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attributio
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3
.vscode/settings.json
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3
.vscode/settings.json
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@ -1,4 +1,5 @@
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{
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{
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"latex-workshop.latex.recipe.default": "latexmk (xelatex)",
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"latex-workshop.latex.recipe.default": "latexmk (xelatex)",
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"tinymist.formatterPrintWidth": 80
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"tinymist.formatterPrintWidth": 80,
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"tinymist.typstExtraArgs": ["--package-path=./lib/typst"]
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}
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}
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3
authors.toml
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authors.toml
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[authors."mark"]
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email = "mark@betalupi.com"
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webpage = "betalupi.com"
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@ -1,3 +1,5 @@
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/// Typst handout library, used for all documents in this repository.
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/// If false, hide instructor info.
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/// If false, hide instructor info.
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///
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///
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@ -238,8 +240,8 @@
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set page(
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set page(
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margin: 20mm,
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margin: 20mm,
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width: 8.5in,
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width: 8in,
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height: 11in,
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height: 11.5in,
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footer: align(
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footer: align(
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center,
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center,
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context counter(page).display(),
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context counter(page).display(),
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6
lib/typst/local/handout/0.1.0/typst.toml
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lib/typst/local/handout/0.1.0/typst.toml
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[package]
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name = "handout"
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version = "0.1.0"
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entrypoint = "handout.typ"
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authors = []
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license = "GPL"
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@ -1,4 +1,4 @@
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#import "./handout.typ": *
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#import "@local/handout:0.1.0": *
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#import "@preview/cetz:0.3.1"
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#import "@preview/cetz:0.3.1"
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#import "./handout.typ": *
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#import "@local/handout:0.1.0": *
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#show: doc => handout(
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#show: doc => handout(
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doc,
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doc,
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@ -1,4 +1,4 @@
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#import "../handout.typ": *
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#import "@local/handout:0.1.0": *
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#import "../macros.typ": *
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#import "../macros.typ": *
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= Tropical Arithmetic
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= Tropical Arithmetic
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@ -62,8 +62,7 @@ Let's expand $#sym.RR$ to include a tropical additive identity.
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#problem()
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#problem()
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Do tropical additive inverses exist? \
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Do tropical additive inverses exist? \
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#note([
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#note([
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Is there an inverse $y$ for every $x$ so that $x #tp y = #sym.infinity$? \
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Is there an inverse $y$ for every $x$ so that $x #tp y = #sym.infinity$?
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Remember that $#sym.infinity$ is the additive identity.
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])
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])
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#solution([
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#solution([
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@ -278,7 +277,7 @@ Fill the following tropical addition and multiplication tables
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#problem()
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#problem()
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Expand and simplify $f(x) = (x #tp 2)(x #tp 3)$, then evaluate $f(1)$ and $f(4)$ \
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Expand and simplify $f(x) = (x #tp 2)(x #tp 3)$, then evaluate $f(1)$ and $f(4)$ \
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#hint([Adjacent parenthesis imply tropical multiplication])
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Adjacent parenthesis imply tropical multiplication
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#solution([
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#solution([
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$
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$
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@ -1,4 +1,4 @@
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#import "../handout.typ": *
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#import "@local/handout:0.1.0": *
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#import "../macros.typ": *
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#import "../macros.typ": *
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#import "@preview/cetz:0.3.1"
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#import "@preview/cetz:0.3.1"
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@ -20,7 +20,7 @@ for some nonnegative integer $n$ and coefficients $c_0, c_1, ..., c_n$. \
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The _degree_ of a polynomial is the largest $n$ for which $c_n$ is nonzero.
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The _degree_ of a polynomial is the largest $n$ for which $c_n$ is nonzero.
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#theorem()
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#theorem()
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The _fundamental theorem of algebra_ states that any non-constant polynomial with real coefficients
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The _fundamental theorem of algebra_ implies that any non-constant polynomial with real coefficients
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can be written as a product of polynomials of degree 1 or 2 with real coefficients.
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can be written as a product of polynomials of degree 1 or 2 with real coefficients.
