AsciiMath | PracticalSeries: Web Development

22.3 AsciiMath

I’m going to say right from the start that I like AsciiMath, it is straight forward to use and is easy to understand.

AsciiMath itself is a form of notation for writing equations. This for example is the quadratic formulae in AsciiMath form:

`x=(-b +- sqrt(b^2 — 4ac))/(2a)`

The one we all know from O level maths:

`x=(-b +- sqrt(b^2 — 4ac))/(2a)`

Now if I stick that equation into the website and put a back-tick (`) character before and after it, like this:

equation html

<div class="formulae" id="js--e99-01">
    <div class="formulae-container"> 
        <div class="formulae-equ"> 
            `x=(-b +- sqrt(b^2 — 4ac))/(2a)`
        </div> 
        <div class="formulae-num"></div>
    </div>
</div>

Code 22.4 Full equation HTML

I’ve taken out the heading, number and caption. It gives me this:

`x=(-b +- sqrt(b^2 – 4ac))/(2a)`

Well, I think it is pretty cool.

Look again at the AsciiMath:

x=(-b +- sqrt(b^2 — 4ac))/(2a)

It’s a bit hard to explain, but at an intuitive level you can see exactly how it works, if you wanted to type that equation in as a single line on a computer terminal, I bet you would come up with something similar to the above.

Here is another that shows how it handles big and small brackets:

sum_(i=1)^n i^3=((n(n+1))/2)^2

It looks like this:

`sum_(i=1)^n i^3=((n(n+1))/2)^2`

Obviously, you need to know what names are given to the symbols; the following tables show them all:

22.3.1 AsciiMath mathematical operators

			example
AsciiMath	Description	Apperance	AsciiMath	Result
+	Plus sign	`+`	x=a+b	`x=a+b`
-	Minus sign	`-`	x=a-b	`x=a-b`
xx	Times sign	`xx`	x=axxb	`x=axxb`
-:	Divide sign	`-:`	x=a-:b	`x=a-:b`
//	Division slash	`//`	x=a//b	`x=a//b`
*	Dot	`*`	x=a*b	`x=a*b`
**	Asterisk	`**`	x=a**b	`x=a**b`
***	Star	`***`	x=a***b	`x=a***b`
sum	Sigma (summation)	`sum`	suma =1+2+...	`suma =1+2+...`
prod	Pi (product)	`prod`	proda =(1)(2)...	`proda =(1)(2)...`

22.3.2 AsciiMath relational symbols

			example
AsciiMath	Description	Apperance	AsciiMath	Result
=	Equals sign	`=`	a=b	`a=b`
!=	Not equals sign	`!=`	a!=b	`a!=b`
<	Less than	`<`	a<b	`a<b`
>	Greater than	`>`	a>b	`a>b`
<=	Less than or equal to	`<=`	a<=b	`a<=b`
>=	Greater than or equal to	`>=`	a>=b	`a>=b`
-=	Equivalent to	`-=`	a-=b	`a-=b`
~=	Approximately equal to	`~=`	a~=b	`a~=b`
~~	Approximately	`~~`	a~~b	`a~~b`
prop	Proportional sign	`prop`	a prop b	`a prop b`

22.3.3 AsciiMath brackets

Brackets grow to accommodate fractions and operators that require more than one line.

			example
AsciiMath	Description	Apperance	AsciiMath	Result
( or )	Normal brackets	`(" ")`	x=((n(n+1))/2)	`x=((n(n+1))/2)`
[ or ]	Square brackets	`[" "]`	x=[(n(n+1))/2]	`x=[(n(n+1))/2]`
{ or }	Braces	`{" "}`	x=[(n{n+1})/2]	`x=[(n{n+1})/2]`
(: or :)	Angle brackets	`(:" ":)`	x=(:a,b:)	`x=(:a,b:)`
\|__ or __\|	Floor brackets	`\|__" "__\|`	x=\|__a-b__\|	`x=\|__a-b__\|`
floor(x)	Floor brackets alternative	`floor(x)`	x=floor(a-b)	`x=floor(a-b)`
\|~ or ~\|	Ceiling brackets	`\|~" "~\|`	x=\|~a-b~\|	`x=\|~a-b~\|`
ceil(x)	Ceiling brackets alternative	`ceil(x)`	x=ceil(a-b)	`x=ceil(a-b)`
abs(x)	Absolute	`abs(x)`	x=abs(a/b)	`x=abs(a/b)`
norm(x)	Normal	`norm(x)`	x=norm(a)	`x=norm(a)`

