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src/mentat_collective/emmy/fdg_ch01.clj renamed to src/mentat_collective/emmy/fdg_prologue.clj

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:clay {:title "Emmy, the Algebra System: Classical Mechanics Prologue"
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:quarto {:author :kloimhardt
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:type :post
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:date "2025-09-10"
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:image "sicm_ch01.png"
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:date "2025-11-12"
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:image "fdg_prologue.png"
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:category :libs
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:tags [:emmy :physics]}}}
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(ns mentat-collective.emmy.fdg-ch01
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(ns mentat-collective.emmy.fdg-prologue
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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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[emmy.env :as e]
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[emmy.env :as e :refer [->infix simplify Lagrange-equations literal-function]]
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[emmy.mechanics.lagrange :as lg]
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[emmy.expression.render :as r :refer [->infix]]
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[civitas.repl :as repl]))
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;; Elemetary introduction to Emmy, taken from the first pages of the open-access book
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;; [Functional Differential Geometry (FDG)](https://mitpress.mit.edu/9780262019347/functional-differential-geometry/).
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;; The code snippets are executable, copy-paste them to the sidebar of the page.
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;; The Emmy maintainer, Sam Ritchie, wrote the source for this page, namely the
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;; The [Emmy]((https://emmy.mentat.org)) maintainer, [Sam Ritchie](https://roadtoreality.substack.com/), wrote the source for this page, namely the
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;; [LaTex version of FDG](https://github.com/mentat-collective/fdg-book/blob/main/scheme/org/prologue.org).
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^:kindly/hide-code
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;; By thinking computationally we have reformulated the Lagrange equations into a
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;; form that is explicit enough to specify a computation. We could convert it into
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;; a program for any symbolic manipulation program because it tells us /how/ to
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;; a program for any symbolic manipulation program because it tells us *how* to
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;; manipulate expressions to compute the residuals of Lagrange’s equations for a
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;; purported solution path.[fn:2]
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;; [note by MAK: the following does not work in the sidebar because I could not get
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;; `literal-function` to work.
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;; As a remedy, I have an [alternative execution environment](https://kloimhardt.github.io/blog/html/sicmutils-as-js-book-part1.html)]
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;; As a remedy, I have an [alternative execution environment](https://kloimhardt.github.io/blog/html/sicmutils-as-js-book-part1.html) ]
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(->infix
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(simplify
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(((e/Lagrange-equations (lg/L-harmonic 'm 'k))
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(e/literal-function 'x))
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(((Lagrange-equations (lg/L-harmonic 'm 'k))
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(literal-function 'x))
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't)))
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;; If this residual is zero we have the Lagrange equation for the harmonic

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