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<!DOCTYPE HTML>
<html><head><TITLE>Surface Evolver Documentation - general syntax</title>
<link rel="stylesheet" type="text/css" href="evdoc-style.css" />
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" >
</head>

<BODY>
<!--NewPage-->

<h1 class="center">
 <a href="http://www.susqu.edu/brakke/evolver/evolver.htm" class="comic">
Surface Evolver</a> Documentation</h1>

<a href="evolver.htm#doc-top">Back to top of Surface Evolver documentation.</a>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<a href="index.htm">Index.</a>

<h1>Surface  Evolver syntax </h1>
Both the datafile and user commands follow a common general syntax
described in this file, with a few differences as noted.
<table><tr><td style="vertical-align:text-top"><ul>
<li><a href="#lexical-format">Lexical format</a>
<li><a href="#comments">Comments</a>
<li><a href="#line-splicing">Line splicing</a>
<li><a href="#case">Case</a>
<li><a href="#whitespace">Whitespace</a>
<li><a href="#identifiers">Identifiers</a>
<li><a href="#numbers">Numbers</a>
<li><a href="#colors">Colors</a>
<li><a href="#atomic-values">Atomic values</a>
<li><a href="#internal-variables">Internal variables</a>
<li><a href="#variables">User-defined variables</a> 
</ul></td><td  style="vertical-align:text-top"><ul>
<li><a href="#attr-values">Element attributes</a>
<li><a href="#arrays">Arrays</a>
<li><a href="#expressions">Arithmetic expressions</a>
<li><a href="#constexpr">Constant expressions</a>
<li><a href="#operators">Arithmetic operators</a>
<li><a href="#boolean-ops">Boolean operators</a>
<li><a href="#precedence">Operator precedences</a>
<li><a href="#functions">Math functions</a>
<li><a href="#stringexpr">String expressions</a>
<li><a href="#misc-functions">Miscellaneous functions</a>

</ul></td></tr>
</table>
<hr><a   id="lexical-format"></a><h2>Lexical format</h2>

         For those who know about such things,
         the datafile and commands are read with a lexical analyzer generated
         by the lex program.  The specification is in datafile.lex.  Commands
         are further parsed by a yacc-generated parser.
<p>
          In parsing an expression, the longest legal expression
          is used.  This permits coordinates to be specified by
          several consecutive expressions  with no special 
          separators.
<hr>
<a   id="comments"></a><h2>Comments</h2>

         Comments may be enclosed in /* */ pairs (as in C) and
         may span lines. // indicates the rest of the line is a comment,
         as in C++.

<hr><a   id="line-splicing"></a><h2>Lines and line splicing</h2>

         The file is made up of lines.  Line breaks are significant.
         The next physical line can be spliced onto the current 
         line by having \ be the last character of the current line.
         Line splicing is not effective in // comments.
         Blank lines and comment lines may be placed freely anywhere.
	 The various combinations of CR and NL that
         various computer systems use are all recognized

<hr><a   id="case"></a><h2>Case</h2>

     Upper and lower case is not significant in the datafile, except in 
     #define macro names.  In run-time commands, case is only 
     significant
     for <a href="single.htm#single-letter">single-letter commands</a>.

<hr><a   id="whitespace"></a><h2>Whitespace</h2>

         In the datafile, whitespace consists of spaces, tabs, commas, colons,
         and semicolons.  So it's fine if you want to use commas to 
         separate coordinate values, and colons to prettify constraint
         definitions.  In commands, whitespace consists of spaces and tabs.
	 CTRL-Z is also whitespace, for the benefit of files imported from
	 DOS.

<hr>
<a   id="identifiers"></a><h2>Identifiers</h2>

         Identifiers follow standard
         C rules (composed of alphanumeric characters and '_'
         with the leading character not a digit) and must not
         be keywords.  Identifiers are used for macro names 
         (in the datafile) and user-defined 
<a href="#variables">variables</a> and 
<a href="commands.htm#command-definition">commands</a>.
         Identifiers must have at least two characters,
	 since single characters can be confused with commands.
         To find out if a name is already in use as a keyword or
         user-defined name interactively, use 
       <a href="commands.htm#help">help</a> command.  In scripts, one
       can use the is_defined function, which has the syntax
<pre> is_defined(<em>stringexpr</em>)
</pre>
The <em>stringexpr</em> must be a quoted string or other string expression.
The return value is 0 if the name is undefined, 1 if defined.
This function is evaluated at run-time, but variables in the whole
command are parsed before the command is executed, so a command
 like <code> if is_defined("newvar") then newvar := 1 else newvar := 2</code>
  will give <code> newvar</code> the value 1 even if this is its first appearance.
A better way in scripts to test is to use the <a href="commands.htm">define</a>
command to define the variable without initialization, and then test to
see if it has the default value, i.e. 0 for a numeric variable and a
<a href="#sizeof">sizeof</a> 0 for a string variable.

<hr><a   id="numbers"></a><a   id="hexadecimal-numbers"></a>
<a   id="binary-numbers"></a>
<h2>Numbers</h2>

         Constant values may be in any of the usual forms.  This
         includes integers, fixed point, and scientific notation
         such as
<pre>      2    -3    .5    23.    5e-10    +0.7D2
</pre>
Hexadecimal integers starting with 0x, as in 0x12Af, are also accepted,
as are binary numbers such as 11001b, indicated by a trailing 'b'.
<a href="#colors">Color</a> names are interpreted as integers.
<hr>

<a   id="clear"></a>
<a   id="black"></a>
<a   id="blue"></a>
<a   id="green"></a>
<a   id="cyan"></a>
<a   id="red"></a>
<a   id="magenta"></a>
<a   id="brown"></a>
<a   id="lightgray"></a>
<a   id="lightgrey"></a>
<a   id="darkgray"></a>	  
<a   id="darkgrey"></a>	  
<a   id="gray"></a>	  
<a   id="grey"></a>	  
<a   id="lightblue"></a>
<a   id="lightgreen"></a>
<a   id="lightcyan"></a>
<a   id="lightred"></a>
<a   id="lightmagenta"></a>
<a   id="yellow"></a>
<a   id="white"></a>
<a   id="transparent"></a>
<a   id="colors"></a><h2>Colors</h2>

 The colors of <a href="elements.htm#color,-edge">edges</a>
 and <a href="elements.htm#color,-facet">facets</a>
 are recorded as integers in the
range -1 through 15.  How these
 integers translate to colors on the screen is determined by how
 Evolver's graphics drivers are written.  The following synonyms are
 supplied, and it is hoped that the
 graphics drivers will be written to display these correctly:<br>
<table><tr><td style="vertical-align:text-top">
-1  CLEAR <br>
0  BLACK  <br>
1 BLUE <br>
2 GREEN <br>
3 CYAN <br>
4 RED <br></td>
<td style="vertical-align:text-top">
5 MAGENTA <br>
6 BROWN <br>
7 LIGHTGRAY <br>
8 DARKGRAY	 	  <br>
9 LIGHTBLUE <br>
10 LIGHTGREEN <br></td>
<td style="vertical-align:text-top">
11 LIGHTCYAN <br>
12 LIGHTRED <br>
13 LIGHTMAGENTA <br>
14 YELLOW <br>
15 WHITE <br></td></tr>
</table>
The special color value CLEAR (-1) makes a facet transparent.
"Transparent" is a synonym for clear.
<p>
These tokens are simply translated to integer values wherever they
occur, so these are reserved words. Edge and facet colors may be
set in the datafile or by the <a href="commands.htm#set">set</a> command.

<hr>
<a   id="expr"></a>
<a   id="expressions"></a><h2>Arithmetic expressions</h2>

 Arithmetic expressions evaluate to real numbers.  Boolean expressions
 are a subclass, with zero as false and nonzero as true; true results
 evaluate as 1.  Ordinary algebraic notation is used.