22.3.4 AsciiMath mathematical symbols

			example
AsciiMath	Description	Apperance	AsciiMath	Result
+-	Plus or minus	`+-`	x=+-2b	`x=+-2b`
/	Fraction	`" "/" "`	x=a/b	`x=a/b`
^	To the power	`x^n`	x=a^b	`x=a^b`
sqrt	Square root	`sqrt`	x=sqrta	`x=sqrta`
root(n)x	n^th root	`root(n)x`	x=root(3)a	`x=root(3)a`
int	Integral	`int`	x=a int b	`x=a int b`
oint	Circular integral	`oint`	x=a oint b	`x=a oint b`
del	Partial differential	`del`		`x=del a`
oo	Infinity	`oo`	x=oo	`x=oo`
grad	Nabla	`grad`	(grad*v)=f(v)	`(grad*v)=f(v)`
/_	Angle	`/_`	a/_b	`a/_b`
:.	Therefore	`:.`	:.a=b	`:.a=b`
:'	Because	`:'`	:'a=b	`:'a=b`

22.3.5 AsciiMath double struck letters

			example
AsciiMath	Description	Apperance	AsciiMath	Result
CC	Complex numbers	`CC`	CC(1,2,3)	`CC(1,2,3)`
NN	Natural numbers	`NN`	NN(1,2,3)	`NN(1,2,3)`
QQ	Rational numbers	`QQ`	QQ(1,2,3)	`QQ(1,2,3)`
RR	Real numbers	`RR`	RR(1.1,2.1,3.1)	`RR(1.1,2.1,3.1)`
ZZ	Integers numbers	`ZZ`	ZZ(1,2,3)	`ZZ(1,2,3)`

22.3.6 AsciiMath accents and colours

			example
AsciiMath	Description	Apperance	AsciiMath	Result
hat	Caret	`hat " "`	hatx	`hatx`
bar	Over bar	`bar" "`	barx	`barx`
ul	Under bar	`ul" "`	ulx	`ulx`
vec	Vector line	`vec" "`	vecx	`vecx`
dot	Dot	`dot" "`	dotx	`dotx`
ddot	Double dot	`ddot" "`	ddotx	`ddotx`
overbrace	Over brace	`overbrace" "`	overbrace(1+2)	`overbrace(1+2)`
underbrace	Under brace	`underbrace" "`	underbrace(1+2)	`underbrace(1+2)`
color(col)()	Apply colour	`color(red)(x)`	color(red)(x)	`color(red)(x)`

The colours available (col) are the same as the keyword colours available to HTML, there is a full list here.

22.3.7 AsciiMath arrows

			example
AsciiMath	Description	Apperance	AsciiMath	Result
uarr darr larr rrarr	Up, down, left, right arrow	`uarr darr larr rarr`	uarrx darrx larrx rarrx	`uarrx darrx larrx rarrx`
harr	Horizontal arrow	`harr`	aharrb	`aharrb`
to	To	`to`	atob	`atob`
>->	Right arrow with tail	`>->`	a>->b	`a>->b`
->>	Two headed right arrow	`->>`	a->>b	`a->>b`
\|->	Maps to	`\|->`	a\|->b	`a\|->b`
lArr rArr	left, right double arrow	`lArr rArr`	lArrx rArrx	`lArrx rArrx`
hArr	Horizontal double arrow	`hArr`	ahArrb	`ahArrb`

22.3.8 AsciiMath Greek lowercase letters

			example
AsciiMath	Description	Apperance	AsciiMath	Result
alpha	Lowercase alpha	`alpha`	f(alpha)	`f(alpha)`
beta	Lowercase beta	`beta`	f(beta)	`f(beta)`
gamma	Lowercase gamma	`gamma`	f(gamma)	`f(gamma)`
delta	Lowercase delta	`delta`	f(delta)	`f(delta)`
epsilon	Lowercase epsilon	`epsilon`	f(epsilon)	`f(epsilon)`
zeta	Lowercase zeta	`zeta`	f(zeta)	`f(zeta)`
eta	Lowercase eta	`eta`	f(eta)	`f(eta)`
theta	Lowercase theta	`theta`	f(theta)	`f(theta)`
iota	Lowercase iota	`iota`	f(iota)	`f(iota)`
kappa	Lowercase kappa	`kappa`	f(kappa)	`f(kappa)`
lambda	Lowercase lambda	`lambda`	f(lambda)	`f(lambda)`
mu	Lowercase mu	`mu`	f(mu)	`f(mu)`
nu	Lowercase nu	`nu`	f(nu)	`f(nu)`
xi	Lowercase xi	`xi`	f(xi)	`f(xi)`
pi	Lowercase pi	`pi`	f(pi)	`f(pi)`
rho	Lowercase rho	`rho`	f(rho)	`f(rho)`
sigma	Lowercase sigma	`sigma`	f(sigma)	`f(sigma)`
alpha	Lowercase alpha	`alpha`	f(alpha)	`f(alpha)`
tau	Lowercase tau	`tau`	f(tau)	`f(tau)`
upsilon	Lowercase upsilon	`upsilon`	f(upsilon)	`f(upsilon)`
phi	Lowercase phi	`phi`	f(phi)	`f(phi)`
chi	Lowercase chi	`chi`	f(chi)	`f(chi)`
psi	Lowercase psi	`psi`	f(psi)	`f(psi)`
omega	Lowercase omega	`omega`	f(omega)	`f(omega)`

