VISUAL PHYSICS
Unconventional Explorations into Uninhabited Areas of Physics
Through Thought Experiments in the Form of Simulations...


This is NOT an educational site. The views expressed here are not those of mainstream physics.
If you want to contribute to the wiki, email me at the address given in the Contact page.
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<table width="230px" align="right" style="background-color:rgb(249,249,249); border: 1px solid rgb(153, 153, 153); padding: 1em; font-size:9pt">
/* CSS placed here will be applied to all skins */
<tr>
<td>
*[http://www1.chapman.edu/%7Ejipsen/mathml/asciimath.html ASCIIMathML HomePage]
*[http://www.mozilla.org/projects/mathml/fonts/ Download Firefox fonts for MathML]
*[http://www.dessci.com/en/products/mathplayer/download.htm Download IE plugin for MathML]
</td>
</tr>
</table>


==ASCIIMathML.js (ver 2.0.9): Syntax and List of Constants==
/* wikitable class for skinning normal tables | Added by GB -- Copied from main.css of Monobook skin of previous Wiki */


You can use your favorite editor to write HTML pages that use this JavaScript program. If the page is viewed by a browser that does not support MathML or JavaScript, the ASCII formulas are still quite readable. Most users will not have to read the technicalities on
font-family { Georgia, Times New Roman; }
this page. If you type


<pre>\`x^2\` or \`a_(mn)\` or \`a_{mn}\` or \`(x+1)/y\` or \`sqrtx\`</pre>
table.wikitable {
  width: 150px;
  font-family: Georgia, Times New Roman;
  margin: 1em 1em 1em 0;
  background: #f9f9f9;
  border: 2px #aaaaaa solid;
  border-collapse: collapse;
}


you pretty much get what you expect: `x^2` or `a_(mn)` or `a_{mn}` or `(x+1)/y` or `sqrtx`. The choice of grouping parenthesis is up to you (they don't have to match either). If the displayed expression can be parsed uniquely without them, they are omitted. Printing the table of constant symbols (below) may be helpful (but is not necessary if you
table.wikitable th, table.wikitable td {
know the LaTeX equivalents).
  border: 1px #aaaaaa solid;
  padding-left: 0.7em;
  padding-right: 0.7em;
  padding-top: 0.2em;
  padding-bottom: 0.3em;
}


It is hoped that this simple input format for MathML will further encourage its use on the web. The remainder of this page gives a fairly detailed specification of the ASCII syntax. <b>The expressions described here correspond to a wellspecified subset of Presentation MathML and behave in a predictable way.</b>
table.wikitable th {
  background: #f2f2f2;
  text-align: center;
}


The syntax is very permissive and does not generate syntax errors. This allows mathematically incorrect expressions to be displayed, which is important for teaching purposes. It also causes less frustration when previewing formulas.
table.wikitable caption {
  margin-left: inherit;
  margin-right: inherit;
  font-weight: bold;
}


The parser uses no operator precedence and only respects the grouping brackets, subscripts, superscript, fractions and (square) roots. This is done for reasons of efficiency and generality. The resulting MathML code can quite easily be processed further to ensure additional syntactic requirements of any particular application.
/* navtable class for skinning template navigation tables | Added by GB -- Copied from previous Wiki */
<br>
<br>


==The grammar==
table.navtable {
Here is a definition of the grammar used to parse ASCIIMathML expressions. In the Backus-Naur form given below, the letter on the left of the ::= represents a category of symbols that could be one of the possible sequences of symbols listed on the right. The vertical bar | separates the alternatives.
  float: right;
  margin: 0 0 1em 1em;
  font-size: 85%;
  border: 1px solid #aaa;
  /*border: 1px solid #e0e0c0;*/
  width: 200px;
  clear: both;
}


<pre>c ::= [A-z] | numbers | greek letters | other constant symbols (see below)
table.navtable tr {
u ::= 'sqrt' | 'text' | 'bb' |    other unary symbols for font commands
  /*background: #f2f2f2;*/
b ::= 'frac' | 'root' | 'stackrel' binary symbols
  background-color: #ffffe0;
l ::= ( | [ | { | (: | {:         left brackets
  text-align: left;
r ::= ) | ] | } | :) | :}         right brackets
}
S ::= c | lEr | uS | bSS | "any"  simple expression
E ::= SE | S/S |S_S | S^S | S_S^S  expression (fraction, sub-, super-, subsuperscript)
</pre>
<br>
<br>
==The translation rules==
Each terminal symbol is translated into a corresponding MathML node. The constants are mostly converted to their respective Unicode symbols. The other expressions are converted
as follows:
<br/>