<ul>
<li> <a href="#atomic-values">atomic values</a>
<li> <a href="#operators">arithmetic operators</a>
<li> <a href="#boolean-ops">boolean operators</a>
<li> <a href="#precedence">operator precedences</a>
<li> <a href="#functions">math functions</a>
<li> <a href="#aggregate-functions">aggregate functions</a>
</ul>

<hr>
<a   id="constant-expressions"></a><h2>Constant expressions</h2>
<a   id="constexpr"></a>
Constant expressions are evaluated when parsed.  They are denoted
by <em>constexpr</em> in various syntax definitions. They occur
mostly in the datafile.  Although they may contain variables, 
changing the variable value after parsing has no effect.
<a   id="var-expr">Variable expressions</a> (denoted by <em>expr</em>
in syntax definitions) are recorded as parse trees and are re-evaluated
each time needed. 
<hr>
<a   id="pi"></a>
<a   id="atomic-values"></a> <h2>Atomic values</h2>
The following evaluate to single numbers in expressions:
<dl>
<dt><b>number</b></dt>
   <dd>  An integer, real, or hexadecimal <a href="#numbers">constant</a>.
         Hex numbers begin with <code>0x</code>. </dd>
<dt><b> pi</b></dt>
   <dd> Mathematical constant, ratio of circle circumference to  radius.</dd>
<dt> <b>x1,x2,...; x,y,z,w </b></dt>
    <dd>   Depending on context, space coordinates, vertex coordinates,
    edge vector components, or facet normal components.</dd>
<dt><b>p1,p2,...</b></dt>
    <dd>Parameters of vertices on 
      <a href="constrnt.htm#parametric-boundaries">boundaries</a>.</dd>
<dt> <a   id="G-value"><b>G</b></a></dt>
  <dd>Current gravitational constant
for calculating <a href="energies.htm#gravity-energy">gravitational energy</a>.
</dd>

<dt><b> <a href="#variables">user-defined variables</a> </b></dt>
  <dd> Arbitrary variables defined in the datafile or at runtime.</dd>
<dt><b> Indexed <a href="#arrays">array</a> variables.</b></dt>
  <dd> User-defined multidimensional arrays of reals or integers, and some internally defined arrays.</dd>
<dt> <a href="#internal-variables"><b>internal variables</b></a></dt>
 <dd> Special pre-defined variables.</dd>
<dt> <a href="#attr-values"><b>element attributes</b></a></dt>
<dd>   Things like vertex coordinates, edge length facet area, colors.</dd>
<dt> <a href="quants.htm#named-quantities"><b>named quantity</b></a> attributes
  </dt><dd> Including modulus, target, value, pressure.</dd>
<dt> <a href="quants.htm#method-instances"><b>method instance</b></a> attributes
  </dt><dd> Including modulus, value.</dd>
<dt><b> toggle name</b></dt> <dd>
Any <a href="toggle.htm">toggle command</a> 
name may be used as a Boolean variable in an
expression (full word toggles, not single letters).  But beware the
ambiguity in interpreting a toggle as a command or a value.
You may have to force the toggle to be interpreted as a value.
"<code>ad := autodisplay</code>" sets ad as a command synonym for
autodisplay, while "<code>ad := (autodisplay)</code>" records the
current boolean value. </dd>
</dl>
<hr>
<a   id="stringexpr"></a><h2>String expressions</h2>
A string expression evaluates to a string of characters.  At present,
the only ways to produce strings are:
<ul>
<li> double-quoted string literals, e.g. <code>"this is a string"</code>.
The following standard C escape sequences are recognized:
  <ul>
  <li> \n   newline
  <li> \r   carriage return
  <li> \t   tab
  <li> \b   backspace
  <li> \q   double-quote mark
  <li> \<em>c</em>   the character <em>c</em> elsewise
  </ul>
In DOS, MS-Windows, or Windows NT paths, use / as the directory separator,
since \ is an escape character.  DOS and Windows have always accepted
/ as a directory separator.
<li> successive double-quoted strings, which are concatenated into
one string when read.
<li> string variables, either internal like <a href="#datafilename">
<code>datafilename</code></a>, or user-defined. 
<li> output from <a href="commands.htm#sprintf"><code>sprintf</code></a>.
</ul>
<hr>
<a   id="operators"></a><h2>Arithmetic operators</h2>
<a   id="idiv"></a>
<a   id="imod"></a>
<a   id="mod"></a>
<a   id="conditional"></a>
These are the arithmetic operators that may appear in 
<a href="#expressions">expressions</a>:
<dl>
<dt> +,-,*,/</dt><dd>Usual real arithmetic; +,-,* also work with arrays.
          NOTE: A '+' or '-' preceded by <a href="syntax.htm#whitespace">
whitespace</a> and followed
          by a number is taken to be a signed number. Thus
          "3 - 5" and "3-5" are single expressions, but
          "3 -5" is not.   This is for convenience in separating
          multiple expressions listed on the same line for 
	  vertex coordinates, metric components, etc. in the datafile.<p></dd>

<dt> idiv </dt><dd>Integer divide. Rounds toward zero, then does
integer division.  Ex:  7 idiv 2 is 3; -3.5 idiv 2.1 is -1;  -3 idiv 2 is -1.
<p></dd> 
<dt>%, mod</dt><dd>Real arithmetic modulus, x % y = x - floor(x/y)*y.<p></dd>
<dt> imod</dt><dd> Integer arithmetic modulus,
x imod y = floor(x) - floor(floor(x)/floor(y))*floor(y). <p></dd>
<dt> =</dt><dd> NOT an assignment operator.  Treated as low-precedence '-'
  so level-set constraint formulas like x^2 + y^2 - R^2 may be written
  naturally as x^2 + y^2 = R^2.<p></dd>
<dt> (,)</dt><dd>  Parentheses for grouping and functional notation.<p></dd>
<dt> ^,**</dt><dd> Raise to  real power.<p></dd>
<dt> ? : </dt><dd> Conditional expression, as in the C language.
    x ? y : z evaluates to y if x is nonzero and to z if x is zero.<p></dd>
<dt> ++,--  </dt><dd> C-style pre- and post-increment and decrement commands.  These work only
       on single variables and only as stand-alone commands, as in "for"
       loops for example:
<pre>
           for ( inx := 1 ; inx &lt;= 10 ; inx++ )  
</pre>
</dd>
</dl>

<hr>
<a   id="and"></a>
<a   id="or"></a>
<a   id="not"></a>
<a   id="boolean-ops"></a><h2>Boolean operators</h2>
 Boolean expressions
 are a subclass of arithmetic expressions, 
with zero as false and nonzero as true; true results
 evaluate as 1. 
<table border>
<tr><td> ==,&gt;,&lt;,&gt;=,&lt;=,!= </td>
  <td> Numerical or boolean comparison.</td></tr>
<tr><td> NOT, !</td><td>  Boolean NOT</td></tr>
<tr><td> AND, &amp;&amp;</td><td>  Boolean AND, with short-circuit evaluation.</td></tr>
<tr><td> OR, || </td><td> Boolean OR, with short-circuit evaluation. </td></tr>
</table>
<hr>
<a   id="precedence"></a><h2>Operator precedences</h2>
Here is the order of operator precedence, listed from high to
low with equal precedence on same line, with associativity.
<table border>
<tr><th>Operator</th><th>  Associativity</th></tr>
<tr><td>^,**</td><td>  left associative </td></tr>
<tr><td>unary -</td><td>  right associative </td></tr>
<tr><td>*,/,%,IMOD,IDIV </td><td>  left associative </td></tr>
<tr><td>+,- </td><td>  left associative </td></tr>
<tr><td>   <a href="elements.htm#on_boundary">on_boundary</a>
<br><a href="elements.htm#on_constraint">on_constraint</a>
<br><a href="elements.htm#hit_constraint">hit_constraint</a>
<br><a href="elements.htm#on_quantity">on_quantity</a>
<br><a href="elements.htm#on_method_instance">on_method_instance</a>
</td><td>  nonassociative </td></tr>
<tr><td>==,&gt;,&lt;,&gt;=,&lt;=,!= </td><td>  right associative </td></tr>
<tr><td>NOT, ! </td><td>  right associative </td></tr>
<tr><td>AND, &amp;&amp; </td><td>  left associative </td></tr>
<tr><td>OR, || </td><td>  left associative </td></tr>
<tr><td>? : </td><td>  left associative </td></tr>
<tr><td>=   </td><td>  left associative </td></tr>
</table>
 <hr>
<a   id="functions"></a> <h2>Math functions</h2>
These are the math functions available in expressions.  They take
one argument in parentheses, except where noted.
<dl>
<dt><a   id="abs"></a>
 abs(x) </dt><dd>      Absolute value. 
<!--EndName-->
<p></dd>
<dt><a   id="sqr"></a>
 sqr(x) </dt><dd>          Square. <p></dd>
<!--EndName-->
<dt><a   id="sqrt"></a>
 sqrt(x)   </dt><dd>        Square root.  Argument must be nonnegative.<p></dd>
<!--EndName-->
<dt><a   id="sin"></a>
<a   id="cos"></a>
<a   id="tan"></a>
 sin(x), cos(x), tan(x)</dt><dd>   Trig functions, argument in radians. <p></dd>
<!--EndName-->
<dt><a   id="acos"></a>
<a   id="asin"></a>
<a   id="atan"></a>
 acos(x), asin(x), atan(x)</dt><dd> Inverse trig functions (acos, asin arguments clamped to [-1,1]). 
   Output in radians.<p></dd>
<!--EndName-->
<dt><a   id="atan2"></a>
 atan2(y,x)</dt><dd>          Inverse tangent, range -pi to pi. <p></dd>
<!--EndName-->
<dt><a   id="log"></a>
<a   id="exp"></a>
 log(x), exp(x)</dt> <dd>       Natural log, exponentiation base e.<p></dd>
<!--EndName-->
<dt><a   id="sinh"></a>
<a   id="cosh"></a>
<a   id="tanh"></a>
 sinh(x), cosh(x), tanh(x)</dt><dd>      Hyperbolic functions.<p></dd>
<!--EndName-->
<dt><a   id="asinh"></a>
<a   id="acosh"></a>
<a   id="atanh"></a>
 asinh(x), acosh(x), atanh(x)</dt><dd>   Inverse hyperbolic functions.<p></dd>
<!--EndName-->
<dt><a   id="pow"></a>
 pow(x,y)    </dt><dd>        Raise x to real power y; x may be negative if y is an integer.<p></dd>
<!--EndName-->
<dt><a   id="ceil"></a>
<a   id="floor"></a>
 ceil(x), floor(x)</dt><dd>     Round up or down to integer. <p></dd>
<!--EndName-->
<dt><a   id="minimum"></a>
<a   id="maximum"></a>
 minimum(a,b), maximum(a,b)</dt><dd> Extreme of two arguments. <p></dd>
<!--EndName-->
<dt><a   id="ellipticK"></a>
<a   id="ellipticE"></a>
 ellipticE(x), ellipticK(x)</dt><dd> Complete elliptic functions.<p></dd>
<!--EndName-->
<dt><a   id="incompleteEllipticF"></a>
<a   id="incompleteEllipticE"></a>
 incompleteEllipticE(phi,m), incompleteEllipticF(phi,m)</dt><dd> Incomplete elliptic functions
 of parameters (phi,m); agrees with Mathematica definition.<p></dd>
<!--EndName-->

