`sum_(i=1)^n i^3=((n(n+1))/2)^2`
\begin{gra ph}width=400; height=300; xmin=-6.3; xmax=6.3;
xscl=1; plot(3cos(x^2)) \end{graph}
amath
Displacement: s = u t + 1/2 a t^2
Trigonometry: tan^2x+1=sec^2x
Summation: pi = 4 sum_(i=1)^(n) ((-1)^(k+1))/(2k-1)
endamath
`$f(x)=\sum_{n=0}^\infty\frac{f^{(n)}(a)}{n!}(x-a)^n$`
`f(x)=sum_{n=0}^oo (f^n (a))/(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.
agraph plot(sin(x)) endagraph
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 |
|---|
| `x^2+y_1+z_12^34` | x2+y1+z1234 | subscripts as in TeX, but numbers are treated as a unit |
| `sin^-1(x)` | sin-1(x) | function names are treated as constants |
| `d/dxf(x)=lim_(h->0)(f(x+h)-f(x))/h` | ddxf(x)=limh→0f(x+h)-f(x)h | complex subscripts are bracketed, displayed under lim |
| $\frac{d}{dx}f(x)=\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}$ | ddxf(x)=limh→0f(x+h)-f(x)h | standard LaTeX notation is an alternative |
| `f(x)=sum_(n=0)^oo(f^((n))(a))/(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 |
| $f(x)=\sum_{n=0}^\infty\frac{f^{(n)}(a)}{n!}(x-a)^n$ | f(x)=∑n=0∞f(n)(a)n!(x-a)n | standard LaTeX produces the same result |
| `int_0^1f(x)dx` | ∫01f(x)dx | subscripts must come before superscripts |
| `[[a,b],[c,d]]((n),(k))` | [abcd](nk) | matrices and column vectors are simple to type |
| `x/x={(1,if x!=0),(text{undefined},if x=0):}` | xx={1ifx≠0undefinedifx=0 | piecewise defined function are based on matrix notation |
| `a//b` | a/b | use // for inline fractions |
| `(a/b)/(c/d)` | abcd | with brackets, multiple fraction work as expected |
| `a/b/c/d` | ab/cd | without brackets the parser chooses this particular expression |
| `((a*b))/c` | (a⋅b)c | only one level of brackets is removed; * gives standard product |
| `sqrt sqrt root3x` | x3 | spaces are optional, only serve to split strings that should not match |
| `<< a,b >> and {:(x,y),(u,v):}` | 〈a,b〉andxyuv | angle brackets and invisible brackets |
| `(a,b]={x in RR | a < x <= b}` | (a,b]={x∈ℝ|a | grouping brackets don't have to match |
| `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 |
| `hat(ab) bar(xy) ulA vec v dotx ddot y` | ab^xy¯A̲v→x.y.. | accents can be used on any expression (work well in IE) |
| `bb{AB3}.bbb(AB].cc(AB).fr{AB}.tt[AB].sf(AB)` | AB3..ℬ..AB.AB | font commands; can use any brackets around argument |
| `stackrel"def"= or \stackrel{\Delta}{=}" "("or ":=)` | =defor=Δ(or:=) | symbols can be stacked |
| `{::}_(\ 92)^238U` | 92238U | prescripts simulated by subsuperscripts |