<table>
table.navtable th {
<tr><td>l`S`r</td><td>`to`</td><td><mrow>l`S`r</mrow>(note that any pair of brackets can be used to delimit subexpressions, they don't have to match)</td></tr>
  text-align: center;
<tr><td>sqrt `S`</td><td>`to`</td><td>&lt;msqrt>`S'`</msqrt></td></tr>
  /*border-bottom: 2px solid #ccf;
<tr><td>text `S`</td><td>`to`</td><td>&lt;mtext>`S'`</mtext></td></tr>
  border: 1px solid #aaa;*/
<tr><td>"any"</td><td>`to`</td><td>&lt;mtext>any&lt;/mtext></td></tr>
  border: 1px solid #c0c0c0;
<tr><td>frac `S_1` `S_2`</td><td>`to`</td><td><mfrac>`S_1'` `S_2'`</mfrac></td></tr>
  font-weight: bold;
<tr><td>root `S_1` `S_2`</td><td>`to`</td><td><mroot>`S_2'` `S_1'`</mroot></td></tr>
}
<tr><td>stackrel `S_1` `S_2`</td><td>`to`</td><td><mover>`S_2'` `S_1'`</mover></td></tr>
<tr><td>`S_1`/`S_2`</td><td>`to`</td><td><mfrac>`S_1'` `S_2'`</mfrac></td></tr>
<tr><td>`S_1`_`S_2`</td><td>`to`</td><td><msub>`S_1` `S_2'`</msub></td></tr>
<tr><td>`S_1`^`S_2`</td><td>`to`</td><td><msup>`S_1` `S_2'`</msup></td></tr>
<tr><td>`S_1`_`S_2`^`S_3`</td><td>`to`</td><td><msubsup>`S_1` `S_2'` `S_3'`</msubsup> or <munderover>`S_1` `S_2'` `S_3'`</munderover> (in some cases)</td></tr>
</table>
In the rules above, the expression `S'` is the same as `S`, except that if
`S` has an outer level of brackets, then `S'` is the expression inside
these brackets.
<br>
<br>


==Matrices:==
table.navtable td {
A simple syntax for matrices is also recognized:
  /*border-bottom: 2px solid #ccf;
<br/>
  border: 1px solid #aaa;
<tt>l(`S_(11)`,...,`S_(1n)`),(...),(`S_(m1)`,...,`S_(mn)`)r</tt>
  border: 1px solid #e0e0c0;*/
&#x00A0; &#x00A0; or &#x00A0; &#x00A0;
  border: 1px solid #c0c0c0;
<tt>l[`S_(11)`,...,`S_(1n)`],[...],[`S_(m1)`,...,`S_(mn)`]r</tt>.
}
<br/>


Here <tt>l</tt> and <tt>r</tt> stand for any of the left and right
h3, h4, h5, h6 {
brackets (just like in the grammar they do not have to match). Both of
border-bottom: 1px solid #aaa;;
these expressions are translated to
}
<br/>


<mrow>l<mtable><mtr><mtd>`S_(11)`</mtd>...
blockquote, code {
<mtd>`S_(1n)`<mtd></mtr>...
  display: block;
<mtr><mtd>`S_(m1)`</mtd>...
  padding: 6px 10px;
<mtd>`S_(mn)`</mtd></mtr></mtable></mrow>.
  border: 1px solid #ccc;
<br/>
  background-color: #eee;
 
  margin-bottom: 10px;
For example
  margin-left: 30px;
<tt>{(S_(11),...,S_(1n)),(vdots,ddots,vdots),(S_(m1),...,S_(mn))]</tt>displays as `{(S_(11),...,S_(1n)),(vdots,ddots,vdots),(S_(m1),...,S_(mn))]`.
  width: 85%;  
<br/>
}
 
Note that each row must have the same number of expressions, and there should be at least two rows.
<br>
<br>
 
==Tokenization:==
The input formula is broken into tokens using a "longest matching initial substring search". Suppose the input formula has been processed from left to right up to a fixed position. The longest string from the list of constants (given below) that matches the initial part of the remainder of the formula is the next token. If there is no matching string, then the first character of the remainder is the next token. The symbol table at the top of the ASCIIMathML.js script specifies whether a symbol is a math operator (surrounded by a &lt;mo> tag) or a math identifier (surrounded by a &lt;mi> tag). For
single character tokens, letters are treated as math identifiers, and non-alphanumeric characters are treated as math operators. For digits, see "Numbers" below.
 
Spaces are significant when they separate characters and thus prevent a certain string of characters from matching one of the constants. Multiple spaces and end-of-line characters are equivalent to a single space.
<br>
<br>
 
==Complete list of constants==
([http://math.chapman.edu/cgi-bin/mathxml.pl?Complete_list_of_LaTeX_constants Standard LaTeX names] also work.)
 