<dt><a   id="matrix_multiply"></a>
 matrix_multiply(A,B,C)</dt><dd>
    Built-in matrix multiplication of arrays.  Stores A*B in C.  A, B, and
C must be stand-alone 1 or 2 dimensional array variables with appropriately
matching dimensions; in particular, you cannot get a scalar product of
vectors with this, unless you declare A to be 1xN, B to be Nx1, and C to
be 1x1.  C must be different from A and B.  Does not return a value.
  Also doesn't work with array attributes yet. Obsolete, since the * operator
now works with vectors and arrays.<p></dd>
<!--EndName-->

<dt><a   id="matrix_inverse"></a>
 matrix_inverse(A,B)</dt><dd>
  Built-in matrix inversion of an array.  Stores the inverse of A in B.  A and
B must be stand-alone  2 dimensional array variables with 
matching dimensions. B can be the same as A.  Returns a value, 1 for success, 0 for failure
or singular matrix.
<p></dd>
<!--EndName-->

<dt><a   id="matrix_determinant"></a>
 matrix_determinant(A)</dt><dd>
  Built-in matrix determinant of a square array.
Has function syntax, so it returns the value of the determinant. 
<p>
Syntax: det := matrix_determinant(A)
<pre>
  Enter command: define aaa real[2][2]
  Enter command: aaa[1][1] := 2; aaa[1][2] := 3; aaa[2][1] := 4; aaa[2][2] := 5
  Enter command: print matrix_determinant(aaa)
                  -2
</pre>
Also works on square 2D array attributes of elements.  Does not modify the array.
<p></dd>
<!--EndName-->

<dt><a   id="wrap_inverse"></a>
 wrap_inverse(w) </dt><dd>Inverse of symmetry group element w, in numerical 
representation.  Useful only if a <a href="model.htm#symmetry-groups">symmetry 
group</a> has been declared in the datafile.<p></dd>
<!--EndName-->
<dt>
<a   id="wrap_compose"></a>
 wrap_compose(w1,w2) </dt><dd> Composition of symmetry group elements w1, w2, in
 numerical
representation.  Useful only if a <a href="model.htm#symmetry-groups">symmetry 
group</a> has been declared in the datafile.<p></dd>
<!--EndName-->
<dt><a   id="usr"></a>
 usr<em>n</em>  </dt><dd>  
<a href="#user-funcs">user-defined functions</a><p></dd>
<!--EndName-->
</dl>

<hr><a   id="misc-functions"></a><h2>Miscellaneous functions</h2>
<ul>
<li><a href="#is_defined">IS_DEFINED</a>
<li><a href="#sizeof">SIZEOF</a>
<li><a href="#valid_boundary">VALID_BOUNDARY</a>
<li><a href="#valid_constraint">VALID_CONSTRAINT</a>
<li><a href="#valid_element">VALID_ELEMENT</a>
</ul>

<p> <a   id="is_defined"></a> <h3>IS_DEFINED</h3>
         To find out if a name is already in use as a keyword or
         user-defined name, use the is_defined function, which
has the syntax
<pre> IS_DEFINED(<em>stringexpr</em>)
</pre>
The <em>stringexpr</em> must be a quoted string or other string expression.
The return value is 0 if the name is undefined, 1 if defined.
This function is evaluated at run-time, but variables in the whole
command are parsed before the command is executed, so a command
 like <code> if is_defined("newvar") then newvar := 1 else newvar := 2</code>
  will give <code> newvar</code> the value 1 even if this is its first appearance.
A better way in scripts to test is to use the <a href="commands.htm">define</a>
command to define the variable without initialization, and then test to
see if it has the default value, i.e. 0 for a numeric variable and a
<a href="#sizeof">sizeof</a> 0 for a string variable.  

<hr>

<a   id="sizeof"></a><h3>SIZEOF</h3>
Returns the number of entries in an <a href="#arrays">array</a> or array 
<a href="elements.htm#extra-attributes">extra attribute</a>.
Can also be applied to a string or string variable to get the number
of characters in the string.
 Syntax:
<pre>
  SIZEOF(name)
  SIZEOF(string)
</pre>
In the first form, name is the name of the array or extra attribute, 
not in quotes.

   
<hr>
<a   id="valid_boundary"></a><h3>VALID_BOUNDARY</h3>

Boolean function.  Returns 1 or 0 depending on whether a parametric
boundary with the given number exists (note that the name of a
named boundary is internally interpreted as a number).  Syntax:
<pre> VALID_BOUNDARY(expression)
</pre>
One use is in looping through all parametric boundaries, in conjunction
with the high_boundary internal variable.  For example,
<pre>
  for ( bnum := 1 ; bnum &lt;= high_boundary ; bnum += 1 )
    if valid_boundary(bnum) then
       printf "Boundary %d has %d vertices on it\n",bnum,
          sum(vertex,on_boundary bnum);
</pre>


<hr>
<a   id="valid_constraint"></a><h3>VALID_CONSTRAINT</h3>
Boolean function.  Returns 1 or 0 depending on whether a level-set
constraint with the given number exists (note that the name of a
named constraint is internally interpreted as a number).  Syntax:
<pre> VALID_CONSTRAINT(expression)
</pre>
One use is in looping through all level-set constraints, in conjunction
with the high_constraint internal variable.  For example,
<pre>
  for ( cnum := 1 ; cnum &lt;= high_constraint ; cnum += 1 )
    if valid_constraint(cnum) then
       printf "Constraint %d has %d vertices on it\n",cnum,
          sum(vertex,on_constraint cnum);
</pre>



<hr>
<a   id="valid_element"></a><h3>VALID_ELEMENT</h3>
Boolean function.
Returns 1 or 0 depending on whether an element of a given index 
exists. Syntax:
<pre> VALID_ELEMENT(indexed_element)
</pre>
Examples:
<pre>
   if valid_element(edge[12]) then refine edge[12]
   if valid_element(body[2]) then set body[2].facet color red
</pre>

<hr>
<a   id="user-funcs"></a><h2>User-defined built-in  functions</h2>
	  User-defined functions can be defined in C in  userfunc.c, so
      you have to be compiling your own Evolver if you want to use these.
	  They are meant for situations where expression interpretation
	  is too slow, or functions such as elliptic integrals are
	  wanted.  Currently, they are automatically functions of
	  the coordinates.  Do not give any arguments in the expression;
	  for example "(usr1 + usr3)/usr10".
<hr>
<a   id="max"></a>
<a   id="min"></a>
<a   id="sum"></a>
<a   id="avg"></a>
<a   id="count"></a>
<a   id="aggregate-functions"></a><h2>Aggregate functions</h2>
The maximum, minimum, sum, or average of an expression over a set
of elements may be done with aggregate functions.  The syntax is
<pre>
   <i>aggregate(generator,expr)</i>
</pre>
where <i>aggregate</i> is <code>max, min, sum, </code> or <code>avg</code>,
and <i>generator</i> is an 
<a href="commands.htm#generators">element generator</a>.  Example: this
prints the total area of all green facets: <pre>
   print sum(facet where color == green, area)
</pre>
"Count" is an aggregate function that gives the number of elements 
generated, regardless of the expression.
<hr>

