;; This constraint cannot be dealt with easily (contrary to constraints that do not depend on velocity but position which can be treated via Lagrange multipliers.)
305+
;; The above is a constraint, i.e. needs to be zero, needs to vanish for all physical paths.
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265-
;; Calculate $dt/ds$
266-
(define t-prime (sqrt (+ (- Lc1-constr)
267-
(square (ref (ref (Gamma Lc-path) 2) 0)))))
307+
;; Contrary to constraints that depend on position, this constraint (being about velocity) cannot be easily treated via Lagrange multipliers.
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269-
(show-tex-expression
270-
(t-prime 's))
309+
;; We proceed to explicitely calculate $(Dt(s))^2$
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272-
;; Maybe not useful, but one could also calculate $d^2t/ds^2$
311+
(define t (literal-function 't))
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^{:kindly/kind :kind/hidden}
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(show-tex-expression
276-
((D t-prime) 's))
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(define Dt-squared
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((eq-transformation
315+
#(- (square (D t)) %))
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Lc-constraint-s))
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^:kindly/hide-code
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(show-eq
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(Dt-squared 's))
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278-
;; Important is that $dt/ds$ leads to $ds/dt$ and the famous $\gamma$ factor (see e.g. Cline)
322+
;; The above is meant as an equality.
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324+
;; We now upgrade the parameter $s$ to a function $s(t)$ which is the inverse of $t(s)$, $s = t^{-1}$.
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(define s (literal-function 's))
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328+
;; Inverse means that $t(s(y)) = y$. While in the math rendering there is a minor risk of confusion, in the underlying code we do not need the auxilary `y`, the function `t` and the symbol `'t` are clearly distinct:
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(define t°s (down (comp t s) identity))
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(show-eq
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(t°s 't))
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;; The derivative results in the number `one`
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(show-eq
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((D t°s) 't))
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;; With this interlude, we return to the constraint. Just by formally replacing $s \rightarrow s(t)$, it reads as
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(show-eq
343+
(Dt-squared (s 't)))
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345+
;; We'd like to get rid of the function `t` and only keep the symbol/parameter `'t`. For this, we multiply the above equation by $(Ds(t))^2$
346+
347+
(define eq1
348+
((eq-transformation
349+
#(* ((square (D s)) 't) %))
350+
(* (Dt-squared (s 't)))))
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352+
(show-eq eq1)
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354+
;; We introduce the following slighly sloppy notation
355+
356+
(show-eq
357+
((down three-path (comp three-path s)) 't))
358+
359+
;; The derivative of this definition is
360+
(show-eq
361+
((D (down three-path (comp three-path s))) 't))
362+
363+
;; With this the constraint becomes
364+
365+
^:kindly/hide-code
366+
(define constraint-1
367+
(down 1 (/ (+ (* (square 'c)
368+
((square (D (literal-function 's))) 't))
369+
((square (D three-path)) 't))
370+
(square 'c))))
371+
372+
(show-eq
373+
constraint-1)
374+
375+
;; Remember that, as shown above, the number `one` appears because of $s = t^{-1}$
376+
377+
;; Isolating $Ds(t)$ on the right hand side
378+
379+
(show-eq
380+
((eq-transformation
381+
#(sqrt (- % (/ ((square (D three-path)) 't) (square 'c)))))
382+
constraint-1))
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384+
;; The above equation, which is just another expression of the constraint $L - pv = 0$, is conventionally written as below, introducing the famous $\gamma$ factor of Special Relativity.
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280386
^:kindly/hide-code
281387
(kind/tex
282388
"\\frac{ds}{dt} = \\sqrt{1- \\frac{v^2}{c^2}} = \\sqrt{1 - \\beta ^ 2} = \\frac{1}{\\gamma}")
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390+
;; Thus, the function $s(t)$ is nothing but the proper time.
391+
284392
;; ## The deBroglie wavelength
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286394
^:kindly/hide-code

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