Numbers: A string of digits, optionally preceded by a minus sign, and optionally followed by a decimal point (a period) and another string of digits, is parsed as a single token and converted to a MathML number, i.e., enclosed with the &lt;mn> tag. If it is not desirable to  have a preceding minus sign be part of the number, a space should be inserted. Thus tt>x-1</tt> is converted to &lt;mi>x&lt;/mi>&lt;mn>-1&lt;/mn>, whereas <tt>x - 1</tt> is converted to &lt;mi>x&lt;/mi>&lt;mo>-&lt;/mo>&lt;mn>1&lt;/mn>.
<br><br>
==Greek letters==
<table border="1" cellpadding="2" style="border: 1px solid #aaa; ">
<tr>
<td style="valign:top">
<table border="1" style="background-color:rgb(249,249,249); border-collapse: collapse; border: 1px solid rgb(153, 153, 153); padding: 1em;">
<tr><td border="1">alpha</td><td  border="1" align="center">`alpha`</td></tr>
<tr><td>beta</td><td align="center">`beta`</td></tr>
<tr><td>chi</td><td align="center">`chi`</td></tr>
<tr><td>delta</td><td align="center">`delta`</td></tr>
<tr><td>Delta</td><td align="center">`Delta`</td></tr>
<tr><td>epsilon</td><td align="center">`epsilon`</td></tr>
<tr><td>varepsilon</td><td align="center">`varepsilon`</td></tr>
<tr><td>eta</td><td align="center">`eta`</td></tr>
<tr><td>gamma</td><td align="center">`gamma`</td></tr>
</table>
</td>
<td style="valign:top">
<table border="1" style="background-color:rgb(249,249,249); border-collapse: collapse; border: 1px solid rgb(153, 153, 153); padding: 1em;">
<tr><td>Gamma</td><td align="center">`Gamma`</td></tr>
<tr><td>iota</td><td align="center">`iota`</td></tr>
<tr><td>kappa</td><td align="center">`kappa`</td></tr>
<tr><td>lambda</td><td align="center">`lambda`</td></tr>
<tr><td>Lambda</td><td align="center">`Lambda`</td></tr>
<tr><td>mu</td><td align="center">`mu`</td></tr>
<tr><td>nu</td><td align="center">`nu`</td></tr>
<tr><td>omega</td><td align="center">`omega`</td></tr>
<tr><td>Omega</td><td align="center">`Omega`</td></tr>
</table>
</td>
<td style="valign:top">
<table border="1" style="background-color:rgb(249,249,249); border-collapse: collapse; border: 1px solid rgb(153, 153, 153); padding: 1em;">
<tr><td>phi</td><td align="center">`phi`</td></tr>
<tr><td>varphi</td><td align="center">`varphi`</td></tr>
<tr><td>Phi</td><td align="center">`Phi`</td></tr>
<tr><td>pi</td><td align="center">`pi`</td></tr>
<tr><td>Pi</td><td align="center">`Pi`</td></tr>
<tr><td>psi</td><td align="center">`psi`</td></tr>
<tr><td>Psi</td><td align="center">`Psi`</td></tr>
<tr><td>rho</td><td align="center">`rho`</td></tr>
<tr><td>sigma</td><td align="center">`sigma`</td></tr>
</table>
</td>
<td style="valign:top">
<table border="1" style="background-color:rgb(249,249,249); border-collapse: collapse; border: 1px solid rgb(153, 153, 153); padding: 1em;">
<tr><td>Sigma</td><td align="center">`Sigma`</td></tr>
<tr><td>tau</td><td align="center">`tau`</td></tr>
<tr><td>theta</td><td align="center">`theta`</td></tr>
<tr><td>vartheta</td><td align="center">`vartheta`</td></tr>
<tr><td>Theta</td><td align="center">`Theta`</td></tr>
<tr><td>upsilon</td><td align="center">`upsilon`</td></tr>
<tr><td>xi</td><td align="center">`xi`</td></tr>
<tr><td>Xi</td><td align="center">`Xi`</td></tr>
<tr><td>zeta</td><td align="center">`zeta`</td></tr></table>
 