22.3.9 AsciiMath Greek uppercase letters

			example
AsciiMath	Description	Apperance	AsciiMath	Result
Gamma	Uppercase gamma	`Gamma`	f(Gamma)	`f(Gamma)`
Delta	Uppercase delta	`Delta`	f(Delta)	`f(Delta)`
Theta	Uppercase theta	`Theta`	f(Theta)	`f(Theta)`
Lambda	Uppercase lambda	`Lambda`	f(Lambda)	`f(Lambda)`
Xi	Uppercase xi	`Xi`	f(Xi)	`f(Xi)`
Pi	Uppercase pi	`Pi`	f(Pi)	`f(Pi)`
Sigma	Uppercase sigma	`Sigma`	f(Sigma)	`f(Sigma)`
Phi	Uppercase phi	`Phi`	f(Phi)	`f(Phi)`
Psi	Uppercase psi	`Psi`	f(Psi)	`f(Psi)`
Omega	Uppercase omega	`Omega`	f(Omega)	`f(Omega)`

22.3.10 AsciiMath logical operators

			example
AsciiMath	Description	Apperance	AsciiMath	Result
\|><	Semi-direct product	`\|><`	N \|><_psi	`N \|><_psi `
><\|	Semi-direct product	`><\|`	N ><\|_psi H	`N ><\|_psi H`
\|><\|	Join	`\|><\|`	N \|><\| H	`N \|><\| H`
@	Composite	`@`	N @ H	`N @ H`
o+	Circled plus	`o+`	N o+ H	`N o+ H`
ox	Circled times	`ox`	N ox H	`N ox H`
o.	Circled dot	`o.`	N o. H	`N o. H`

22.3.11 AsciiMath sets and groups

			example
AsciiMath	Description	Apperance	AsciiMath	Result
^^	Wedge	`^^`	N ^^ H	`N ^^ H`
^^^	Large wedge	`^^^`	N ^^^ H	`N ^^^ H`
vv	Vee	`vv`	N vv H	`N vv H`
vvv	Large Vee	`vvv`	N vvv H	`N vvv H`
nn	Cap	`nn`	N nn H	`N nn H`
nnn	Large cap	`nnn`	N nnn H	`N nnn H`
uu	Cup	`uu`	N uu H	`N uu H`
uuu	Large cup	`uuu`	N uuu H	`N uuu H`
\|><\|	Join	`\|><\|`	N \|><\| H	`N \|><\| H`
in	Element of	`in`	N in H	`N in H`
!in	Not an element of	`!in`	N !in H	`N !in H`
sub	Subset of	`sub`	N sub H	`N sub H`
sube	Subset of or equal to	`sube`	N sube H	`N sube H`
supe	Superset of or equal to	`supe`	N supe H	`N supe H`
-<	Precedes	`-<`	N -< H	`N -< H`
-<=	Precedes or equal to	`-<=`	N -<= H	`N -<= H`
>-	Supersedes	`>-`	N >- H	`N >- H`
>-=	Supersedes or equal to	`>-=`	N >-= H	`N >-= H`

22.3.12 AsciiMath subscripts and superscripts

			example
AsciiMath	Description	Apperance	AsciiMath	Result
_	Subscript	`a_i`	x=a_i	`x=a_i`
^	Superscript	`a^i`	x=e^t	`x=e^t`

Subscripts and superscripts also work with large operators:

			example
AsciiMath	Description	Apperance	AsciiMath	Result
int_()	Integral with lower limit	`int_(lim)`	x=aint_(-t)b	`x=aint_(-t)b`
int^()	Integral with upper limit	`int^(lim)`	x=aint^(+t)b	`x=aint^(+t)b`
int_()^()	Integral with upper and lower limits	`int_(lim)^(lim)`	x=aint _(-t)^(+t)b	`x=aint _(-t)^(+t)b`

Where both subscripts and superscripts are applied to an object, the subscript must come first.

22.3.13 AsciiMath text in equation

Text can be added to any equation by surrounding it in quotes ".

			example
AsciiMath	Description	Apperance	AsciiMath	Result
"anytext"	Text string	`"anytext"`	x="something"	`x="something"`

22.3.14 AsciiMath matrices

	example
Description	AsciiMath	Result
Standard matrices (normal)	((a,b),(c,d))	`((a,b),(c,d))`
Standard matrices (square)	[[a,b],[c,d]]	`[[a,b],[c,d]]`
Column vector (normal)	((a),(b))	`((a),(b))`
Column vector (square)	[[a],[b]]	`[[a],[b]]`
Complex	{(2x,+,17y,=,23),(x,-,y,=,5):}}	`{(2x,+,17y,=,23),(x,-,y,=,5):}}`

There are two delimiters for matrices (: and :), these act as invisible brackets to force things to line up.

22.3.15 AsciiMath notes on syntax

AsciiMath (and MathJax) ignore space, add them or remove them as you wish. For example, a prop b and apropb both give `apropb`.