<a   id="attr-values"></a><h2>Element attribute values in expressions</h2>
The value of any 
<a href="elements.htm#geometric-elements">element attribute</a>
 may be used in an expression.
The attribute name alone may be used if there is a default element active.
Example:<pre>
   foreach facet do print area
</pre>
Otherwise the attribute is referred to as a field of the element:
<pre>
   foreach facet ff do print ff.area
</pre>
Indexed 
<a href="elements.htm#extra-attributes">extra attributes</a>
 need an index in square brackets:
<pre>
   foreach facet ff do print ff.something[3]
</pre>
Index values are rounded down to integer values.  Indexing starts with 1.
<p>
Most attributes are numerical or boolean, but some are 
<a href="commands.htm#generators">element generators</a>.
<p>
The following  attributes are available (for details, see
<a href="elements.htm#geometric-elements">elements</a>):
<dl>
          <dt> X1,X2,...,X,Y,Z,W</dt><dd>Coordinates of vertices, components of
		  edge vector or facet normal.  May also be referred to in index form as x[1], x[2], etc. </dd>
          <dt> P1,P2  </dt><dd>Parameters for 
<a href="constrnt.htm#parametric-boundaries">parametric boundaries</a>. </dd>
          <dt> ID</dt><dd> Element identifying number. </dd>
          <dt> OID</dt><dd> Oriented element identifying number. </dd>
          <dt> ORIGINAL</dt><dd>Number of parent datafile element.</dd>
<dt> COLOR</dt><dd> Integer representing color of facet
		   (color of front if back different) or edge.</dd>
          <dt> FRONTCOLOR</dt><dd> Color of front of facet. </dd>
          <dt> BACKCOLOR</dt><dd> Color of back of facet. </dd>
          <dt> VALENCE</dt><dd>Number of edges on a vertex,  facets on edge, edges on a facet, or facets, or on a body. </dd>
          <dt> AREA</dt><dd>Area of facet. </dd>
          <dt> LENGTH</dt><dd>Length of edge. </dd>
          <dt> VOLUME</dt><dd>Actual volume of body. </dd>
          <dt> TARGET</dt><dd>Target fixed volume of body. </dd>
          <dt> VOLCONST</dt><dd>Constant added to calculated volume of body. </dd>
          <dt> DENSITY</dt><dd>Density of edge, facet, or body.</dd>
          <dt> DIHEDRAL</dt><dd>Dihedral angle of facets on an edge.</dd>
          <dt> ORIENTATION</dt><dd>Sign for oriented integrals of edges or facets.</dd> 
<dt> ON_CONSTRAINT <em>n</em> </dt><dd>True if element on given 
<a href="constrnt.htm#level-set-constraints">constraint</a>. <em>n</em> may be a constraint number or a constraint name.</dd>
<dt> HIT_CONSTRAINT <em>n</em> </dt><dd>True if element is exacty on a constraint.
Useful for 
<a href="constrnt.htm#one-sided-constraints">one-sided constraints</a>. <em>n</em> may be a constraint number or a constraint name.</dd>
<dt> ON_BOUNDARY <em>n</em></dt><dd>True if element on given 
<a href="constrnt.htm#parametric-boundaries">boundary</a>. <em>n</em> may be a boundary number or a boundary name.</dd>
<dt> ON_QUANTITY <em>quantityname</em></dt><dd> True if the
  given named quantity applies to the element.</dd>
<dt> ON_METHOD_INSTANCE <em>instancename</em></dt><dd> True if the
  given method instance applies to the element.</dd>
          <dt> WRAP</dt><dd>Numerical edge wrap in 
<a href="model.htm#torus-model">torus model</a> or other  
<a href="model.htm#quotient-spaces">quotient space</a>. </dd>
	<dt>	quantity_name</dt><dd> Contribution of an element to a 
<a href="quants.htm#named-quantities">named quantity</a>.</dd>
	<dt>	instance_name</dt><dd> Contribution of an element to a 
<a href="quants.htm#method-instances">named method instance</a>.</dd>
	<dt>	 extra_attribute[expr]</dt><dd> Name of user-defined 
<a href="elements.htm#extra-attributes">extra attribute</a>,
 with subscript if needed. </dd>
   <dt> VERTEX</dt><dd> 
<a href="commands.htm#generators">Generator</a> of edge or facet vertices. </dd>
   <dt> MIDV</dt><dd> Id of edge midpoint in quadratic model. </dd>
   <dt> EDGE</dt><dd> 
<a href="commands.htm#generators">Generator</a> of edges attached to vertex, or edges around a facet. </dd>
   <dt> FACET</dt><dd> 
<a href="commands.htm#generators">Generator</a> of facets around a vertex or an edge. </dd>
   <dt> BODY</dt><dd> 
<a href="commands.htm#generators">Generator</a> of bodies that a facet is on.</dd> 
</dl>

<hr>
<a   id="variables"></a><h2>Variables</h2>
The Evolver command language has its own version of the user-defined variables
common to most programming languages.  Variables are typed according to
the types of the values assigned to them: numeric or string.
Users may define numeric variables either by <a href="datafile.htm#datafile-variables">
variable declarations</a> in the datafile, or both types by 
<a href="commands.htm#variable-assignment">assigning</a> a value
to an identifier in a command.   A variable may be subjected to optimization
by declaring it an <a href="datafile.htm#optimizing_parameter">
optimizing_parameter</a> in the datafile.

<hr>
<p><a   id="arrays"></a>
<h2>Arrays</h2>
It is possible to define multidimensional arrays of integers or reals
with the syntax
<pre>
   DEFINE <em>variablename</em>  REAL|INTEGER|STRING <em>expr</em>]...
</pre>
This syntax works both in the datafile header and at the command prompt.
If the array already exists, it will be resized, with old elements
kept as far as possible.  Do not resize with a different number of
dimensions. Note that array indexing starts at 1.  A size of 0 is legal,
and useful if you are not using an array at the moment and want to
free storage space.  There is runtime checking of array bounds. Example:
<pre>
   define fvalues integer[10][4]
   define basecoord real[10][space_dimension]
   define primcol string[3]
</pre>
Identifier names declared <a href="commands.htm#local">local</a>
can be used in array declarations in procedures and functions; 
dynamic sizes can be used, but static sizes may be a bit faster
since memory doesn't need to be dynamically allocated.
<p>

In the top of the datafile, arrays may be initialized with
nested bracket initializers following the definition.  For example:
<pre>
   define qwerty integer[4] = { 23, 45, 12, 2 }
   define vmat real[3][2] = {{1,2},{3,4},{5,6}}
   define primcol string[3] = {"red","green","blue"}
</pre>
Initializers need not be complete; missing values will be zero.
<p>
Array elements may be assigned  and referenced as is usual for programming
languages:
<pre>
   fvalues[3][4] := 234;
   if basecoord[3][1] &gt; 2 then print "hello world!\n";
</pre>

<p>
Array initialization syntax works for runtime assignments to
arrays and array slices, including element attributes that
are arrays.  The entries in the initializer must be single
numbers, not arrays.  The number of dimensions on the left
and right side of the assignment must agree, but the sizes
in each dimension need not agree.  Missing elements on the
right side are regarded as zero.  Examples:
<pre>
   vertex[1].__x := { 1.2, 3.1, 4.7 }
   define mat real[2][2];
   mat := {{1,2},{3,4}}
</pre>
The right side is evaluated each time the assignment is
executed, so the entries on the right can be any expressions
that evaluate to numbers.  Assignment with += and -= also
work, as does *= and /=, but note that all of these
work element-wise (i.e. *= and /= are not matrix multiplication
and division).
<p>

The <a href="commands.htm#print">print</a> command
 may be used to print whole arrays or array slices
in bracketed form. Example:
<pre>
   print fvalues
   print fvalues[4]
</pre>

There are some basic whole-array operations that permit arrays on
the left side of an assignment statement:
<pre>
   array := scalar
   array := array 
   array := scalar * array
   array := array + array
   array := array - array
   array := array * array
   scalar := array * array  // dot product if both rhs arrays one-dimensional
</pre>
Here "array" on both sides of the assignment means a single whole array;
 not an array-producing expression  or array slice.
But "scalar" can be any expression that evaluates to a single value.
For multiplication, the arrays must be two-dimensional with properly
matching sizes.  These operations also apply to element attributes 
that are arrays.

<p>
There is also a <a href="#matrix_inverse">matrix_inverse</a> procedure and a
<a href="#matrix_determinant">matrix_determinant</a> function. 
<p>
<a   id="dot_product"></a>
For one-dimensional arrays, the * operator  gives the
sum of the product of corresponding entries.  Example:
<pre>
   print vertex[1].__velocity * facet[3].__facet_normal
</pre>

<hr>
<a   id="internal-variables"></a><h2>Internal variables</h2>
These are pre-defined names for some of Evolver's internal variables.
They may be used in the same way as user-defined variables, except
the values of read-only variables may not be changed by the user.

