#### Here are a few more examples:

Type this See that Comment
\x^2+y_1+z_12^34\ x^2+y_1+z_12^34 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\ d/dxf(x)=lim_(h->0)(f(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}\$ $\frac{d}{dx}f(x)=\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}$ standard LaTeX notation is an alternative
\f(x)=sum_(n=0)^oo(f^((n))(a))/(n!)(x-a)^n\ f(x)=sum_(n=0)^oo(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\$ $f(x)=\sum_{n=0}^\infty\frac{f^{(n)}(a)}{n!}(x-a)^n$ standard LaTeX produces the same result
\int_0^1f(x)dx\ int_0^1f(x)dx subscripts must come before superscripts
\[[a,b],[c,d]]((n),(k))\ [[a,b],[c,d]]((n),(k)) matrices and column vectors are simple to type
\x/x={(1,if x!=0),(text{undefined},if x=0):}\ x/x={(1,if x!=0),(text{undefined},if x=0):} piecewise defined function are based on matrix notation
\a//b\ a//b use // for inline fractions
\(a/b)/(c/d)\ (a/b)/(c/d) with brackets, multiple fraction work as expected
\a/b/c/d\ a/b/c/d 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\ sqrt sqrt root3x spaces are optional, only serve to split strings that should not match
\<< a,b >> and {:(x,y),(u,v):}\ << a,b >> and {:(x,y),(u,v):} angle brackets and invisible brackets
\(a,b]={x in RR | a < x <= b}\ (a,b]={x in RR | a < x <= b} 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\ hat(ab) bar(xy) ulA vec v dotx ddot y accents can be used on any expression (work well in IE)
\bb{AB3}.bbb(AB].cc(AB).fr{AB}.tt[AB].sf(AB)\ bb{AB3}.bbb(AB].cc(AB).fr{AB}.tt[AB].sf(AB) font commands; can use any brackets around argument
\stackrel"def"= or \stackrel{\Delta}{=}" "("or ":=)\ stackrel"def"= or \stackrel{\Delta}{=}" "("or ":=) symbols can be stacked
\{::}_(\ 92)^238U\ {::}_(\ 92)^238U prescripts simulated by subsuperscripts