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-- This file:
-- http://angg.twu.net/LATEX/2022-1-C2-P2.lua.html
-- http://angg.twu.net/LATEX/2022-1-C2-P2.lua
-- (find-angg "LATEX/2022-1-C2-P2.lua")
-- Author: Eduardo Ochs <eduardoochs@gmail.com>
--
-- (defun e () (interactive) (find-angg "LATEX/2022-1-C2-P2.tex"))
-- (defun l () (interactive) (find-angg "LATEX/2022-1-C2-P2.lua"))
-- (defun l2 () (interactive) (find-angg "LUA/Lazy2.lua"))
-- (defun l3 () (interactive) (find-angg "LUA/Lazy3.lua"))
-- (defun l4 () (interactive) (find-angg "LUA/Lazy4.lua"))
-- (defun l5 () (interactive) (find-angg "LUA/Lazy5.lua"))
--
-- (defun a () (interactive) (find-angg "LUA/Pict2e1.lua"))
-- (defun b () (interactive) (find-angg "LUA/Pict2e1-1.lua"))
-- (defun ab () (interactive) (find-2b '(a) '(b)))
-- (defun et () (interactive) (find-angg "LATEX/2022pict2e.tex"))
-- (defun eb () (interactive) (find-angg "LATEX/2022pict2e-body.tex"))
-- (defun ao () (interactive) (find-angg "LATEX/2022pict2e.lua"))
-- (defun pv () (interactive) (find-pdftools-page "~/LATEX/2022pict2e.pdf"))
-- (defun tb () (interactive) (find-ebuffer (eepitch-target-buffer)))
-- (defun etv () (interactive) (find-wset "13o2_o_o" '(tb) '(pv)))
-- (setenv "PICT2ELUADIR" "~/LATEX/")
--
-- (find-sh0 "cd ~/LUA/; cp -v Lazy5.lua Pict2e1.lua Verbatim1.lua ~/LATEX/")
-- «.output» (to "output")
-- «.basic-ops» (to "basic-ops")
-- «.subst-trig» (to "subst-trig")
-- «.edovs» (to "edovs")
-- «.edo-2a-ordem» (to "edo-2a-ordem")
require "Lazy5" -- (find-anggfile "LUA/Lazy5.lua")
var = Lazy.var
fun = Lazy.fun
ang = Lazy.ang
funs = function (bigstr) map(fun, split(bigstr)) end
vars = function (bigstr) map(var, split(bigstr)) end
namedformula = Lazy.namedformula
namedang = Lazy.namedang
namedsubst = Subst.named
-- «output» (to ".output")
out = ""
if not output then
output = function (str, verbose)
if verbose then print(); print(str) end
out = out.."\n"..str
Show.preamble = out
end
verbose = false
end
-- «basic-ops» (to ".basic-ops")
-- (find-angg "LUA/Lazy3.lua" "basic-ops")
funs " ddx eq mul f g fp gp und "
vars " x y t "
fun("mul", "<1> <2>")
fun("Mul", "<1> · <2>")
fun("und", "\\und{<1>}{<2>}")
fun("uu", "\\und{<1>}{}")
fun("ddx", "\\frac{d}{dx} <1>")
fun("ddvar", "\\frac{d}{d<1>} <2>")
fun("plus", "<1> + <2>")
fun("minus", "<1> - <2>")
fun("eq", "<1> = <2>")
fun("exp", "e^{<1>}")
fun("pot", "{<1>}^{<2>}")
fun("frac", "\\frac{<1>}{<2>}")
fun("sqrt", "\\sqrt{<1>}")
fun("paren", "(<1>)")
fun("Paren", "\\left(<1>\\right)")
fun("sen", "\\sen <1>")
fun("sin", "\\sin <1>")
fun("cos", "\\cos <1>")
fun("tan", "\\tan <1>")
fun("ln", "\\ln <1>")
fun("lnp", "\\ln' <1>")
fun("mod", "|<1>|")
fun("uminus", "-<1>")
fun("sen", "\\sen(<1>)")
fun("sin", "\\sin(<1>)")
