The encoding is quite simple and flexible. All valid formulas have the form {-} , \$OP(...) or a sequence of several such expressions seperated by operators. Here are some examples.

Ordinary InFix Expressions:

``` {a}, -{a}, {a}+{b}, {{a}+{b}-{d}}/{c}, {a}^{x}
{a} = {b}/{c}, {f({x}+{h})} apprx {2x}+{h}^{2}/{2}```

Prefix Operators:

` \$I(a,b,f(x),dx),  \$S(This is text converted to a math object),  \$M([]C;1,2,3; 4,5,6; 7,8,9) `

Combinations or Infix and Prefix:

` \$I(a,b, {sin(x)}/{x} , dx),  \$M([]C;1,-{2},3; {a}+{5},5,6; 7,8,9) `

Embedded text; Primitive Mathematical Expressions:

You can convert any text to a valid formula by enclosing it inside either \$S(-) or {-}, as in

`\$S(The fat cat sat on the mat.), or \$(This is text).`
The "\$S(-)" option treats spacing in the same way as HTML, the {-} option ignores spacing. If you wish to include single mathematical operators within text, you should precede them by dollar signs and follow them by a space, as in \$S(if x \$> 5). You can also force spaces by inserting "\$ " (dollar + space).

Notes

• You can actually encode all valid formulas using only prefix notation. (The utility actually converst all infix expressions to prefix before processing.) The format for prefiix operators is
`    \$operator(a,b), `
where "operator" is an operation (such as +, -, F, ^,...see the table below) and a and b are recursively defined valid formulas or just text. For example, \$+(a,b) will return "a+b," and \$F(a,b) will return "a/b" in fraction form. These are equivalent to the infiix {a}+{b} and {a}/{b} respectively.
• You can use any text as an argument within braces {-}, but spaces will be ignored, For instance, {a}-{b   c} will return "a - bc." To force a space anywhere in an expression, either use \$S(-) instead of {-}, or insert "\$ " (dollar + space), as in {a}-{b \$ c}, which will return "a-b c."
• Never use infix operators within text, as in {a+b}, or strange things may happen, including Netscape crashes! Instead, you should use {a}+{b}, or {a \$+ b} , which will treat the "+" as text. (see the paragraph following).
• The usual order of operations is followed with infix. If you wish to use parentheses to change the order, as in a/(b+c), us {-} to parenthesize, as in {a} / { {b}+{c} }.

The following table describes all the operations presently installed. Lowercase letters a,b,... stand for any recursively constructed formula (or just text when used as primitiv arguments in a prefix expression or within {-}).

 Format Example Bracket \$B(a) \$B( {sin(x)}/{x} ) Fractions \$F(a,b) {a}/{b} \$F(1, {2x}+{5}), {1}/{ {2x}+{5} }\$F (\$B (\$F(x,y)),cx){a}/\$B({b}/{d}) ExponentsSubscripts {a}^{b} or \$^(a,b){a}^{{b};#} or \$^(a,b;#){a}_{b} or or \$_(a,b){a}_{ {b};#} or \$_(a,b;#) # = 0,1,2.. for additional offset(double-negative values (--#; do not use single negative) decrease offset) {e}^{3x}{e}^{{x}_{2};1}\$^( e,\$^(x,2 ) ;1 ){e}^{-\$I(p(x),dx) } SumDifferenceProductEqualsNotequalApproximatelyLess than, Greater ThanLess or Equal,Greater or Equal {a}+{b} or \$+(a,b) {a}-{b} or \$-(a,b){a}{b} or \$.(a,b){a} = {b} or \$=(a,b){a} notequal {b} or \$notequal(a,b) or \$Z(a,b) {a} apprx {b} or \$apprx(a,b){a} < {b} or \$<(a,b){a} <= {b} or \$<=(a,b) {1} = {2}-{1}{a}/{b} + {c}\$F(a,b) + {c}\$=(1,2x+5)\$F (\$- (\$F(x,y),z),w) \$F(a,b) = \$F(c,d) +{a}{a}/{b} <= {e}^{x}-{a} Negative of expression a -{a} or \$-(,a) -{4}{e}^\$-(,\$I(p(x),dx)) Radical \$R(a)\$R(a;#) for #-th root \$R({a}/{b} )\$R( \$F(a,b) ; 4 ) Indefinite IntegralDefinite Integral \$I(f,dx) \$I(a,b,f,dx) \$I(\$B(\$F(sin(x),x)),dx)\$I(0,1,x2,dx) Summation \$G(variabile, inf, sup, funzione, escludi) \$=( \$=( \$S(Fibonacci(n)), \$G(i,1,n,i)), \$F({n}{(n+1)},2))\$G(n,-\$infinity,\$infinity,\$F({n},\$^(n,2,1)),\$Z(n,\$plusminus 1) Matrix/Array of formulas \$M(LRA; a,b,c; d,e,f; g,h,i) L = [, {, |, or N (none) left border R = ], }, |, or N right border A = L (left), R (right) or C (center) alignment of entries rows seperated by semicolons entries in each row seperated by commas \$M([]R; 1,2,\$-(,3); 4,5,6) Commas, Spaces, Dollar Signs, Slashes Since commas and dollar signs part of the syntax, and spaces are ignored, you must precede these by \$ signs if you want them to work.For string expressions such as \$S(the fat cat sat), the browser will handle the argument as it normally handles spaces. For extra space, include forced spaces.Do not use "\$op" adjacent to infix operators, as this will conduse the interpreter. For example, use "{a\$ }+{b}" for extra space after the "a", and not "{a} \$ + {b}." \$F(1\$,000\$,000,a) {a\$ } + {\$ b} for extra space in the expression "a+b" {Cost} = {\$\$46.43} \$S(very \$ \$ \$ widely \$ \$ \$ spaced \$ \$ \$ text) \$S(the fraction a \$/ b is represented as ) \$F(a,b) Arrows {a} -> {b} or \$->(a,b) {a}<-{b} or \$<-(a,b){a}<->{b} or \$<->(a,b) {F: \$ } {R}^{n}->{R} {F(x)} = {x}^{2} Limits \$L(lim,{x} -> {a}), \$L(lim,\$->(x,a)) \$L(lim,\$->(x,a)){f(x)} = {L} Symbols, Greek: ± \$infinity \$pi \$plusminus {x} -> {\$infinity} \$I(-{\$pi},{\$pi},sin x,dx) = {0} \$F(b \$plusminus \$R(\$-({b}^{2},{4ac}))