<table><tr><td style="vertical-align:text-top"><ul>
<li><a href="#ambient_pressure_value"> ambient_pressure_value</a>
<li><a href="#background"> background</a>
<li><a href="#body_count"> body_count</a>
<li><a href="#breakflag"> breakflag</a>
<li><a href="#body_dissolve_count"> body_dissolve_count</a>
<li><a href="#brightness"> brightness</a>
<li><a href="#check_count"> check_count</a>
<li><a href="#clock">clock</a>
<li><a href="#console_title">onsole_title</a>
<li><a href="#constraint_tolerance"> constraint_tolerance</a>
<li><a href="#cpu_counter">cpu_counter</a>
<li><a href="#datafilename"> datafilename</a>
<li><a href="#date_and_time"> date_and_time</a>
<li><a href="#delete_count"> delete_count</a>
<li><a href="#detorus_epsilon"> detorus_epsilon</a>
<li><a href="model.htm#display_origin"> display_origin</a>
<li><a href="#dissolve_count"> dissolve_count</a>
<li><a href="#edge_count"> edge_count</a>
<li><a href="#edge_delete_count"> edge_delete_count</a>
<li><a href="#edge_dissolve_count"> edge_dissolve_count</a>
<li><a href="#edge_refine_count"> edge_refine_count</a>
<li><a href="#edge_pop_count"> edge_pop_count</a>
<li><a href="#edgeswap_count"> edgeswap_count</a>
<li><a href="#eigenneg">eigenneg</a>
<li><a href="#eigenpos">eigenpos</a>
<li><a href="#eigenvalues">eigenvalues</a>
<li><a href="#eigenzero">eigenzero</a>
</ul></td><td  style="vertical-align:text-top"><ul>
<li><a href="#equi_count"> equi_count</a>
<li><a href="#estimated_change"> estimated_change</a>
<li><a href="#facet_count"> facet_count</a>
<li><a href="#facetedge_count"> facetedge_count</a>
<li><a href="#facet_delete_count"> facet_delete_count</a>
<li><a href="#facet_dissolve_count"> facet_dissolve_count</a>
<li><a href="#fix_count"> fix_count</a>
<li><a href="#graphics_title"> graphics_title</a>
<li><a href="#gravity_constant"> gravity_constant</a>
<li><a href="#hessian_epsilon"> hessian_epsilon</a>
<li><a href="#hessian_slant_cutoff"> hessian_slant_cutoff</a>
<li><a href="#high_boundary"> high_boundary</a>
<li><a href="#high_constraint"> high_constraint</a>
<li><a href="#instance_name-modulus"><em>instance_name</em>.modulus</a>
<li><a href="#instance_name-value"> <em>instance_name</em>.value</a>
<li><a href="#inverse_periods"> inverse_periods</a>
<li><a href="#integral_order">integral_order</a>
<li><a href="#integral_order_1d">integral_order_1d</a>
<li><a href="#integration_order_2d">integral_order_2d</a>
<li><a href="#iteration_counter"> iteration_counter </a>
<li><a href="#jiggle_temperature"> jiggle_temperature</a>
<li><a href="#lagrange_order"> lagrange_order </a>
<li><a href="#last_eigenvalue"> last_eigenvalue</a>
<li><a href="#last_error">last_error</a>
<li><a href="#last_hessian_scale"> last_hessian_scale</a>
</ul></td><td style="vertical-align:text-top"><ul>
<li><a href="#linear_metric_mix">  linear_metric_mix </a>
<li><a href="#memory_arena"> memory_arena</a>
<li><a href="#memory_used"> memory_used</a>
<li><a href="#notch_count"> notch_count</a>
<li><a href="#pickvnum">  pickvnum </a>
<li><a href="#pickenum">  pickenum </a>
<li><a href="#pickfnum">  pickfnum </a>
<li><a href="#pop_count"> pop_count</a>
<li><a href="#pop_edge_to_tri_count"> pop_edge_to_tri_count</a>
<li><a href="#pop_quad_to_quad_count"> pop_quad_to_quad_count</a>
<li><a href="#pop_tri_to_edge_count"> pop_tri_to_edge_count</a>
<li><a href="#quadratic_metric_mix">  quadratic_metric_mix </a>
<li><a href="#quantity_name-modulus"><em>quantity_name</em>.modulus</a>
<li><a href="#quantity_name-pressure"> <em>quantity_name</em>.pressure</a>
<li><a href="#quantity_name-target"> <em>quantity_name</em>.target</a>
<li><a href="#quantity_name-value"> <em>quantity_name</em>.value</a>
<li><a href="#random">random </a>
<li><a href="#random_seed"> random_seed</a>
<li><a href="#refine_count"> refine_count </a>
<li><a href="#rotation_order"> rotation_order</a>
<li><a href="#scale"> scale</a>
<li><a href="#scale_scale"> scale_scale</a>
<li><a href="#scrollbuffersize"> scrollbuffersize</a>
<li><a href="#scrollbuffersize"> scrollbuffersize</a>
</ul></td><td style="vertical-align:text-top" ><ul>
<li><a href="#self_sim_coeff"> self_sim_coeff</a>
<li><a href="#simplex_representation"> simplex_representation</a>
<li><a href="#space_dimension"> space_dimension</a>
<li><a href="#string_curve_tolerance"> string_curve_tolerance</a>
<li><a href="#surface_dimension"> surface_dimension</a>
<li><a href="#symmetry_group"> symmetry_group</a>
<li><a href="#t1_edgeswap_count"> t1_edgeswap_count</a>
<li><a href="#target_tolerance"> target_tolerance</a>
<li><a href="#temperature"> temperature</a>
<li><a href="#thickness"> thickness</a>
<li><a href="#torus"> torus </a>
<li><a href="#torus_periods"> torus_periods</a>
<li><a href="#total_area"> total_area</a>
<li><a href="#total_energy"> total_energy</a>
<li><a href="#total_length"> total_length</a>
<li><a href="#total_time"> total_time</a>
<li><a href="#transform_count"> transform_count</a>
<li><a href="#unfix_count"> unfix_count</a>
<li><a href="#vertex_count"> vertex_count</a>
<li><a href="#vertex_dissolve_count"> vertex_dissolve_count</a>
<li><a href="#vertex_pop_count"> vertex_pop_count</a>
<li><a href="#view_transforms_unique_point"> view_transforms_unique_point</a>
<li><a href="#where_count"> where_count</a>
<li><a href="#window_aspect_ratio"> window_aspect_ratio</a>
</ul>
</td></tr>
</table>
<dl>

<dt><a   id="ambient_pressure_value"> ambient_pressure_value</a></dt>
<dd> Internal read-write variable. Value of the external pressure in the ideal gas model.</dd>

<dt><a   id="background"> background </a></dt>
   <dd> Internal read-write variable. Background color used 
   in certain screen graphics (xgraph and Windows, at the moment).
   </dd>
<dt><a   id="body_count"> body_count </a></dt>
		    <dd>Internal read-only variable.  Number of bodies. 
		    </dd>
<dt><a   id="breakflag"> breakflag </a></dt>
		    <dd>Internal read-write variable. 
            When set to a non-zero value, causes the command interpreter
         to abort and return to the command prompt.  Software equivalent
          of hitting the keyboard interrupt (typically CTRL-C).  The
          break doesn't happen immediately, but at a certain point  in
           the interpreter loop when it periodically checks for user 
        interrupt.  Meant for bailing out of nested commands, since 
        <a href="commands.htm#return">return</a> only breaks out
        of the current procedure.

<dt><a   id="body_dissolve_count"> body_dissolve_count</a> </dt>
	<dd>Internal read-only variable.  Number of bodies dissolved by 
		     <a href="commands.htm#dissolve">dissolve</a> command.
Prints and resets to 0 at the end of a command execution, or when 
<a href="commands.htm#flush_counts">flush_counts</a> is done.  
Also reset by <a href="commands.htm#reset_counts">reset_counts</a>.
		     </dd>

<dt><a   id="brightness"> brightness </a></dt>
		    <dd>Internal read-only variable. Median gray level used
                  in PostScript output and screen graphics. 
		  </dd>
<dt><a   id="check_count"> check_count </a></dt>
		    <dd>Internal read-only variable.  
    Number of errors found by the most recent <a href="single.htm#C">C</a>
  command.
		    </dd>

<dt><a   id="clock">clock </a></dt>
    <dd> Internal read-only variable.  Total elapsed Evolver execution
time in seconds.  Reads system process elapsed time, which often has
a fairly coarse resolution of 0.01 seconds.  For nanosecond timing,
see <a href="#cpu_counter">cpu_counter</a>.
</dd>


<dt><a   id="console_title">console_title </a></dt>
<dd>Internal read-write string variable.  This is the title that is
displayed on the Evolver command console window.  The default value is
"Surface Evolver - datafilename" (with the name of the current datafile, of
course).  Useful when you are simultaneously running various instances, and
you want to tell which is running in which console window.  Just assigning
a string to console_title automatically changes the title on the window.
</dd>

<dt><a   id="constraint_tolerance"> constraint_tolerance </a></dt>
		<dd>  Internal read-write variable. When vertices are
projected to 
<a href="constrnt.htm#level-set-constraints">level-set constraints</a>,
 projection by Newton's method
is repeated until the level-set function is smaller than constraint_tolerance.
Default value 1e-12.
</dd>

<dt><a   id="cpu_counter">cpu_counter </a></dt>
    <dd> Internal read-only variable.  Processor cycle counter, available
only on systems I know how to access this (x86 for now).   Gives the number
of CPU cycles since the system booted.  Note that this is wall clock time,
not process time.  Also note that it resets to zero when a computer
hibernates, so it is not guaranteed to be monotone increasing during the
life of a process!  Also, multiple processors in a machine may not have
identical CPU counters, so the Evolver process should be assigned to
a particular processor (in Windows, this may be done in Task Manager
by setting the process "affinity" in its properties). 
For process elapsed time,
see <a href="#clock">clock</a>.
</dd>


<dt><a   id="datafilename"> datafilename </a></dt>
   <dd>Internal read-only variable. String containing name of current datafile. 
    </dd>

<dt><a   id="delete_count"> delete_count </a></dt>
		    <dd>Internal read-only variable. 
   Sum of <a href="#edge_delete_count">edge_delete_count</a>
and <a href="#facet_delete_count">facet_delete_count</a>. 
Kept for backwards compatibility.
		    </dd>

<dt><a   id="detorus_epsilon"> detorus_epsilon </a></dt>
		    <dd>Internal read-write variable 
that is the tolerance for detorus to identify vertices when
detorus_sticky is toggled on.