</td>
</tr>
</table>
 
 
<br><br>
 
==Symbols==
 
<table border="2" style="background-color:rgb(249,249,249); border-collapse: collapse; border: 1px solid rgb(153, 153, 153); padding: 1em;">
<tr valign="top"><td style="border: 1px solid #aaa;" align="center">
'''Operation symbols'''</td><td style="border: 1px solid #aaa;" align="center">'''Relation symbols'''</td>
<td style="border: 1px solid #aaa;" align="center">
'''Logical symbols'''</td><td style="border: 1px solid #aaa;" align="center">'''Miscellaneous symbols'''</td>
<td style="border: 1px solid #aaa;" align="center">
'''Standard functions'''</td><td style="border: 1px solid #aaa;" align="center">'''Grouping brackets'''</td>
<td style="border: 1px solid #aaa;" align="center">
'''Accents'''</td><td style="border: 1px solid #aaa;" align="center">'''Font commands'''</td>
<td style="border: 1px solid #aaa;" align="center">
'''Arrows'''</td></tr>
<tr valign="top"><td style="border: 1px solid #aaa;" align="center">
<table border="2" cellpadding="2" style="background-color:rgb(249,249,249); border-collapse: collapse; border: 1px solid rgb(153, 153, 153); padding: 1em;">
<tr><th style="border: 1px solid #aaa;" >Type</th><th style="border: 1px solid #aaa;">See</th></tr>
<tr><td style="border: 1px solid #aaa;">+</td><td style="border: 1px solid #aaa;" align="center">`+`</td></tr>
<tr><td style="border: 1px solid #aaa">-</td><td style="border: 1px solid #aaa;" align="center">`-`</td></tr>
<tr><td style="border: 1px solid #aaa;" ><nowiki>*</nowiki></td><td style="border: 1px solid #aaa;" align="center">`*`</td></tr>
<tr><td style="border: 1px solid #aaa;" >**</td><td  style="border: 1px solid #aaa;" align="center">`**`</td></tr>
<tr><td style="border: 1px solid #aaa;" >//</td><td  style="border: 1px solid #aaa;" align="center">`//`</td></tr>
<tr><td style="border: 1px solid #aaa;" >\\</td><td  style="border: 1px solid #aaa;" align="center">`\\ `</td></tr>
<tr><td style="border: 1px solid #aaa;" >xx</td><td  style="border: 1px solid #aaa;" align="center">`xx`</td></tr>
<tr><td style="border: 1px solid #aaa;" >-:</td><td  style="border: 1px solid #aaa;" align="center">`-:`</td></tr>
<tr><td style="border: 1px solid #aaa;" >@</td><td  style="border: 1px solid #aaa;" align="center">`@`</td></tr>
<tr><td style="border: 1px solid #aaa;" >o+</td><td  style="border: 1px solid #aaa;" align="center">`o+`</td></tr>
<tr><td style="border: 1px solid #aaa;" >ox</td><td  style="border: 1px solid #aaa;" align="center">`ox`</td></tr>
<tr><td style="border: 1px solid #aaa;" >o.</td><td  style="border: 1px solid #aaa;" align="center">`o.`</td></tr>
<tr><td style="border: 1px solid #aaa;" >sum</td><td  style="border: 1px solid #aaa;" align="center">`sum`</td></tr>
<tr><td style="border: 1px solid #aaa;" >prod</td><td  style="border: 1px solid #aaa;" align="center">`prod`</td></tr>
<tr><td style="border: 1px solid #aaa;" >^^</td><td  style="border: 1px solid #aaa;" align="center">`^^`</td></tr>
<tr><td style="border: 1px solid #aaa;" >^^^</td><td  style="border: 1px solid #aaa;" align="center">`^^^`</td></tr>
<tr><td style="border: 1px solid #aaa;" >vv</td><td  style="border: 1px solid #aaa;" align="center">`vv`</td></tr>
<tr><td style="border: 1px solid #aaa;" >vvv</td><td  style="border: 1px solid #aaa;" align="center">`vvv`</td></tr>
<tr><td style="border: 1px solid #aaa;" >nn</td><td  style="border: 1px solid #aaa;" align="center">`nn`</td></tr>
<tr><td style="border: 1px solid #aaa;" >nnn</td><td  style="border: 1px solid #aaa;" align="center">`nnn`</td></tr>
<tr><td style="border: 1px solid #aaa;" >uu</td><td  style="border: 1px solid #aaa;" align="center">`uu`</td></tr>
<tr><td style="border: 1px solid #aaa;" >uuu</td><td  style="border: 1px solid #aaa;" align="center">`uuu`</td></tr>
</table>
</td><td style="border: 1px solid #aaa;" align="center">
<table border="1" style="background-color:rgb(249,249,249); border-collapse: collapse; border: 1px solid rgb(153, 153, 153); padding: 1em;" >
<tr><th style="border: 1px solid #aaa;" >Type</th><th style="border: 1px solid #aaa;" >See</th></tr>
<tr><td style="border: 1px solid #aaa;" >=</td><td  style="border: 1px solid #aaa;" align="center">`=`</td></tr>
<tr><td style="border: 1px solid #aaa;" >!=</td><td  style="border: 1px solid #aaa;" align="center">`!=`</td></tr>
<tr><td style="border: 1px solid #aaa;" >< </td><td  style="border: 1px solid #aaa;" align="center">`<`</td></tr>
<tr><td style="border: 1px solid #aaa;" >></td><td  style="border: 1px solid #aaa;" align="center">`>`</td></tr>
<tr><td style="border: 1px solid #aaa;" ><=</td><td  style="border: 1px solid #aaa;" align="center">`<=`</td></tr>
<tr><td style="border: 1px solid #aaa;" >>=</td><td  style="border: 1px solid #aaa;" align="center">`>=`</td></tr>
<tr><td style="border: 1px solid #aaa;" >-<</td><td  style="border: 1px solid #aaa;" align="center">`-<`</td></tr>
<tr><td style="border: 1px solid #aaa;" >>-</td><td  style="border: 1px solid #aaa;" align="center">`>-`</td></tr>
<tr><td style="border: 1px solid #aaa;" >in</td><td  style="border: 1px solid #aaa;" align="center">`in`</td></tr>
<tr><td style="border: 1px solid #aaa;" >!in</td><td  style="border: 1px solid #aaa;" align="center">`notin`</td></tr>
<tr><td style="border: 1px solid #aaa;" >sub</td><td  style="border: 1px solid #aaa;" align="center">`sub`</td></tr>
<tr><td style="border: 1px solid #aaa;" >sup</td><td  style="border: 1px solid #aaa;" align="center">`sup`</td></tr>
<tr><td style="border: 1px solid #aaa;" >sube</td><td  style="border: 1px solid #aaa;" align="center">`sube`</td></tr>
<tr><td style="border: 1px solid #aaa;" >supe</td><td  style="border: 1px solid #aaa;" align="center">`supe`</td></tr>
<tr><td style="border: 1px solid #aaa;" >-=</td><td  style="border: 1px solid #aaa;" align="center">`-=`</td></tr>
<tr><td style="border: 1px solid #aaa;" >~=</td><td  style="border: 1px solid #aaa;" align="center">`~=`</td></tr>
<tr><td style="border: 1px solid #aaa;" >~~</td><td  style="border: 1px solid #aaa;" align="center">`~~`</td></tr>
<tr><td style="border: 1px solid #aaa;" >prop</td><td  style="border: 1px solid #aaa;" align="center">`prop`</td></tr>
</table>
</td><td style="border: 1px solid #aaa;" align="center">
<table border="2" cellpadding="2" style="background-color:rgb(249,249,249); border-collapse: collapse; border: 1px solid #aaa; padding: 1em;">
<tr><th style="border: 1px solid #aaa;" >Type</th><th style="border: 1px solid #aaa;" align="center">See</th></tr>
<tr><td style="border: 1px solid #aaa">and</td><td style="border: 1px solid #aaa;" align="center">`and`</td></tr>
<tr><td style="border: 1px solid #aaa;" >or</td><td style="border: 1px solid #aaa;" align="center">`or`</td></tr>
<tr><td style="border: 1px solid #aaa;" >not</td><td style="border: 1px solid #aaa;" align="center">`not`</td></tr>
<tr><td style="border: 1px solid #aaa;" >=></td><td style="border: 1px solid #aaa;" align="center">`=>`</td></tr>
<tr><td style="border: 1px solid #aaa;" >if</td><td style="border: 1px solid #aaa;" align="center">`if`</td></tr>
<tr><td style="border: 1px solid #aaa;" >iff</td><td style="border: 1px solid #aaa;" align="center">`iff`</td></tr>
<tr><td style="border: 1px solid #aaa;" >AA</td><td style="border: 1px solid #aaa;" align="center">`AA`</td></tr>
<tr><td style="border: 1px solid #aaa;" >EE</td><td style="border: 1px solid #aaa;" align="center">`EE`</td></tr>
<tr><td style="border: 1px solid #aaa;" >_|_</td><td style="border: 1px solid #aaa;" align="center">`_|_`</td></tr>
<tr><td style="border: 1px solid #aaa;" >TT</td><td style="border: 1px solid #aaa;" align="center">`TT`</td></tr>
<tr><td style="border: 1px solid #aaa;" >|--</td><td style="border: 1px solid #aaa;" align="center">`|--`</td></tr>
<tr><td style="border: 1px solid #aaa;" >|==</td><td style="border: 1px solid #aaa;" align="center">`|==`</td></tr>
</table>
 
</td><td style="border: 1px solid #aaa;" align="center">
<table border="2" cellpadding="2" style="background-color:rgb(249,249,249); border-collapse: collapse; border: 1px solid rgb(153, 153, 153); padding: 1em;">
<tr><th style="border: 1px solid #aaa;" >Type</th><th style="border: 1px solid #aaa;">See</th></tr>
<tr><td style="border: 1px solid #aaa;" >int</td><td style="border: 1px solid #aaa;" align="center">`int`</td></tr>
<tr><td style="border: 1px solid #aaa;" >oint</td><td style="border: 1px solid #aaa;" align="center">`oint`</td></tr>
<tr><td style="border: 1px solid #aaa;" >del</td><td style="border: 1px solid #aaa;" align="center">`del`</td></tr>
<tr><td style="border: 1px solid #aaa;" >grad</td><td style="border: 1px solid #aaa;" align="center">`grad`</td></tr>
<tr><td style="border: 1px solid #aaa;" >+-</td><td style="border: 1px solid #aaa;" align="center">`+-`</td></tr>
<tr><td style="border: 1px solid #aaa;" >O/</td><td style="border: 1px solid #aaa;" align="center">`O/`</td></tr>
<tr><td style="border: 1px solid #aaa;" >oo</td><td style="border: 1px solid #aaa;" align="center">`oo`</td></tr>
<tr><td style="border: 1px solid #aaa;" >aleph</td><td style="border: 1px solid #aaa;" align="center">`aleph`</td></tr>
<tr><td style="border: 1px solid #aaa;" >/_</td><td style="border: 1px solid #aaa;" align="center">`/_`</td></tr>
<tr><td style="border: 1px solid #aaa;" >:.</td><td style="border: 1px solid #aaa;" align="center">`:.`</td></tr>
<tr><td style="border: 1px solid #aaa;" >|...|</td><td style="border: 1px solid #aaa;" align="center">|`...`|</td></tr>
<tr><td style="border: 1px solid #aaa;" >|cdots|</td><td style="border: 1px solid #aaa;" align="center">|`cdots`|</td></tr>
<tr><td style="border: 1px solid #aaa;" >vdots</td><td style="border: 1px solid #aaa;" align="center">`vdots`</td></tr>
<tr><td style="border: 1px solid #aaa;" >ddots</td><td style="border: 1px solid #aaa;" align="center">`ddots`</td></tr>
<tr><td style="border: 1px solid #aaa;" >|\ |</td><td style="border: 1px solid #aaa;" align="center">|`\ `|</td></tr>
<tr><td style="border: 1px solid #aaa;" >|quad|</td><td style="border: 1px solid #aaa;" align="center">|`quad`|</td></tr>
<tr><td style="border: 1px solid #aaa;" >diamond</td><td style="border: 1px solid #aaa;" align="center">`diamond`</td></tr>
<tr><td style="border: 1px solid #aaa;" >square</td><td style="border: 1px solid #aaa;" align="center">`square`</td></tr>
<tr><td style="border: 1px solid #aaa;" >|__</td><td style="border: 1px solid #aaa;" align="center">`|__`</td></tr>
<tr><td style="border: 1px solid #aaa;" >__|</td><td style="border: 1px solid #aaa;" align="center">`__|`</td></tr>
<tr><td style="border: 1px solid #aaa;" >|~</td><td style="border: 1px solid #aaa;" align="center">`|~`</td></tr>
<tr><td style="border: 1px solid #aaa;" >~|</td><td style="border: 1px solid #aaa;" align="center">`~|`</td></tr>
<tr><td style="border: 1px solid #aaa;" >CC</td><td style="border: 1px solid #aaa;" align="center">`CC`</td></tr>
<tr><td style="border: 1px solid #aaa;" >NN</td><td style="border: 1px solid #aaa;" align="center">`NN`</td></tr>
<tr><td style="border: 1px solid #aaa;" >QQ</td><td style="border: 1px solid #aaa;" align="center">`QQ`</td></tr>
<tr><td style="border: 1px solid #aaa;" >RR</td><td style="border: 1px solid #aaa;" align="center">`RR`</td></tr>
<tr><td style="border: 1px solid #aaa;" >ZZ</td><td style="border: 1px solid #aaa;" align="center">`ZZ`</td></tr>
</table>
</td><td style="border: 1px solid #aaa;" align="center">
<table border="2" cellpadding="2" style="background-color:rgb(249,249,249); border-collapse: collapse; border: 1px solid rgb(153, 153, 153); padding: 1em;">
<tr><th style="border: 1px solid #aaa;" >Type</th><th style="border: 1px solid #aaa;">See</th></tr>
<tr><td style="border: 1px solid #aaa;" >sin</td><td style="border: 1px solid #aaa;" align="center">`sin`</td></tr>
<tr><td style="border: 1px solid #aaa;" >cos</td><td style="border: 1px solid #aaa;" align="center">`cos`</td></tr>
<tr><td style="border: 1px solid #aaa;" >tan</td><td style="border: 1px solid #aaa;" align="center">`tan`</td></tr>
<tr><td style="border: 1px solid #aaa;" >csc</td><td style="border: 1px solid #aaa;" align="center">`csc`</td></tr>
<tr><td style="border: 1px solid #aaa;" >sec</td><td style="border: 1px solid #aaa;" align="center">`sec`</td></tr>
<tr><td style="border: 1px solid #aaa;" >cot</td><td style="border: 1px solid #aaa;" align="center">`cot`</td></tr>
<tr><td style="border: 1px solid #aaa;" >sinh</td><td style="border: 1px solid #aaa;" align="center">`sinh`</td></tr>
<tr><td style="border: 1px solid #aaa;" >cosh</td><td style="border: 1px solid #aaa;" align="center">`cosh`</td></tr>
<tr><td style="border: 1px solid #aaa;" >tanh</td><td style="border: 1px solid #aaa;" align="center">`tanh`</td></tr>
<tr><td style="border: 1px solid #aaa;" >log</td><td style="border: 1px solid #aaa;" align="center">`log`</td></tr>
<tr><td style="border: 1px solid #aaa;" >ln</td><td style="border: 1px solid #aaa;" align="center">`ln`</td></tr>
<tr><td style="border: 1px solid #aaa;" >det</td><td style="border: 1px solid #aaa;" align="center">`det`</td></tr>
<tr><td style="border: 1px solid #aaa;" >dim</td><td style="border: 1px solid #aaa;" align="center">`dim`</td></tr>
<tr><td style="border: 1px solid #aaa;" >lim</td><td style="border: 1px solid #aaa;" align="center">`lim`</td></tr>
<tr><td style="border: 1px solid #aaa;" >mod</td><td style="border: 1px solid #aaa;" align="center">`mod`</td></tr>
<tr><td style="border: 1px solid #aaa;" >gcd</td><td style="border: 1px solid #aaa;" align="center">`gcd`</td></tr>
<tr><td style="border: 1px solid #aaa;" >lcm</td><td style="border: 1px solid #aaa;" align="center">`lcm`</td></tr>
<tr><td style="border: 1px solid #aaa;" >min</td><td style="border: 1px solid #aaa;" align="center">`min`</td></tr>
<tr><td style="border: 1px solid #aaa;" >max</td><td style="border: 1px solid #aaa;" align="center">`max`</td></tr>
</table>
 
</td><td style="border: 1px solid #aaa;" align="center">
<table border="2" cellpadding="2" style="background-color:rgb(249,249,249); border-collapse: collapse; border: 1px solid rgb(153, 153, 153); padding: 1em;" id="table1">
<tr><th style="border: 1px solid #aaa;" >Type</th><th style="border: 1px solid #aaa;">See</th></tr>
<tr><td style="border: 1px solid #aaa;" >(</td><td style="border: 1px solid #aaa;" align="center">`(`</td></tr>
<tr><td style="border: 1px solid #aaa;" >)</td><td style="border: 1px solid #aaa;" align="center">`)`</td></tr>
<tr><td style="border: 1px solid #aaa;" >[</td><td style="border: 1px solid #aaa;" align="center">`[`</td></tr>
<tr><td style="border: 1px solid #aaa;" >]</td><td style="border: 1px solid #aaa;" align="center">`]`</td></tr>
<tr><td style="border: 1px solid #aaa;" >{</td><td style="border: 1px solid #aaa;" align="center">`{`</td></tr>
<tr><td style="border: 1px solid #aaa;" >}</td><td style="border: 1px solid #aaa;" align="center">`}`</td></tr>
<tr><td style="border: 1px solid #aaa;" >(:</td><td style="border: 1px solid #aaa;" align="center">`(:`</td></tr>
<tr><td style="border: 1px solid #aaa;" >:)</td><td style="border: 1px solid #aaa;" align="center">`:)`</td></tr>
<tr><td style="border: 1px solid #aaa;" >{:</td><td style="border: 1px solid #aaa;" align="center">`{:`</td></tr>
<tr><td style="border: 1px solid #aaa;" >:}</td><td style="border: 1px solid #aaa;" align="center">`{::}`</td></tr>
</table>
 
</td><td style="border: 1px solid #aaa;" align="center">
<table border="2" cellpadding="2" style="width:70px; background-color:rgb(249,249,249); border-collapse: collapse; border: 1px solid rgb(153, 153, 153); padding: 1em;" id="table2">
<tr><th style="border: 1px solid #aaa;" >Type</th><th style="border: 1px solid #aaa;">See</th></tr>
<tr><td style="border: 1px solid #aaa;" >hat x</td><td style="border: 1px solid #aaa;" align="center">`hat x`</td></tr>
<tr><td style="border: 1px solid #aaa;" >bar x</td><td style="border: 1px solid #aaa;" align="center">`bar x`</td></tr>
<tr><td style="border: 1px solid #aaa;" >ul x</td><td style="border: 1px solid #aaa;" align="center">`ul x`</td></tr>
<tr><td style="border: 1px solid #aaa;" >vec x</td><td style="border: 1px solid #aaa;" align="center">`vec x`</td></tr>
<tr><td style="border: 1px solid #aaa;" >dot x</td><td style="border: 1px solid #aaa;" align="center">`dot x`</td></tr>
<tr><td style="border: 1px solid #aaa;" >ddot x</td><td style="border: 1px solid #aaa;" align="center">`ddot x`</td></tr>
</table>
 
</td><td style="border: 1px solid #aaa;" align="center">
<table border="2" cellpadding="2" style="width:70px; background-color:rgb(249,249,249); border-collapse: collapse; border: 1px solid rgb(153, 153, 153); padding: 1em;" id="table3">
<tr><th style="border: 1px solid #aaa;" >Type</th><th style="border: 1px solid #aaa;">See</th></tr>
<tr><td style="border: 1px solid #aaa;" >bb A</td><td style="border: 1px solid #aaa;" align="center">`bb A`</td></tr>
<tr><td style="border: 1px solid #aaa;" >bbb A</td><td style="border: 1px solid #aaa;" align="center">`bbb A`</td></tr>
<tr><td style="border: 1px solid #aaa;" >cc A</td><td style="border: 1px solid #aaa;" align="center">`cc A`</td></tr>
<tr><td style="border: 1px solid #aaa;" >tt A</td><td style="border: 1px solid #aaa;" align="center">`tt A`</td></tr>
<tr><td style="border: 1px solid #aaa;" >fr A</td><td style="border: 1px solid #aaa;" align="center">`fr A`</td></tr>
<tr><td style="border: 1px solid #aaa;" >sf A</td><td style="border: 1px solid #aaa;" align="center">`sf A`</td></tr>
</table>
 
</td><td style="border: 1px solid #aaa;" align="center">
<table border="2" cellpadding="2" style="background-color:rgb(249,249,249); border-collapse: collapse; border: 1px solid rgb(153, 153, 153); padding: 1em;">
<tr><th style="border: 1px solid #aaa;" >Type</th><th style="border: 1px solid #aaa;">See</th></tr>
<tr><td style="border: 1px solid #aaa;" >uarr</td><td style="border: 1px solid #aaa;" align="center">`uarr`</td></tr>
<tr><td style="border: 1px solid #aaa;" >darr</td><td style="border: 1px solid #aaa;" align="center">`darr`</td></tr>
<tr><td style="border: 1px solid #aaa;" >rarr</td><td style="border: 1px solid #aaa;" align="center">`rarr`</td></tr>
<tr><td style="border: 1px solid #aaa;" >-></td><td style="border: 1px solid #aaa;" align="center">`->`</td></tr>
<tr><td style="border: 1px solid #aaa;" >|-></td><td style="border: 1px solid #aaa;" align="center">`|->`</td></tr>
<tr><td style="border: 1px solid #aaa;" >larr</td><td style="border: 1px solid #aaa;" align="center">`larr`</td></tr>
<tr><td style="border: 1px solid #aaa;" >harr</td><td style="border: 1px solid #aaa;" align="center">`harr`</td></tr>
<tr><td style="border: 1px solid #aaa;" >rArr</td><td style="border: 1px solid #aaa;" align="center">`rArr`</td></tr>
<tr><td style="border: 1px solid #aaa;" >lArr</td><td style="border: 1px solid #aaa;" align="center">`lArr`</td></tr>
<tr><td style="border: 1px solid #aaa;" >hArr</td><td style="border: 1px solid #aaa;" align="center">`hArr`</td></tr>
</table>
 
</td></tr>
</table>
 
<br><br>
 
==Examples==
 
<table border="1" cellpadding="2" style="border: 1px solid #aaa; background-color:rgb(249,249,249); ">
<tr>
<th style="border: 1px solid #aaa; width: 270px">Type this</th>
<th style="border: 1px solid #aaa; width: 150px">See that</th>
<th style="border: 1px solid #aaa;">Comment</th>
</tr>
<tr>
<td style="border: 1px solid #aaa;">\`x^2+y_1+z_12^34\`</td>
<td style="border: 1px solid #aaa;">`x^2+y_1+z_12^34`</td>
<td style="border: 1px solid #aaa;">subscripts as in TeX, but numbers are treated as a unit</td>
</tr>
<tr>
<td style="border: 1px solid #aaa;">\`sin^-1(x)\`</td>
<td style="border: 1px solid #aaa;">`sin^-1(x)`</td>
<td style="border: 1px solid #aaa;">function names are treated as constants</td>
</tr>
<tr>
<td style="border: 1px solid #aaa;">\`d/dxf(x)=lim_(h->0)(f(x+h)-f(x))/h\`</td>
<td style="border: 1px solid #aaa;">`d/dxf(x)=lim_(h->0)(f(x+h)-f(x))/h`</td>
<td style="border: 1px solid #aaa;">complex subscripts are bracketed, displayed under lim</td>
</tr>
<tr>
<td style="border: 1px solid #aaa;">\`\frac{d}{dx}f(x)=\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}\`</td>
<td style="border: 1px solid #aaa;">`\frac{d}{dx}f(x)=\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}`</td>
<td style="border: 1px solid #aaa;">standard LaTeX notation is an alternative</td>
</tr>
<tr>
<td style="border: 1px solid #aaa;">\`f(x)=sum_(n=0)^oo(f^((n))(a))/(n!)(x-a)^n\`</td>
<td style="border: 1px solid #aaa;">`f(x)=sum_(n=0)^oo(f^((n))(a))/(n!)(x-a)^n`</td>
<td style="border: 1px solid #aaa;">f^((n))(a) must be bracketed, else the numerator is only `a`</td>
</tr>
<tr>
<td style="border: 1px solid #aaa;">\`f(x)=\sum_{n=0}^\infty\frac{f^{(n)}(a)}{n!}(x-a)^n\`</td>
<td style="border: 1px solid #aaa;">`f(x)=\sum_{n=0}^\infty\frac{f^{(n)}(a)}{n!}(x-a)^n`</td>
<td style="border: 1px solid #aaa;">standard LaTeX produces the same result</td>
</tr>
<tr>
<td style="border: 1px solid #aaa;">\`int_0^1f(x)dx\`</td>
<td style="border: 1px solid #aaa;">`int_0^1f(x)dx`</td>
<td style="border: 1px solid #aaa;">subscripts must come before superscripts</td>
</tr>
<tr>
<td style="border: 1px solid #aaa;">\`[[a,b],[c,d]]((n),(k))\`</td>
<td style="border: 1px solid #aaa;">`[[a,b],[c,d]]((n),(k))`</td>
<td style="border: 1px solid #aaa;">matrices and column vectors are simple to type</td>
</tr>
<tr>
<td style="border: 1px solid #aaa;">\`x/x={(1,if x!=0),(text{undefined},if x=0):}\`</td>
<td style="border: 1px solid #aaa;">`x/x={(1,if x!=0),(text{undefined},if x=0):}`</td>
<td style="border: 1px solid #aaa;">piecewise defined function are based on matrix notation</td>
</tr>
<tr>
<td style="border: 1px solid #aaa;">\`a//b\`</td>
<td style="border: 1px solid #aaa;">`a//b`</td>
<td style="border: 1px solid #aaa;">use // for inline fractions</td>
</tr>
<tr>
<td style="border: 1px solid #aaa;">\`(a/b)/(c/d)\`</td>
<td style="border: 1px solid #aaa;">`(a/b)/(c/d)`</td>
<td style="border: 1px solid #aaa;">with brackets, multiple fraction work as expected</td>
</tr>
<tr>
<td style="border: 1px solid #aaa;">\`a/b/c/d\`</td>
<td style="border: 1px solid #aaa;">`a/b/c/d`</td>
<td style="border: 1px solid #aaa;">without brackets the parser chooses this particular expression</td>
</tr>
<tr>
<td style="border: 1px solid #aaa;">\`((a*b))/c\`</td>
<td style="border: 1px solid #aaa;">`((a*b))/c`</td>
<td style="border: 1px solid #aaa;">only one level of brackets is removed; * gives standard product</td>
</tr>
<tr>
<td style="border: 1px solid #aaa;">\`sqrtsqrtroot3x\`</td>
<td style="border: 1px solid #aaa;">`sqrtsqrtroot3x`</td>
<td style="border: 1px solid #aaa;">spaces are optional, only serve to split strings that should not match</td>
</tr>
<tr>
<td style="border: 1px solid #aaa;">\`(:a,b:) and {:(x,y),(u,v):}\`</td>
<td style="border: 1px solid #aaa;">`(:a,b:) and {:(x,y),(u,v):}`</td>
<td style="border: 1px solid #aaa;">angle brackets and invisible brackets</td>
</tr>
<tr>
<td style="border: 1px solid #aaa;">\`(a,b]={x in RR : a < x <= b}\`</td>
<td style="border: 1px solid #aaa;">`(a,b]={x in RR : a < x <= b}`</td>
<td style="border: 1px solid #aaa;">grouping brackets don't have to match</td>
</tr>
<tr>
<td style="border: 1px solid #aaa;">\`abc-123.45^-1.1\`</td>
<td style="border: 1px solid #aaa;">`abc-123.45^-1.1`</td>
<td style="border: 1px solid #aaa;">non-tokens are split into single characters,<br/>
but decimal numbers are parsed with possible sign</td>
</tr>
<tr>
<td style="border: 1px solid #aaa;">\`hat(ab) bar(xy) ulA vec v dotx ddot y\`</td>
<td style="border: 1px solid #aaa;">`hat(ab) bar(xy) ulA vec v dotx ddot y`</td>
<td style="border: 1px solid #aaa;">accents can be used on any expression (work well in IE)</td>
</tr>
<tr>
<td style="border: 1px solid #aaa;">\`bb{AB3}.bbb(AB].cc(AB).fr{AB}.tt[AB].sf(AB)\`</td>
<td style="border: 1px solid #aaa;">`bb{AB3}.bbb(AB].cc(AB).fr{AB}.tt[AB].sf(AB)`</td>
<td style="border: 1px solid #aaa;">font commands; can use any brackets around argument</td>
</tr>
<tr>
<td style="border: 1px solid #aaa;">\`stackrel"def"= or \stackrel{\Delta}{=}" "("or ":=)\`</td>
<td style="border: 1px solid #aaa;">`stackrel"def"= or \stackrel{\Delta}{=}" "("or ":=)`</td>
<td style="border: 1px solid #aaa;">symbols can be stacked</td>
</tr>
<tr>
<td style="border: 1px solid #aaa;">\`{::}_(\ 92)^238U\`</td>
<td style="border: 1px solid #aaa;">`{::}_(\ 92)^238U`</td>
<td style="border: 1px solid #aaa;">prescripts simulated by subsuperscripts</td>
</tr>
</table>
 
[[Category:Help]]

Revision as of 12:13, 12 October 2015

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