fun("cos", "\\cos(<1>)")
fun("tan", "\\tan(<1>)")
funs"f g h F G H"
vars"a b c t u x y z w s"
fun("fp", "f'(<1>)")
fun("gp", "g'(<1>)")
var("th", "\\theta ")
fun("Intx", "\\D \\Intx{<1>}{<2>}{<3>}")
fun("Intu", "\\D \\Intu{<1>}{<2>}{<3>}")
fun("Ints", "\\D \\Ints{<1>}{<2>}{<3>}")
fun("Intth", "\\D \\Intth{<1>}{<2>}{<3>}")
fun("difx", "\\difx{<1>}{<2>}{<3>}")
fun("difu", "\\difu{<1>}{<2>}{<3>}")
fun("ddvar", "\\frac{d}{d<1>}<2>")
fun("intvar", "\\intvar{<1>}{<2>}")
fun("Intvar", "\\D \\Intvar{<1>}{<2>}{<3>}{<4>}")
fun("difvar", "\\difvar{<1>}{<2>}{<3>}{<4>}")
fun("intx", "\\D \\intx{<1>}")
fun("intu", "\\D \\intu{<1>}")
fun("inty", "\\D \\inty{<1>}")
fun("ints", "\\D \\ints{<1>}")
fun("intth", "\\D \\intth{<1>}")
-- ____ _ _ _ _
-- / ___| _ _| |__ ___| |_ | |_ _ __(_) __ _
-- \___ \| | | | '_ \/ __| __| | __| '__| |/ _` |
-- ___) | |_| | |_) \__ \ |_ | |_| | | | (_| |
-- |____/ \__,_|_.__/|___/\__| \__|_| |_|\__, |
-- |___/
-- «subst-trig» (to ".subst-trig")
-- (c2m221p2p 2 "subst-trig")
-- (c2m221p2a "subst-trig")
-- (find-pdftoolsr-page "~/LATEX/2022-1-C2-P2.pdf" 2)
namedformula("RC", "RC", Paren(eq( ddx(f(g(x))), Mul(fp(g(x)), gp(x)))))
namedformula("MV2", "MV _2", Paren(eq( Intvar(x, a, b, Mul(fp(g(x)), gp(x))),
Intvar(u, g(a), g(b), fp(u)))))
TRIG1L = ints(mul(pot(s,4), pot(sqrt(minus(1,pot(s,2))),10)))
TRIG1R = ints(mul(mul(pot(sen(th),4),
pot(sqrt(minus(1,pot(paren(sen(th)),2))),10)),
cos(th)))
namedformula("TRIG1", "TRIG _1", Paren(eq(TRIG1L, TRIG1R)))
namedsubst("STrig0", "STrig _0", [[
g(x) := sen(x)
gp(x) := cos(x)
]])
namedsubst("STrig1", "STrig _1", [[
g(x) := sen(x)
gp(x) := cos(x)
x := th
u := s
]])
namedsubst("STrig2", "STrig _2", [[
g(x) := sen(x)
gp(x) := cos(x)
x := th
u := s
fp(x) := pot(sqrt(x),10)
]])
namedsubst("STrig3", "STrig _3", [[
g(x) := sen(x)
gp(x) := cos(x)
x := th
u := s
fp(x) := pot(minus(1,sqrt(x)),10)
]])
namedsubst("STrig4", "STrig _4", [[
g(x) := sen(x)
gp(x) := cos(x)
x := th
u := s
fp(s) := mul(pot(s,4),pot(sqrt(minus(1,pot(s,2))),10))
]])
namedang("TRIGSOLUTION", nil, [[
\begin{array}{rcl}
<TRIG1_> &=& <TRIG1> \\
<MV2_> &=& <MV2> \\
<MV2_><STrig0:bsm()> &=& <STrig0(MV2)> \\
<MV2_><STrig1:bsm()> &=& <STrig1(MV2)> \\
<MV2_><STrig2:bsm()> &=& <STrig2(MV2)> \\
<MV2_><STrig3:bsm()> &=& <STrig3(MV2)> \\
<MV2_><STrig4:bsm()> &=& <STrig4(MV2)> \\
\end{array}
]])
--[==[
* (eepitch-lua51)
* (eepitch-kill)
* (eepitch-lua51)
dofile "2022-1-C2-P2.lua"
= TRIGSOLUTION:show("0.6 d")
* (etv)
= TRIG1L:tree()
= TRIG1R:tree()
= TRIG1:tree()
= STrig4(MV2):tree()
= TRIG1:totex()
= TRIG1:show("dd")
* (etv)
--]==]
-- _____ ____ _____ ______
-- | ____| _ \ / _ \ \ / / ___|
-- | _| | | | | | | \ \ / /\___ \
-- | |___| |_| | |_| |\ V / ___) |