<dt><a   id="display_origin-vector"> display_origin </a></dt>
   <dd>Internal read-write vector.  For a torus mode surface,
if clipped mode is in effect, the center of the clip box is
set with this array, whose dimension is the dimension of 
the ambient space.  This array does not exist by default,
it has to be created by the user. 
<a href="model.htm#display_origin">Details.</a>

    </dd>


<dt><a   id="dissolve_count"> dissolve_count </a></dt>
		    <dd>Internal read-only variable. 
   Sum of <a href="#vertex_dissolve_count">vertex_dissolve_count</a>
<a href="#edge_dissolve_count">edge_dissolve_count</a>, 
 <a href="#facet_dissolve_count">facet_dissolve_count</a>, 
and <a href="#body_dissolve_count">body_dissolve_count</a>. 
Kept for backwards compatibility.
		    </dd>

<dt><a   id="date_and_time"> date_and_time </a></dt>
   <dd>Internal read-only variable. String containing current date and time. 
    </dd>

<dt><a   id="edge_count"> edge_count </a></dt>
		    <dd>Internal read-only variable.  Number of 
		    <a href="elements.htm#edges">edges</a>. 
		    </dd>

<dt><a   id="edge_delete_count"> edge_delete_count </a></dt>
	<dd>Internal read-only variable.  Number of edges deleted by 
		     <a href="commands.htm#delete">delete</a> command.
This does not count the secondary edge deletions caused by deleting
an edge. 
Prints and resets to 0 at the end of a command execution, or when 
<a href="commands.htm#flush_counts">flush_counts</a> is done.  
Also reset by <a href="commands.htm#reset_counts">reset_counts</a>.
		     </dd>

<dt><a   id="edge_dissolve_count"> edge_dissolve_count </a></dt>
	<dd>Internal read-only variable.  Number of edges dissolved by 
		     <a href="commands.htm#dissolve">dissolve</a> command.
Prints and resets to 0 at the end of a command execution, or when 
<a href="commands.htm#flush_counts">flush_counts</a> is done.  
Also reset by <a href="commands.htm#reset_counts">reset_counts</a>.
		     </dd>

<dt><a   id="edge_refine_count"> edge_refine_count </a></dt>
	<dd>Internal read-only variable.  Number of edges refined by 
		     <a href="commands.htm#refine">refine edges</a> command.
Prints and resets to 0 at the end of a command execution, or when 
<a href="commands.htm#flush_counts">flush_counts</a> is done.  
Also reset by <a href="commands.htm#reset_counts">reset_counts</a>.
		     </dd>

<dt><a   id="edge_pop_count"> edge_pop_count </a></dt>
	<dd>Internal read-only variable.  Number of edges popd by 
		     <a href="commands.htm#pop">pop edges</a>,
		     <a href="single.htm#o">o</a>, or
		     <a href="single.htm#O">O</a>,
 commands.
Prints and resets to 0 at the end of a command execution, or when 
<a href="commands.htm#flush_counts">flush_counts</a> is done.  
Also reset by <a href="commands.htm#reset_counts">reset_counts</a>.
		     </dd>

<dt><a   id="edgeswap_count"> edgeswap_count </a></dt>
	<dd>Internal read-only variable.  Number of edges swapped by 
		     <a href="commands.htm#edgeswap">edgeswap</a> command.
Prints and resets to 0 at the end of a command execution, or when 
<a href="commands.htm#flush_counts">flush_counts</a> is done.  
Also reset by <a href="commands.htm#reset_counts">reset_counts</a>.
		     </dd>


<dt><a   id="eigenneg"> </a><a   id="eigen_neg"> eigenneg </a></dt>
	<dd>Internal read-only variable. Number of negative eigenvalues in last
<a href="eigentut.htm">Hessian</a>
		       factoring. 
		       </dd>

<dt><a   id="eigenpos"> </a><a   id="eigen_pos"> eigenpos</a> </dt>
	<dd>Internal read-only variable. Number of positive eigenvalues in last
<a href="eigentut.htm">Hessian</a>
	    factoring.  
	    </dd>

<dt><a   id="eigenvalues"> eigenvalues[]</a> </dt>
	<dd>Internal read-only array. Contains the list of eigenvalues
produced by the <a href="commands.htm#ritz">ritz</a> command.  Example:
<code>print eigenvalues[2]</code>
</dd>

<dt><a   id="eigenzero"> </a><a   id="eigen_zero"> eigenzero </a></dt>
	<dd>Internal read-only variable. Number of zero eigenvalues in last 
<a href="eigentut.htm">Hessian</a> factoring.
</dd>

<dt><a   id="equi_count"> equi_count </a></dt>
      <dd>Internal read-only variable. Number of edges flipped  by 
<a href="single.htm#u">equiangulation</a>.  
Prints and resets to 0 at the end of a command execution, or when 
<a href="commands.htm#flush_counts">flush_counts</a> is done.  
Also reset by <a href="commands.htm#reset_counts">reset_counts</a>.
</dd>

<dt><a   id="estimated_change"> estimated_change </a></dt>
                     <dd> Internal read-only variable.  Estimated 
                  change of energy during last iteration with
                  <a href="toggle.htm#estimate">estimate</a> option in effect.
                     </dd>

<dt><a   id="facet_count"> facet_count </a></dt>
		    <dd>Internal read-only variable.  Number of 
		    <a href="elements.htm#facets">facets</a>. 
		    </dd>

<dt><a   id="facetedge_count"> facetedge_count </a></dt>
		    <dd>Internal read-only variable.  Number of
		    <a href="elements.htm#facetedges">facetedges</a>. 
		    </dd>

<dt><a   id="facet_delete_count"> facet_delete_count </a></dt>
	<dd>Internal read-only variable.  Number of facets deleted by 
		     <a href="commands.htm#delete">delete</a> command.
Prints and resets to 0 at the end of a command execution, or when 
<a href="commands.htm#flush_counts">flush_counts</a> is done.  
Also reset by <a href="commands.htm#reset_counts">reset_counts</a>.
		     </dd>

<dt><a   id="facet_dissolve_count"> facet_dissolve_count </a></dt>
	<dd>Internal read-only variable.  Number of facets dissolved by 
		     <a href="commands.htm#dissolve">dissolve</a> command.
Prints and resets to 0 at the end of a command execution, or when 
<a href="commands.htm#flush_counts">flush_counts</a> is done.  
Also reset by <a href="commands.htm#reset_counts">reset_counts</a>.
		     </dd>

<dt><a   id="facet_refine_count"> facet_refine_count </a></dt>
	<dd>Internal read-only variable.  Number of facets refined by 
		     <a href="commands.htm#refine">refine facets</a> command.
Prints and resets to 0 at the end of a command execution, or when 
<a href="commands.htm#flush_counts">flush_counts</a> is done.  
Also reset by <a href="commands.htm#reset_counts">reset_counts</a>.
		     </dd>

<dt><a   id="fix_count"> fix_count </a></dt>
	<dd>Internal read-only variable.  Number of elements fixed by 
		     <a href="commands.htm#pop">fix</a> command.
Prints and resets to 0 at the end of a command execution, or when 
<a href="commands.htm#flush_counts">flush_counts</a> is done.  
Also reset by <a href="commands.htm#reset_counts">reset_counts</a>.
		     </dd>


<dt><a   id="graphics_title"></a>  <a   id="graphics_title2"> </a> <a   id="graphics_title3">graphics_title </a></dt>
	<dd>Internal read-write string variable. 
              This is the title that is
displayed on the Evolver graphics window.  The default value is
the datafile name.  Useful when you are simultaneously running various instances, and
you want to tell which is running in which graphics window.  Just assigning
a string to graphics_title automatically changes the title on the window.
There are also graphics_title2 and graphics_title3 variables if you
have a second or third graphics window.
	</dd>

<dt><a   id="gravity_constant"> gravity_constant </a></dt>
	<dd>Internal read-write variable. Value of the gravitational 
	constant, which can also be set by the <a href="single.htm#G">G</a>
	command. 
	</dd>

<dt><a   id="hessian_epsilon"> hessian_epsilon </a></dt>
<dd>  Internal read-write variable. Magnitude regarded as zero by 
<a href="commands.htm#hessian-command">hessian command</a> when factoring
the Hessian matrix.  If a zero appears on the diagonal at the pivot
during factoring, a check is made to see if the rest of the row is zero.
If it is, then a 1 is placed on the diagonal; else an error is reported. 
</dd>

<dt><a   id="hessian_slant_cutoff"> hessian_slant_cutoff </a></dt>
<dd>  Internal read-write variable. 
Hessian commands treat vertices whose normal 
vector is nearly perpendicular
to constraints as fixed.  hessian_slant_cutoff is the cosine
of angle.  Works on vertices with one degree of freedom in
hessian_normal mode. Default value 0.

