Math equation input 2

${\displaystyle \sum _{i=1}^n{i}^3={\left(\frac{n(n+1)}{2}\right)}^2}$

\begin{gra ph}width=400; height=300; xmin=-6.3; xmax=6.3;
xscl=1; plot(3cos(x^2)) \end{graph}


Displacement: ${\displaystyle s=ut+\frac{1}{2}a{t}^2}$
Trigonometry: ${\displaystyle {tan}^{2}x+1={sec}^{2}x}$
Summation: ${\displaystyle \pi =4\sum _{i=1}^n\frac{{(-1)}^{k+1}}{2k-1}}$



${\displaystyle }$${\displaystyle f\left(x\right)=\sum _{n=0}^{\infty }\frac{f^{\left(n\right)}\left(a\right)}{n!}(x-a{)}^n}$${\displaystyle }$

${\displaystyle f\left(x\right)=\sum _{n=0}^{\infty }\frac{f^n\left(a\right)}{n!}{(x-a)}^n}$

Matrices

AB=(8451)(-851-15)=(8×-8+4×18×5+4×-155×-8+1×15×5+1×-15)

=(-60-20-3910)
Quadratic Equation

If ax2+bx+c=0, then

x=-b±b2-4ac2a
Fractions on Fractions

6x+232x+4=6x+2 ÷ 32x+4=6x+2×2(x+2)3=4
Roots

x3≠3x
Another matrix example

This next example was one I tried to create using WPMathPub but had trouble because it wasn’t very intuitive (see WPMathPub article).

[53cos26701-2sin5]

Now, that was much easier compared to WPMathPub! This is the code I used for the above ASCIIMathML:

[(5, 3, cos 2), (6, 7, 0), (1,-2, sin 5)]

In ASCIIMathML, it can be rendered easily like this:

3∫x2 dx+5∫x dx+9∫ dx


This is some example code:

\begin{gra ph}width=400; height=300; xmin=-6.3; xmax=6.3;
xscl=1; plot(3cos(x^2)) \end{graph}

Here is the resulting graph. Move your mouse cursor over the graph – it tells you the x- and y-coordinates of the cursor position.

1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 1 2 3 4 -1 -2 -3 -4
Update
width=400; height=300; xmin=-6.3; xmax=6.3;xscl=1; axes(); plot(3cos(x^2))

I’ll do a separate article soon about the graphing capabilities of ASCIIMathML.

axes(); plot(sin(x))

setBorder(0)
initPicture(-5,5)
axes(2, 1, "labels", 1)

stroke = "blue"
plot("sin(x)")

stroke = "red"
plot(["5*t*cos(pi*t)", "5*t*sin(pi*t)"],0,1)

stroke = "green"
strokewidth = "2"
marker = "arrowdot"
line([0,1], [pi/2,1])
dot([pi,0], "open", cpi)

text([-2.5,-2.5], "ASCIIsvg Example")

Type this	See that	Comment
${\displaystyle x^2+y_1+z_{12}^{34}}$	x2+y1+z1234	subscripts as in TeX, but numbers are treated as a unit
${\displaystyle {sin}^{-1}\left(x\right)}$	sin-1(x)	function names are treated as constants
${\displaystyle \frac{d}{dx}f\left(x\right)=\underset{h\to 0}{lim}\frac{f(x+h)-f\left(x\right)}{h}}$	ddxf(x)=limh→0f(x+h)-f(x)h	complex subscripts are bracketed, displayed under lim
${\displaystyle \frac{d}{dx}f\left(x\right)=\underset{h\to 0}{lim}\frac{f(x+h)-f\left(x\right)}{h}}$	ddxf(x)=limh→0f(x+h)-f(x)h	standard LaTeX notation is an alternative
${\displaystyle f\left(x\right)=\sum _{n=0}^{\infty }\frac{f^{\left(n\right)}\left(a\right)}{n!}{(x-a)}^n}$	f(x)=∑n=0∞f(n)(a)n!(x-a)n	f^((n))(a) must be bracketed, else the numerator is only a
${\displaystyle f\left(x\right)=\sum _{n=0}^{\infty }\frac{f^{\left(n\right)}\left(a\right)}{n!}(x-a{)}^n}$	f(x)=∑n=0∞f(n)(a)n!(x-a)n	standard LaTeX produces the same result
${\displaystyle {\int }_0^{1}f\left(x\right)dx}$	∫01f(x)dx	subscripts must come before superscripts
${\displaystyle \left[\begin{array}{cc}a& b\\ c& d\end{array}\right]\left(\begin{array}{c}n\\ k\end{array}\right)}$	[abcd](nk)	matrices and column vectors are simple to type
${\displaystyle \frac{x}{x}=\{\begin{array}{ll}1& ifx\ne 0\\ \text{undefined}& ifx=0\end{array}}$	xx={1ifx≠0undefinedifx=0	piecewise defined function are based on matrix notation
${\displaystyle a/b}$	a/b	use // for inline fractions
${\displaystyle \frac{\frac{a}{b}}{\frac{c}{d}}}$	abcd	with brackets, multiple fraction work as expected
${\displaystyle \frac{a}{b}/\frac{c}{d}}$	ab/cd	without brackets the parser chooses this particular expression
${\displaystyle \frac{(a\cdot b)}{c}}$	(a⋅b)c	only one level of brackets is removed; * gives standard product
${\displaystyle \sqrt{\sqrt{\sqrt[3]{x}}}}$	x3	spaces are optional, only serve to split strings that should not match
	〈a,b〉andxyuv	angle brackets and invisible brackets
	(a,b]={x∈ℝ|a	grouping brackets don't have to match
${\displaystyle abc-{123.45}^{-1.1}}$	abc-123.45-1.1	non-tokens are split into single characters, but decimal numbers are parsed with possible sign
${\displaystyle \widehat{ab}\overline{xy}\underline{A}\overrightarrow{v}\stackrel{.}{x}\stackrel{..}{y}}$	ab^xy¯A̲v→x.y..	accents can be used on any expression (work well in IE)
${\displaystyle AB3..ℬ..AB.AB}$	AB3..ℬ..AB.AB	font commands; can use any brackets around argument
	=defor=Δ(or:=)	symbols can be stacked
${\displaystyle {}_{ 92}^{238}U}$	92238U	prescripts simulated by subsuperscripts