-- |_____|____/ \___/ \_/ |____/
--
-- «edovs» (to ".edovs")
-- (c2m221p2p 3 "edovs")
-- (c2m221p2a "edovs")
-- (find-angg "LUA/Lazy4.lua" "EDOVSG")
-- (find-pdftoolsr-page "~/LATEX/2022-1-C2-P2.pdf" 3)
var("C1", "C_1")
var("C2", "C_2")
var("C3", "C_3")
fun("Hinv", "H^{-1}(<1>)")
namedang("EDOVSG", "EDOVSG", [[
\left(\begin{array}{rcl}
\D \dydx &=& \D <frac(g(x),h(y))> \\
<h(y)>\,dy &=& <g(x)>\,dx \\
<inty(h(y))> &=& <intx(g(x))> \\
\mcc{\veq} & & \mcc{\veq} \\
\mcc{<plus(H(y),C1)>} & & \mcc{<plus(G(x),C2)>} \\
<H(y)> &=& <plus(G(x),minus(C2,C1))> \\
&=& <plus(G(x),C3)> \\
<Hinv(H(y))> &=& <Hinv(plus(G(x),C3))> \\
\mcc{\veq} & & \\
\mcc{y} & & \\
\end{array}
\right)
]])
namedang("EDOVSP", "EDOVSP", [[
\left(\begin{array}{rcl}
\D \dydx &=& \D <frac(g(x),h(y))> \\
<Hinv(H(y))> &=& <Hinv(plus(G(x),C3))> \\
\mcc{\veq} & & \\
\mcc{y} & & \\
\end{array}
\right)
]])
namedsubst("SE1", "SE _1", [[
g(x) := uminus(mul(2,x))
G(x) := uminus(pot(x,2))
h(x) := mul(2,x)
H(x) := pot(x,2)
Hinv(x) := uminus(sqrt(x))
C1 := 4
C2 := 29
C3 := 25
]])
namedang("EDOVSa", "EDOVSa", [[
\begin{array}{rcl}
<EDOVSG_> &=& <EDOVSG> \\ \\[-5pt]
<EDOVSG_><SE1> &=& <SE1(EDOVSG)> \\
\end{array}
]])
--[==[
* (eepitch-lua51)
* (eepitch-kill)
* (eepitch-lua51)
dofile "2022-1-C2-P2.lua"
= EDOVSa:show("0.5 d")
* (etv)
-- <SE1_> &=& <SE1:bsm()> \\
= EDOVSG
= EDOVSG:tree()
= EDOVSG:totex()
= SE1
= SE1:bmat()
= SE1:totex()
= SE1(EDOVSP):totex()
= ang("_", "<EDOVSG_> = <EDOVSG>"):totex()
= ang("_", "<EDOVSG_> = <EDOVSG>"):show("0.8 d")
= ang("_", "<EDOVSP_> = <EDOVSP>"):show("0.8 d")
= ang("_", "<SE1_> = <SE1>"):show("0.8 d")
= ang("_", "<SE1_> = <SE1:bsm()>"):show("0.8 d")
* (etv)
--]==]
-- _____ ____ ___ ____ _
-- | ____| _ \ / _ \ |___ \ __ _ ___ _ __ __| | ___ _ __ ___
-- | _| | | | | | | | __) / _` | / _ \| '__/ _` |/ _ \ '_ ` _ \
-- | |___| |_| | |_| | / __/ (_| | | (_) | | | (_| | __/ | | | | |
-- |_____|____/ \___/ |_____\__,_| \___/|_| \__,_|\___|_| |_| |_|
--
-- «edo-2a-ordem» (to ".edo-2a-ordem")
-- (c2m221p2p 3 "edo-2a-ordem")
-- (c2m221p2a "edo-2a-ordem")
-- (c2m221p2p 10 "edo-2a-ordem-gab")
-- (c2m221p2a "edo-2a-ordem-gab")
vars("j k")
var("a2", "a_2")
var("a5", "a_5")
var("a7", "a_7")
var("a10", "a_{10}")
var("aa", "α")
var("bb", "β")
var("gg", "γ")
var("dd", "δ")
var("ii", "i")
namedang("EDOLP0", "EDOLP _0", [[
\left(
\begin{array}{rcl}
f''(x) + <a7> f'(x) + <a10> f(x) &=& 0 \\
(D^2 + <a7> D + <a10>) f &=& 0 \\
(D^2 + (<a2>+<a5>)D + (<a2>·<a5>))f &=& 0 \\
(D^2 + <a7>D + <a10>)(<gg>e^{-<a2>x} + <dd>e^{-<a5>x}) &=& 0 \\
\end{array}
\right)
]])
namedang("EDOLP1", "EDOLP _1", [[
\left(
\begin{array}{rcl}
f''(x) + <a7> f'(x) + <a10> f(x) &=& 0 \\
(D^2 + <a7> D + <a10>) f &=& 0 \\
(D^2 + <a7> D + <a10>) f &=& 0 \\
