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MathCheck Brief Instructions

This document is as of 2021-11-16. It lacks all more recent features of MathCheck.

In ready-made problems, the use of commands may have been restricted to those relevant for the problem.

Arithmetic and Parentheses

$54321$	54321
$frac(54)(321)$	54/321
$54 frac(3)(21)$	54 3/21
$54.321$	54.321
$pi$	pi
$e$	e

$+$	+
$−$	-
$*$	*
$x/y$	x/y
$frac(x+1)(2y)$	(x+1)/(2y)
$x^y$	x^y
$x^(-y z)$	x^(-y z)

$($	(
$)$	)
$($	#(
$)$	#)
$[$	[
$]$	]
$\ text(div)\$	div
$mod$	mod
$n!$	n!

$sqrt x+1$	sqrt x+1
$sqrt(x+1)$	sqrt(x+1)
$root(n)(x+1)$	root(n)(x+1)
$\|x+1\|$	\|x+1\| abs(x+1)
$\|__x+1__\|$	\|_x+1_\| floor(x+1)
$\|~x+1~\|$	\|^x+1^\| ceil(x+1)
$d/(d x) sin 5x$	DD x sin 5x

$sin$	sin
$cos$	cos
$tan$	tan
$cot$	cot
$ln$	ln
$log$	log
$log_2$	log2
$sinh$	sinh
$cosh$	cosh
$tanh$	tanh

The input symbols ( and ) denote ordinary parentheses and #( and #) denote hard parentheses. MathCheck removes unnecessary ordinary parentheses, but always prints hard parentheses even if they are unnecessary.

Comparisons and Logic

$<=$	<=
$<$	<
$=$	=
$!=$	!=
$>=$	>=
$>$	>

$not$	! not
$^^$	/\ and ^^
$vv$	\/ or vv
$rarr$	-->
$harr$	<->
$sf"F"$	FF
$sf"U"$	UU
$sf"T"$	TT

$\ sf"&&"\$	&&
$\ sf"\|\|"\$	\|\|
$AA x:$	AA x:
$AA i; 1 <= i <= n:$	AA i; 1 <= i <= n:
$EE x:$	EE x:
$EE i; 1 <= i <= n:$	EE i; 1 <= i <= n:

$rArr$	==>
$lArr$	<==
$hArr$	<=>
$-=$	===

Reasoning Chains

A reasoning chain may contain ⇐, ⇔, ⇒ and ≡, and the following:

assume x != 1 /\ y >= x;	Set a condition that is assumed to hold throughout the (sub)proof. One may use `enda` instead of `;`.
original	Refers to the first formula in a reasoning chain. If `original` is the first formula of a subproof, then it refers to the first formula of the parent proof.
subend	Ends a subproof.
subproof	Starts a subproof.

What formulas in a reasoning chain may contain depends on the problem mode. Typically most logical and comparison operators are allowed, but only a small set of arithmetic operators.

Greek Letters

$alpha$	al
$beta$	be
$gamma$	ga
$delta$	de
$varepsilon$	ve
$epsilon$	ep
$zeta$	ze

$eta$	et
$theta$	th
$vartheta$	vt
$iota$	io
$kappa$	ka
$lambda$	la
$mu$	mu

$nu$	nu
$xi$	xi
$rho$	rh
$sigma$	si
$tau$	ta
$upsilon$	up

$phi$	ph
$varphi$	vp
$chi$	ch
$psi$	ps
$omega$	om

$Gamma$	Ga GA
$Delta$	De DE
$Theta$	Th TH
$Lambda$	La LA
$Xi$	Xi XI

$Pi$	Pi PI
$Sigma$	Si SI
$Phi$	Ph PH
$Psi$	Ps PS
$Omega$	Om OM

Lexical Rules

Spaces and newlines may be freely used between tokens. If a non-numeric token ends and the next one starts with a letter or digit, there must be at least one space or newline in between.

These symbols can also be given as Unicode characters: ¬ ² ³ Γ Δ Θ Λ Ξ Π Σ Φ Ψ Ω α β γ δ ε ζ η θ ι κ λ μ ν ξ π ρ σ τ υ φ χ ψ ω ϑ ϕ ϵ ← → ↔ ↠ ⇐ ⇒ ⇔ ∀ ∃ − √ ∧ ∨ ≠ ≡ ≤ ≥ ⋅ ⌈ ⌉ ⌊ ⌋

Special Commands

/**/	Start a new line. A new line may also be started by putting the ⇔, ⇒, etc., to the very beginning of the line. In problem modes that do not support them, put =, >, etc., to the very beginning of the line.
/* two to the $n$ is $2^n$ */	Write a comment and start a new line. Passages surrounded by grave accent characters will be shown as mathematics.
assume x != 1 /\ y^2 < sin x;	Restrict the range of variables. Any comparisons and propositional operators may be used in the condition. One may use `enda` instead of `;`. Works in the arithmetic and draw function modes, and almost all problem modes that support logical reasoning chains. Unless otherwise stated, this must be next to the problem mode keyword.