// Copied from https://github.com/typst/templates
//
// MIT No Attribution
//
// Permission is hereby granted, free of charge, to any person obtaining a copy of this
// software and associated documentation files (the "Software"), to deal in the Software
// without restriction, including without limitation the rights to use, copy, modify,
// merge, publish, distribute, sublicense, and/or sell copies of the Software, and to
// permit persons to whom the Software is furnished to do so.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED,
// INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A
// PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
// OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
// SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

// unequivocal-ams/template/main.typ

// Sizes used across the template.
#let script-size = 7.97224pt
#let footnote-size = 8.50012pt
#let small-size = 9.24994pt
#let normal-size = 10.00002pt
#let large-size = 11.74988pt

// Workaround for the lack of an `std` scope.
#let std-bibliography = bibliography

// This function gets your whole document as its `body` and formats
// it as an article in the style of the American Mathematical Society.
#let ams-article(
// The article's title.
title: [Paper title],

// An array of authors. For each author you can specify a name,
// department, organization, location, and email. Everything but
// but the name is optional.
authors: (),

// Your article's abstract. Can be omitted if you don't have one.
abstract: none,

// The article's paper size. Also affects the margins.
paper-size: "us-letter",

// The result of a call to the `bibliography` function or `none`.
bibliography: none,

// The document's content.
body,
) = {
// Formats the author's names in a list with commas and a
// final "and".
let names = authors.map(author => author.name)
let author-string = if authors.len() == 2 {
names.join(" and ")
} else {
names.join(", ", last: ", and ")
}

// Set document metadata.
set document(title: title, author: names)

// Set the body font. AMS uses the LaTeX font.
set text(size: normal-size, font: "New Computer Modern")

// Configure the page.
set page(
paper: paper-size,
// The margins depend on the paper size.
margin: if paper-size != "a4" {
(
top: (116pt / 279mm) * 100%,
left: (126pt / 216mm) * 100%,
right: (128pt / 216mm) * 100%,
bottom: (94pt / 279mm) * 100%,
)
} else {
(
top: 117pt,
left: 118pt,
right: 119pt,
bottom: 96pt,
)
},

// The page header should show the page number and list of
// authors, except on the first page. The page number is on
// the left for even pages and on the right for odd pages.
header-ascent: 14pt,
header: locate(loc => {
let i = counter(page).at(loc).first()
if i == 1 { return }
set text(size: script-size)
grid(
columns: (6em, 1fr, 6em),
if calc.even(i) [#i],
align(center, upper(
if calc.odd(i) { title } else { author-string }
)),
if calc.odd(i) { align(right)[#i] }
)
}),

// On the first page, the footer should contain the page number.
footer-descent: 12pt,
footer: locate(loc => {
let i = counter(page).at(loc).first()
if i == 1 {
align(center, text(size: script-size, [#i]))
}
})
)

// Configure headings.
set heading(numbering: "1.")
show heading: it => {
// Create the heading numbering.
let number = if it.numbering != none {
counter(heading).display(it.numbering)
h(7pt, weak: true)
}

// Level 1 headings are centered and smallcaps.
// The other ones are run-in.
set text(size: normal-size, weight: 400)
if it.level == 1 {
set align(center)
set text(size: normal-size)
smallcaps[
#v(15pt, weak: true)
#number
#it.body
#v(normal-size, weak: true)
]
counter(figure.where(kind: "theorem")).update(0)
} else {
v(11pt, weak: true)
number
let styled = if it.level == 2 { strong } else { emph }
styled(it.body + [. ])
h(7pt, weak: true)
}
}

// Configure lists and links.
set list(indent: 24pt, body-indent: 5pt)
set enum(indent: 24pt, body-indent: 5pt)
show link: set text(font: "New Computer Modern Mono")

// Configure equations.
show math.equation: set block(below: 8pt, above: 9pt)
show math.equation: set text(weight: 400)

// Configure citation and bibliography styles.
set std-bibliography(style: "springer-mathphys", title: [References])

show figure: it => {
show: pad.with(x: 23pt)
set align(center)

v(12.5pt, weak: true)

// Display the figure's body.
it.body

// Display the figure's caption.
if it.has("caption") {
// Gap defaults to 17pt.
v(if it.has("gap") { it.gap } else { 17pt }, weak: true)
smallcaps(it.supplement)
if it.numbering != none {
[ ]
it.counter.display(it.numbering)
}
[. ]
it.caption.body
}

v(15pt, weak: true)
}

// Theorems.
show figure.where(kind: "theorem"): it => block(above: 11.5pt, below: 11.5pt, {
strong({
it.supplement
if it.numbering != none {
[ ]
counter(heading).display()
it.counter.display(it.numbering)
}
[.]
})
emph(it.body)
})

// Display the title and authors.
v(35pt, weak: true)
align(center, upper({
text(size: large-size, weight: 700, title)
v(25pt, weak: true)
text(size: footnote-size, author-string)
}))

// Configure paragraph properties.
set par(first-line-indent: 1.2em, justify: true, leading: 0.58em)
show par: set block(spacing: 0.58em)

// Display the abstract
if abstract != none {
v(20pt, weak: true)
set text(script-size)
show: pad.with(x: 35pt)
smallcaps[Abstract. ]
abstract
}

// Display the article's contents.
v(29pt, weak: true)
body

// Display the bibliography, if any is given.
if bibliography != none {
show std-bibliography: set text(footnote-size)
show std-bibliography: pad.with(x: 0.5pt)
bibliography
}

// The thing ends with details about the authors.
show: pad.with(x: 11.5pt)
set par(first-line-indent: 0pt)
set text(script-size)

for author in authors {
let keys = ("department", "organization", "location")

let dept-str = keys
.filter(key => key in author)
.map(key => author.at(key))
.join(", ")

smallcaps(dept-str)
linebreak()

if "email" in author [
_Email address:_ #link("mailto:" + author.email) \
]

if "url" in author [
_URL:_ #link(author.url)
]

v(12pt, weak: true)
}
}

// The ASM template also provides a theorem function.
#let theorem(body, numbered: true) = figure(
body,
kind: "theorem",
supplement: [Theorem],
numbering: if numbered { "1" },
)

// And a function for a proof.
#let proof(body) = block(spacing: 11.5pt, {
emph[Proof.]
[ ] + body
h(1fr)
box(scale(160%, origin: bottom + right, sym.square.stroked))
})

// unequivocal-ams/lib.typ

#import "@preview/unequivocal-ams:0.1.0": ams-article, theorem, proof

#show: ams-article.with(
title: [Mathematical Theorems],
authors: (
(
name: "Ralph Howard",
department: [Department of Mathematics],
organization: [University of South Carolina],
location: [Columbia, SC 29208],
email: "howard@math.sc.edu",
url: "www.math.sc.edu/~howard"
),
),
abstract: lorem(100),
bibliography: bibliography("refs.bib"),
)

Call me Ishmael. Some years ago --- never mind how long precisely ---
having little or no money in my purse, and nothing particular to
interest me on shore, I thought I would sail about a little and see
the watery part of the world. It is a way I have of driving off the
spleen, and regulating the circulation. Whenever I find myself
growing grim about the mouth; whenever it is a damp, drizzly November
in my soul; whenever I find myself involuntarily pausing before coffin
warehouses, and bringing up the rear of every funeral I meet; and
especially whenever my hypos get such an upper hand of me, that it
requires a strong moral principle to prevent me from deliberately
stepping into the street, and methodically knocking people's hats off
--- then, I account it high time to get to sea as soon as I can. This
is my substitute for pistol and ball. With a philosophical flourish
Cato throws himself upon his sword; I quietly take to the ship. There
is nothing surprising in this. If they but knew it, almost all men in
their degree, some time or other, cherish very nearly the same
feelings towards the ocean with me. @netwok2020

There now is your insular city of the Manhattoes, belted round by
wharves as Indian isles by coral reefs - commerce surrounds it with
her surf. Right and left, the streets take you waterward. Its extreme
down-town is the battery, where that noble mole is washed by waves,
and cooled by breezes, which a few hours previous were out of sight of
land. Look at the crowds of water-gazers there.

Anyone caught using formulas such as $\$sqrt(x+y)=sqrt(x)+sqrt(y)\$$
or $\$1/(x+y)\; =\; 1/x\; +\; 1/y\$$ will fail.

The binomial theorem is
$\$\; (x+y)^n=sum\_(k=0)^n\; binom(n,\; k)\; x^k\; y^(n-k).\; \$$

A favorite sum of most mathematicians is
$\$\; sum\_(n=1)^oo\; 1/n^2\; =\; pi^2\; /\; 6.\; \$$

Likewise a popular integral is
$\$\; integral\_(-oo)^oo\; e^(-x^2)\; dif\; x\; =\; sqrt(pi)\; \$$

#theorem[
The square of any real number is non-negative.
]

#proof[
Any real number $\$x\$$ satisfies $\$x\; >\; 0\$$, $\$x\; =\; 0\$$, or . If $\$x\; =\; 0\$$,
then $\$x^2\; =\; 0\; >=\; 0\$$. If $\$x\; >\; 0\$$ then as a positive time a positive is
positive we have $\$x^2\; =\; x\; x\; >\; 0\$$. If then $\$-x\; >\; 0\$$ and so by
what we have just done $\$x^2\; =\; (-x)^2\; >\; 0\$$. So in all cases $\$x^2\; \ge \; 0\$$.
]

= Introduction
This is a new section.
You can use tables like @solids.

#figure(
table(
columns: (1fr, auto, auto),
inset: 5pt,
align: horizon,
[], [*Area*], [*Parameters*],
[*Cylinder*],
$\$\; pi\; h\; (D^2\; -\; d^2)\; /\; 4\; \$$,
[$\$h\$$: height \
$\$D\$$: outer radius \
$\$d\$$: inner radius],
[*Tetrahedron*],
$\$\; sqrt(2)\; /\; 12\; a^3\; \$$,
[$\$a\$$: edge length]
),
caption: "Solids",
)

== Things that need to be done
Prove theorems.

= Background
#lorem(40)