58 lines
1.9 KiB
Plaintext
58 lines
1.9 KiB
Plaintext
#import "template/template.typ": *
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#show: paper => configuration(
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title: "Short guide to math-typst.",
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authors: (
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(
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name: "Orca",
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affiliation: "git.disroot.org/orca/math-typst",
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email: "orcinus_orca@disroot.org",
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),
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),
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abstract: "This PDF explains how to use math-typst.",
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paper
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)
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= Introduction
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This packages aims to provide a good enough interface for writing a mathematical course in it.
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As of now, it consists of the most used mathematical environments in courses #footnote[The environments provided are: `proposition`, `lemma`, `theorem`, `corollary`,
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`definition`, `remark`, `example`, `exercise`, `proof`, and `numbered-equation`.].
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= How to use
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With the exception of `proof`, environments behave like `theorem`. Simply type the environment name followed by it's body
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in square brackets. You may name the particular environment by appending `(name: "The name")` after the environment name.
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== Example
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#theorem(name: "Orca")[
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Let $P in ZZ[X]$ and $N in NN^*$ be such that for all $n in NN$, if $n >= N$, then $P(n)$ is prime.
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We have that $P$ is constant.
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] <orca>
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#proof[
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Let's consider
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$ P: x |-> sum_(i = 0)^(deg P) a_i x^i, " with " a_i in ZZ " for " i in [|0, deg P|]. $
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Suppose there exists $N in NN^*$ such that for all $n >= N$, $P(n)$ is prime.
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We have, for $alpha, beta in NN^*$,
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#numbered-equation(name: "E")[
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$ P(alpha + beta) = P(alpha) + k beta, " with " k in ZZ $
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] <eq>
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The equation @eq follows from the definition of $P$ and the binomial theorem.
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In particular, if $alpha >= N$ and $beta = n abs(P(alpha))$ with $n in NN^*$, then $P(alpha)$ divides $P(alpha + beta)$.
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Since they're both primes, we have $epsilon P(alpha) = P(alpha + beta)$, with $epsilon in {-1, 1}$ and $n$ a variable.
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We then find that $P - epsilon P(alpha)$ cancels an infinite amount of times, showing that $P$ is constant.
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]
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Unfortunately, it seems like the theorem @orca is not useful at all.
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