</dd>

<dt><a   id="high_boundary"> high_boundary </a></dt>
<dd>  
Internal read-only variable giving the number of the highest
parametric boundary defined.  Remember that the name of a named
boundary is internally interpreted as a number, and that boundary
may be referred to by that number.   Useful in iterating through
all boundaries, for example
<pre>
  for ( bnum := 1 ; bnum &lt;= high_boundary ; bnum += 1 )
    if valid_boundary(bnum) then
       printf "Boundary %d has %d vertices on it\n",bnum,
          sum(vertex,on_boundary bnum);
</pre>
</dd>

<dt><a   id="high_constraint"> high_constraint </a></dt>
<dd>  
Internal read-only variable giving the number of the highest
level-set constraint.  Remember that the name of a named
constraint is internally interpreted as a number, and that constraint
may be referred to by that number.   Useful in iterating through
all constraints, for example
<pre>
  for ( cnum := 1 ; cnum &lt;= high_constraint ; cnum += 1 )
    if valid_constraint(cnum) then
       printf "Constraint %d has %d vertices on it\n",cnum,
          sum(vertex,on_constraint cnum);
</pre>

<dt><a   id="instance_name-modulus"><em>instance_name</em>.modulus </a></dt>
		<dd> Internal read-write variable.  
<a href="quants.htm#instance-modulus">Modulus</a> of a 
<a href="quants.htm#method-instances">named method instance</a>. 
</dd>
<dt><a   id="instance_name-value"> <em>instance_name</em>.value</a></dt>
	<dd> Internal read-only variable. Value of a 
<a href="quants.htm#method-instances">named method instance</a>. 
</dd>
<dt><a   id="inverse_periods"> inverse_periods[<i>expr</i>][<i>expr</i>] </a></dt> <dd>
Internal read-only variable.  Inverse matrix of the
<a href="#torus_periods">torus_periods</a> matrix. Uses 1-based indexes.
Useful for normalizing vertex coordinates to period basis.
The syntax for calculating the period basis coordinates would be like
<pre>
   define perx real[space_dimension];
   perx := vertex[1].__x * inverse_periods
</pre>
</dd>

<dt><a   id="integral_order"></a><a   id="integration_order"></a>integral_order </dt>
		 <dd> Internal read-write variable. 
		    Order of polynomial done by 1D and 2D Gaussian integration.
                      Much better to set 1D and 2D separately.
                    Synonym: integration_order
		    </dd>
<dt><a   id="integral_order_1d"></a>
<a   id="integration_order_1d"> integral_order_1d </a> </dt>
		 <dd> Internal read-write variable. 
		    Order of polynomial done by 1D Gaussian integration.
                    Synonym: integration_order_1D
		    </dd>
<dt><a   id="integration_order_2d"></a>
 <a   id="integral_order_2d"> integral_order_2d </a> </dt>
		 <dd> Internal read-write variable. 
		    Order of polynomial done by 2D Gaussian integration.
                    Synonym: integration_order_2D
		    </dd>

<dt><a   id="iteration_counter"> iteration_counter  </a></dt><dd>
       Internal read-only variable. Loop count of last loop in a command. 
       </dd>
<dt><a   id="jiggle_temperature"> jiggle_temperature </a></dt>
	<dd> Internal read-only variable. Current temperature for 
<a href="single.htm#j">jiggling</a>. 
</dd>

<dt><a   id="lagrange_order"> lagrange_order </a> </dt>
		 <dd> Internal read-only variable. 
    Order of <a href="model.htm#Lagrange-model">Lagrange model</a>.
    Set with the <a href="commands.htm#lagrange-command">lagrange 
    <em>n</em></a> command.
    </dd>
<dt><a   id="last_eigenvalue"> last_eigenvalue </a></dt>
	<dd>Internal read-only variable. Eigenvalue from last 
<a href="commands.htm#saddle">saddle</a> or
	     <a href="commands.htm#ritz">ritz</a> command.  
</dd>
<dt><a   id="last_error">last_error </a></dt><dd>Internal read-write
variable.  Has error number of last error message.</dd>

<dt><a   id="last_hessian_scale"> last_hessian_scale </a></dt>
	<dd> Internal read-only variable. Stepsize from last 
<a href="commands.htm#saddle">saddle</a> or 
      <a href="commands.htm#hessian_seek">hessian_seek</a> command.
      </dd>
<dt><a   id="linear_metric_mix">  linear_metric_mix </a></dt>
                 <dd>  Internal read-write variable. 
		       Fraction of linear interpolation in 
<a href="eigentut.htm#hessian-metric">Hessian metric</a>. 
</dd>

<dt><a   id="memory_arena"> memory_arena </a></dt>
  <dd> Internal read-only variable. 
  Total memory allocated to the program's heap.  Available only
  on SGI and Win32 versions. 
  </dd>

<dt><a   id="memory_used"> memory_used </a></dt>
  <dd> Internal read-only variable. 
  Total memory used in the program's heap.  Available only
  on SGI and Win32 versions. 
  </dd>

<dt><a   id="notch_count"> notch_count </a></dt>
	<dd>Internal read-only variable. Number of edges notched in last 
		      <a href="single.htm#n">notch</a> command.
		      </dd>
<dt><a   id="pickvnum">  pickvnum  </a></dt>
                <dd>  Internal read-write variable. Number of last vertex 
<a href="graphics.htm#picking">picked</a>
		       in the graphics window. 
		       </dd>
<dt><a   id="pickenum">  pickenum  </a></dt>
                <dd>  Internal read-write variable. Number of last edge 
<a href="graphics.htm#picking">picked</a>
		       in the graphics window. 
		       </dd>
<dt><a   id="pickfnum">  pickfnum  </a></dt>
                <dd>  Internal read-write variable. Number of last facet 
<a href="graphics.htm#picking">picked</a>
		       in the graphics window. 
		       </dd>

<dt><a   id="pop_count"> pop_count </a></dt>
	<dd>Internal read-only variable.
Sum of <a href="#vertex_pop_count">vertex_pop_count</a> and
<a href="#edge_pop_count">edge_pop_count</a>. Kept for 
backwards compatibility.
		       </dd>

<dt><a   id="pop_edge_to_tri_count"> pop_edge_to_tri_count </a></dt>
	<dd>Internal read-only variable.  Number of edges flipped to triangles by 
the	 <a href="commands.htm#pop_edge_to_tri">pop_edge_to_tri</a> command.
Prints and resets to 0 at the end of a command execution, or when 
<a href="commands.htm#flush_counts">flush_counts</a> is done.  
Also reset by <a href="commands.htm#reset_counts">reset_counts</a>.
		     </dd>

<dt><a   id="pop_quad_to_quad_count"> pop_quad_to_quad_count </a></dt>
	<dd>Internal read-only variable.  Number of quadrilaterals flipped  by 
the	 <a href="commands.htm#pop_quad_to_quad">pop_quad_to_quad</a> command.
Prints and resets to 0 at the end of a command execution, or when 
<a href="commands.htm#flush_counts">flush_counts</a> is done.  
Also reset by <a href="commands.htm#reset_counts">reset_counts</a>.
		     </dd>

<dt><a   id="pop_tri_to_edge_count"> pop_tri_to_edge_count</a> </dt>
	<dd>Internal read-only variable.  Number of triangles flipped to edges by 
the	 <a href="commands.htm#pop_tri_to_edge">pop_tri_to_edge</a> command.
Prints and resets to 0 at the end of a command execution, or when 
<a href="commands.htm#flush_counts">flush_counts</a> is done.  
Also reset by <a href="commands.htm#reset_counts">reset_counts</a>.
		     </dd>


<dt><a   id="quadratic_metric_mix">  quadratic_metric_mix  </a></dt>
                 <dd>  Internal read-write variable. 
		       Fraction of linear interpolation in 
<a href="eigentut.htm#hessian-metric">Hessian metric</a> in the
quadratic model. Not very useful.
</dd>

<dt><a   id="quantity_name-modulus"><em>quantity_name</em>.modulus</a> </dt>
		<dd> Internal read-write variable.  
<a href="quants.htm#quantity-modulus">Modulus</a> of a 
<a href="quants.htm#named-quantities">named quantity</a>.
</dd>
<dt><a   id="quantity_name-pressure"> <em>quantity_name</em>.pressure </a></dt>
	<dd> Internal read-only variable. 
<a href="quants.htm#quantity-pressure">Lagrange multiplier</a> for
      a <a href="quants.htm#fixed-quantity">constrained named quantity</a>.
      </dd>
<dt><a   id="quantity_name-target"> <em>quantity_name</em>.target </a></dt>
	<dd> Internal read-write variable.  Constrained value of a 
<a href="quants.htm#fixed-quantity">named quantity</a>.
</dd>
<dt><a   id="quantity_name-value"> <em>quantity_name</em>.value </a></dt>
	<dd> Internal read-only variable. Value of a 
<a href="quants.htm#named-quantities">named quantity</a>.
</dd>
<dt><a   id="random">random  </a></dt><dd> Internal read-only variable.
  Random number between 0 and 1.
  </dd>
<dt><a   id="random_seed"> random_seed </a></dt>
            <dd> Internal read-write variable.  Seed for random number
	    generator, used for example in <a href="single.htm#j">jiggling</a>
or in finding random initial vectors in various 
<a href="eigentut.htm">Hessian</a> eigenvector algorithms.
  Defaults to 1 at start of datafile. 
  </dd>
<dt><a   id="refine_count"> refine_count </a> </dt><dd>
        Internal read-only variable. Number of elements refined in last refine command.
	</dd>
<dt><a   id="rotation_order"> rotation_order </a></dt>
            <dd> Internal read-write variable.  Order of rotation group
for symmetry groups <a href="model.htm#rotate-symmetry-group">rotate</a> and
<a href="model.htm#flip-rotate-symmetry-group">flip_rotate</a>.
</dd>
<dt><a   id="scale"> scale </a></dt>
		<dd> Internal read-write variable.  Current scale factor for
		multiplying the force to get the motion in the 
		'<code><a href="single.htm#g">g</a></code>' command. 
		</dd>
<dt><a   id="scale_scale"> scale_scale </a></dt>
		<dd> Internal read-write variable.  Multiplier for the
		scale factor used in the 
		'<code><a href="single.htm#g">g</a></code>' command. Default 
		value 1.
		</dd>