(D^2 + <a7>D + <a10>)(<gg>e^{-<a2>x} + <dd>e^{-<a5>x}) &=& 0 \\
\end{array}
\right)
]])
namedsubst("SL0", "S _0", [[
a2 := 2
a5 := 5
a7 := 7
a10 := 10
]])
namedformula("EDOLP", "EDOLP", SL0(EDOLP0))
namedsubst("SL1", "SL _1", [[
a2 := aa
a5 := bb
a7 := 7
a10 := 10
]])
namedsubst("S1", "S _1", [[
aa := 2
bb := 5
]])
namedformula("EDOLG1", "EDOLG _1", SL1(EDOLP0))
namedsubst("SL2", "SL _2", [[
a2 := aa
a5 := bb
a7 := j
a10 := k
]])
namedsubst("S2", "S _2", [[
aa := 2
bb := 5
j := 7
k := 10
]])
namedformula("EDOLG2", "EDOLG _2", SL2(EDOLP0))
namedsubst("S3", "S _3", [[
j := paren(plus(aa,bb))
k := paren(Mul(aa,bb))
]])
namedformula("EDOLG3", "EDOLG _3", S3(EDOLG2))
namedformula("EDOLG", "EDOLG", S3(EDOLG2))
namedang("EDO2aordem_EDOLG", nil, [[
\begin{array}{rcll}
<EDOLP_> &=& <EDOLP> \\ \\[-5pt]
<EDOLG1_> &=& <EDOLG1> & <S1_>=<S1> \\ \\[-5pt]
<EDOLG2_> &=& <EDOLG2> & <S2_>=<S2> \qquad <S3_>=<S3> \\ \\[-5pt]
<EDOLG2_><S3_> &=& <S3(EDOLG2)> & <EDOLG_> = <EDOLG2_><S3_> \\ \\[-5pt]
<EDOLG_> &=& <EDOLG> \\ \\[-5pt]
<EDOLG_><S1> &=& <S1(EDOLG)>, & \text{que é ``muito parecido'' com o } <EDOLP_>... \\
\end{array}
]])
namedsubst("SVSA1", "SE _1", [[
aa := paren( plus(-2,mul(10,ii)))
bb := paren(minus(-2,mul(10,ii)))
]])
namedformula("EVSA1", "E _1", SVSA1(EDOLG))
namedang("EDOLPVSA1", "EDOLP _1", [[
\left(
\begin{array}{rcl}
f''(x) + <a7> f'(x) + <a10> f(x) &=& 0 \\
(D^2 + <a7> D + <a10>) f &=& 0 \\
(D^2 + <a7> D + <a10>) f &=& 0 \\
(D^2 + <a7>D + <a10>)(<gg>e^{-<a2>x} + <dd>e^{-<a5>x}) &=& 0 \\
\end{array}
\right)
]])
namedsubst("SVSA2", "SE _2", [[
a2 := paren( plus(-2,mul(10,ii)))
a5 := paren(minus(-2,mul(10,ii)))
a7 := paren(-4)
a10 := 104
]])
namedformula("EVSA2", "E _2", SVSA2(EDOLPVSA1))
--[==[
* (eepitch-lua51)
* (eepitch-kill)
* (eepitch-lua51)
dofile "2022-1-C2-P2.lua"
= ang("_", [[
\begin{array}{rcll}
<EDOLP_> &=& <EDOLP> \\
<EDOLG1_> &=& <EDOLG1> & <S1_>=<S1> \\
<EDOLG2_> &=& <EDOLG2> & <S2_>=<S2> \qquad <S3_>=<S3> \\
<EDOLG2_><S3_> &=& <S3(EDOLG2)> & <EDOLG_> = <EDOLG2_><S3_> \\
<EDOLG_> &=& <EDOLG> \\
<EDOLG_><S1> &=& <S1(EDOLG)>, & \text{que é ``muito parecido'' com o } <EDOLP_>... \\
\end{array}
]]):show("0.5 d")
* (etv)
= ang("_", [[
\begin{array}{rcll}
<EDOLG_> &=& <EDOLG> \\
\end{array}
]]):show("0.5 d")
* (etv)
= ang("_", [[
\begin{array}{rcll}
<SVSA1_> &=& <SVSA1> \\
<EDOLG_><SVSA1_> &=& <SVSA1(EDOLG)> \\
<EDOLG_><SVSA1> &=& <EVSA1> \\
<EVSA1_>
\end{array}
]]):show("0.6 d")
* (etv)
* (eepitch-lua51)
* (eepitch-kill)
* (eepitch-lua51)
dofile "2022-1-C2-P2.lua"
= ang("_", [[
\begin{array}{l}
<EDOLG_> = <EDOLG> \\ \\[-5pt]
<EVSA1_> = <EDOLG_><SVSA1> = \\ \\[-5pt]
= <EVSA1> \\ \\[-5pt]
= <EVSA2> \\
\end{array}
]]):show("0.6 d")
* (etv)
--]==]
-- Local Variables:
-- coding: utf-8-unix
-- End: