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. |