<dt><a   id="scrollbuffersize"> scrollbuffersize </a></dt>
		<dd> Internal read-write variable. 
    The command window scroll buffer size on Windows
machines.  Meant for non-NT Windows that don't
have menu properties option for this. 
  </dd>

<dt><a   id="self_sim_coeff"> self_sim_coeff </a></dt>
		<dd> Internal read-write variable. 
Used as magnitude coefficent when
<a href="toggle.htm#self_similar">self_similar</a> is toggled on.

<dt><a   id="simplex_representation"> simplex_representation </a></dt>
		<dd>Internal read-only variable.  Whether 
the <a href="model.htm#simplex-model">simplex model</a> is in effect.
</dd>
<dt><a   id="space_dimension"> space_dimension </a></dt>
		<dd>Internal read-only variable.     
<a href="model.htm#space-dimension">Dimension</a> of ambient space. 
</dd>

<dt><a   id="sq_curvature_modulus"> sq_curvature_modulus </a></dt>
		<dd>Internal read-write variable.     
Multiplier for the <a href="datafile.htm#squared_curvature">
squared_curvature</a> energy when it is declared the old way
in the top of the datafile.
</dd>

<dt><a   id="string_curve_tolerance">string_curve_tolerance</a></dt>
		<dd>Internal read-write variable.  
 In the <a href="model.htm#quadratic-model">quadratic model</a>,
the smoothness of graphing of curved quadratic edges can be
controlled with the internal variable
<code>string_curve_tolerance</code>,
which is the desired angle in degrees between successive graphed segments
making up the edge.
		</dd>


<dt><a   id="surface_dimension"> surface_dimension </a></dt>
		<dd>Internal read-only variable.  Dimension of surface. 
		</dd>
<dt><a   id="symmetry_group"> symmetry_group </a></dt>
		<dd>Internal read-only variable.  Whether  any 
<a href="model.htm#symmetry-groups">symmetry group</a> is active  (Boolean).
</dd>
<dt><a   id="t1_edgeswap_count"> t1_edgeswap_count </a></dt>
	<dd>Internal read-only variable.  Number of edges swapped by 
		     <a href="commands.htm#t1_edgeswap">t1_edgeswap</a> command.
Prints and resets to 0 at the end of a command execution, or when 
<a href="commands.htm#flush_counts">flush_counts</a> is done.  
Also reset by <a href="commands.htm#reset_counts">reset_counts</a>.
		     </dd>

<dt><a   id="target_tolerance"> target_tolerance </a></dt>
		<dd>  Internal read-write variable.
When <a href="elements.htm#target-volume">volume constraints</a>
 or <a href="constrnt.htm#named-quantity-constraints">named quantity 
constraints</a> are enforced,
Newton's method is repeated until the total deviation from target values
is less than <code>target_tolerance</code>.  Default value 1e-4.
</dd>
<dt><a   id="temperature"> temperature </a></dt>
  <dd> Internal read-only variable.
  Amplitude for <a href="toggle.htm#jiggle">jigglinge</a>.
  </dd>
<dt><a   id="thickness"> thickness </a></dt>
  <dd> Internal read-only variable.
  Thickness for thickened surfaces in graphics output in 
<a href="single.htm#P">P</a> command.  Used when facet
<a href="elements.htm#frontcolor">frontcolor</a> and 
<a href="elements.htm#backcolor">backcolor</a> are different.
Default value 0.001 times the maximum linear dimension of the surface.
If you get backside color showing through,
increase the thickness.
</dd>
<dt><a   id="torus"> torus </a> </dt><dd>Internal read-only variable.  Whether 
the <a href="model.htm#torus-model">torus model</a> is in effect. (Boolean).
</dd>
<dt><a   id="torus_periods"> torus_periods[<i>expr</i>][<i>expr</i>]  </a></dt><dd>
Internal read-only variable.  Current values of the period vectors in the
<a href="model.htm#torus-model">torus model</a>.  Torus_periods[i][j]
is component j of vector i.  Uses 1 based indexes.
For changing the torus_periods, define the
periods in the datafile with variables, and alter the variables.
</dd>
<dt><a   id="total_area"> total_area </a></dt>
    <dd>Internal read-only variable.  Total area of the surface
in <a href="model.htm#soapfilm-model">soapfilm</a> or 
<a href="model.htm#simplex-model">simplex</a> models. 
Beware that this is not continuously updated with every
change in the surface, but rather upon return to the command prompt.  If
a script needs the current total_area recalculated, it should do the
"recalc" command before using total_area.
</dd>
<dt><a   id="total_energy"> total_energy</a> </dt>
    <dd>Internal read-only variable.  Total energy of the surface. 
Beware that this is not continuously updated with every
change in the surface, but rather upon return to the command prompt.  If
a script needs the current total_energy recalculated, it should do the
"recalc" command before using total_energy.
    </dd>
<dt><a   id="total_length"> total_length </a></dt>
    <dd>Internal read-only variable.  Total length of the surface 
in the <a href="model.htm#string-model">string model</a>. 
</dd>
<dt><a   id="total_time"> total_time </a></dt>
    <dd>Internal read-only variable.  Elapsed evolution time in the form of 
total <a href="iterate.htm#scale-factor">scale factors</a>. 
</dd>

<dt><a   id="transform_count"> transform_count </a></dt>
    <dd>Internal read-only variable.  Number of image transforms
    active, as generated by the <a href="commands.htm#transform_expr">
    <code>transform_expr</code></a> command.
    </dd>


<dt><a   id="unfix_count"> fix_count </a></dt>
	<dd>Internal read-only variable.  Number of elements unfixed by 
		     <a href="commands.htm#pop">unfix</a> command.
Prints and resets to 0 at the end of a command execution, or when 
<a href="commands.htm#flush_counts">flush_counts</a> is done.  
Also reset by <a href="commands.htm#reset_counts">reset_counts</a>.
		     </dd>

<dt><a   id="vertex_count"> vertex_count </a></dt>
    <dd>Internal read-only variable.  Number of vertices.
    </dd>

<dt><a   id="vertex_dissolve_count"> vertex_dissolve_count </a></dt>
	<dd>Internal read-only variable.  Number of vertices dissolved by 
		     <a href="commands.htm#dissolve">dissolve</a> command.
Prints and resets to 0 at the end of a command execution, or when 
<a href="commands.htm#flush_counts">flush_counts</a> is done.  
Also reset by <a href="commands.htm#reset_counts">reset_counts</a>.
		     </dd>

<dt><a   id="vertex_pop_count"> vertex_pop_count </a></dt>
	<dd>Internal read-only variable.  Number of vertices popped by 
		     <a href="commands.htm#pop">pop</a> or
<a href="single.htm#o">o</a> command.
Prints and resets to 0 at the end of a command execution, or when 
<a href="commands.htm#flush_counts">flush_counts</a> is done.  
Also reset by <a href="commands.htm#reset_counts">reset_counts</a>.
		     </dd>

<dt><a   id="view_transforms_unique_point"> view_transforms_unique_point </a></dt>
	<dd>Internal read-write vector variable. Used by 
  <a href="toggle.htm#view_transforms_use_unique_point">
view_transforms_use_unique_point</a> mode for the definition of duplicate view transforms. 


<dt><a   id="where_count"> where_count </a></dt>
<dd>Internal read-only variable. Number of items satisfying  last 
	       <code>where</code> condition.
Prints and resets to 0 at the end of a command execution, or when 
<a href="commands.htm#flush_counts">flush_counts</a> is done.  
Also reset by <a href="commands.htm#reset_counts">reset_counts</a>.
	       </dd>


<dt><a   id="window_aspect_ratio"> window_aspect_ratio </a></dt>
<dd>Internal read-write variable.  The ratio of the the vertical to
horizontal dimensions of the display window.  If set, this locks the
aspect ratio to the given value.  The window may be resized with the
mouse, but the aspect ratio will stay the same.  The unset value of
window_aspect_ratio is 0; setting window_aspect_ratio to 0 will 
unlock the aspect ratio.  Applies also to the PostScript bounding box,
if <a href="toggle.htm#full_bounding_box">full_bounding_box</a> is on.
Currently implemented only in Evolver with GLUT graphics.
Caveat: the window doesn't always fully follow the mouse; just keep trying. 
	       </dd>

</dl>
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