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#v(2mm)
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#v(2mm)
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@ -30,8 +30,8 @@ can be written as $(x^2 + 2x+5)(x-2)(x+4)(x+4)$
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#v(2mm)
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#v(2mm)
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A similar theorem exists for polynomials with complex coefficients. \
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A similar theorem exists for polynomials with complex coefficients. \
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These coefficients may be found using the _roots_ of this polynomial. \
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These coefficients may be found using the roots of this polynomial. \
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As you already know, there are formulas that determine the roots of quadratic, cubic, and quartic #note([(degree 2, 3, and 4)]) polynomials. There are no formulas for the roots of polynomials with larger degrees---in this case, we usually rely on appropriate roots found by computers.
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As it turns out, there are formulas that determine the roots of quadratic, cubic, and quartic #note([(degree 2, 3, and 4)]) polynomials. There are no formulas for the roots of polynomials with larger degrees---in this case, we usually rely on approximate roots found by computers.
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#v(2mm)
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#v(2mm)
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In this section, we will analyze tropical polynomials:
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In this section, we will analyze tropical polynomials:
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@ -100,7 +100,7 @@ In other words, find $r$ and $s$ so that
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),
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),
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)
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)
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#note([Naturally, we will call $r$ and $s$ the _roots_ of $f$.])
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we will call $r$ and $s$ the _roots_ of $f$.
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#solution([
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#solution([
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Because $(x #tp r)(x #tp s) = x^2 #tp (r #tp s)x #tp s r$, we must have $r #tp s = 1$ and $r #tm s = 4$. \
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Because $(x #tp r)(x #tp s) = x^2 #tp (r #tp s)x #tp s r$, we must have $r #tp s = 1$ and $r #tm s = 4$. \
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@ -116,8 +116,7 @@ In other words, find $r$ and $s$ so that
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#v(1fr)
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#v(1fr)
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#problem()
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#problem()
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Can you see the roots of this polynomial in the graph? \
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How can we use the graph to determine these roots?
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#hint([Yes, you can. What "features" do the roots correspond to?])
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#solution([The roots are the corners of the graph.])
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#solution([The roots are the corners of the graph.])
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@ -317,7 +316,7 @@ into linear factors.
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#v(2mm)
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#v(2mm)
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Whenever we say "the roots of $f$", we really mean "the roots of $accent(f, macron)$." \
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Whenever we say "the roots of $f$", we really mean "the roots of $accent(f, macron)$." \
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Also, $f$ and $accent(f, macron)$ might be the same polynomial.
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$f$ and $accent(f, macron)$ might be the same polynomial.
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#problem()
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#problem()
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If $f(x) = a x^2 #tp b x #tp c$, then $accent(f, macron)(x) = a x^2 #tp B x #tp c$ for some $B$. \
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If $f(x) = a x^2 #tp b x #tp c$, then $accent(f, macron)(x) = a x^2 #tp B x #tp c$ for some $B$. \
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#import "../handout.typ": *
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#import "@local/handout:0.1.0": *
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#import "../macros.typ": *
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#import "../macros.typ": *
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#import "@preview/cetz:0.3.1"
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#import "@preview/cetz:0.3.1"
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BIN
src/Intermediate/Slide Rules/resources/ISRC.pdf
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BIN
src/Intermediate/Slide Rules/resources/ISRC.pdf
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src/Intermediate/Slide Rules/resources/rule.pdf
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src/Intermediate/Slide Rules/resources/rule.pdf
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@ -4,3 +4,8 @@ title = "Odd Dice"
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[publish]
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[publish]
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handout = true
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handout = true
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solutions = true
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solutions = true
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[[attribution]]
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who = "mark"
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when = 2024-02-13
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what = "Initial version of handout"
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[
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[
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TYPST_PATH,
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TYPST_PATH,
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"compile",
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"compile",
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"--package-path",
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f"{ROOT}/lib/typst",
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"--ignore-system-fonts",
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"--ignore-system-fonts",
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"main.typ",
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"--input",
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"--input",
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"show_solutions=false",
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"show_solutions=false",
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"main.typ",
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f"{out}/{handout_file}",
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f"{out}/{handout_file}",
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],
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],
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cwd=source_dir,
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cwd=source_dir,
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[
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[
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TYPST_PATH,
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TYPST_PATH,
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"compile",
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"compile",
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"--package-path",
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f"{ROOT}/lib/typst",
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"--ignore-system-fonts",
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"--ignore-system-fonts",
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"main.typ",
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"main.typ",
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f"{out}/{solutions_file}",
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f"{out}/{solutions_file}",
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Reference in New Issue
Block a user